research article an algorithm for mining of association...

Research ArticleAn Algorithm for Mining of Association Rulesfor the Information Communication Network Alarms Based onSwarm Intelligence

Yang Wang12 Guocai Li12 Yakun Xu12 and Jie Hu12

1 MicroNano System Research Center College of Information Engineering Taiyuan University of Technology TaiyuanShanxi 030024 China

2 Key Lab of Advanced Transducers and Intelligent Control System of the Ministry of Education Taiyuan University of TechnologyTaiyuan Shanxi 030024 China

Correspondence should be addressed to Jie Hu hujie0351gmailcom

Received 5 August 2013 Accepted 17 November 2013 Published 19 January 2014

Academic Editor Orwa Jaber Housheya

Copyright copy 2014 Yang Wang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Due to the centralized management of information communication network the network operator have to face these pressureswhich come from the increasing network alarms and maintenance efficiency The effective analysis on mining of the networkalarm association rules is achieved by incorporating classic data associationmining algorithm and swarm intelligence optimizationalgorithm From the related concept of the information communication network the paper analyzes the data characteristics andassociation logic of the network alarms Besides the alarm data are preprocessed and the main standardization information fieldsare screened The APPSO algorithm is proposed on the basis of combining the evaluation method for support and confidencecoefficient in the Apriori (AP) algorithm as well as the particle swarm optimization (PSO) algorithm By establishing a sparselinked list the algorithm is able to calculate the particle support thus further improving the performance of the APPSO algorithmBased on the test for the network alarmdata it is discovered that rational setting of the particle swarm scale and number of iterationsof the APPSO algorithm can be used to mine the vast majority and even all of the association rules and the mining efficiency issignificantly improved compared with Apriori algorithm

1 Introduction

The operation and maintenance management of informationcommunication network mainly refers to timely discoverylocating and handling of any network fault to ensure smoothand efficient operation as well as guarantee in major emer-gencies pertinent to network operation complaints aboutnetwork quality from customers assessment and analysis ofnetwork quality prediction of planning construction and soforthThe time consumed during fault location and judgmentin the application layer of a large-scale network accountsfor 93 of its total time for failure of recovery [1] Thehuge network structure and multifunctional device typesalso bring about large amounts of alarm data due to suchcharacteristics of the information communication network

as topological structure densification network device micro-miniaturization communication board precision and soforth Therefore the foundation of the network operationand maintenance is the effective management of the networkalarms

As an important supportingmeans for network operationandmaintenancemanagement networkmanagement systemdirectly influences the quality of service which the infor-mation communication network provides to its customers[2] The network management system is developing towardintegrated service network management update from inde-pendent device network management manufacturer devicenetwork management and integrated professional networkmanagementThe centralizedmonitoringmanagement func-tion of the professional information communication network

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 894205 14 pageshttpdxdoiorg1011552014894205

2 Mathematical Problems in Engineering

operation management will make problems exhibit a sharpfull data increasing including network faults device alarmsand customer complaints

As the information communication system consists ofvarious medium interlinked network devices and operatingsystems implicit and complex-correlated logic is ubiquitousamong network elements that is a certain fault point maytrigger numerous alarms in the whole network The suddenintensive alarms not only consume the resources of thenetwork management system but also obscure the positionof the network fault source points thus severely impedingtrouble shooting by the network operation and maintenancepersonnel Several alarms are incorporated into a single alarmor source alarm with a large amount of information bysuch links as paraphrasing and explaining eliminating andfiltering information integration and correlating and trans-forming and so forth It aims at assisting the operation andmaintenance personnel to analyse fault messages and locatefaults quickly that is mining analysis on alarm associationrules

Mining of alarm association rules refers to a processof analysis on the association between the attributive char-acteristic logic of the alarms within devices and the topo-logical hierarchy of network devices It aims at achievingclear critical alarms accurate fault location and trouble-shooting and intelligent fault prediction and evaluationThemining of alarm association rules can be divided into threelevels analysis on alarm association in the device within theprofession analysis on topological alarm association of thenetwork device within the profession and analysis on inter-professional topological alarm association of the networkdevice but their core ismining algorithm for association rules[3]

The centralized management of information communi-cation network brings about large amounts of alarm dataA rapid mining analysis on the network alarm associationrules is achieved by the classic Apriori association miningalgorithm and PSO algorithm under the context of big dataThe alarm association relationship can be used to add andmerge the fault alarms maintain the work order improvethe centralized monitoring efficiency and reduce the cost ofnetwork maintenance

The Apriori is an association rules mining algorithmbased on characteristics of frequent item sets (priori knowl-edge) whose core concept is a layer-wise iterative search of thetheory of frequent item sets However the Apriori algorithmthought also presents some inevitable problems For instancefrequent repeated scans of the information in the sampledatabase lead to a heavy load on the system IO large itemsets lead to a sharp increase in the number of the candidatefrequent item sets and a significant increase in operation timeand so forth

Swarm intelligence refers to the macroscopic intelli-gent group behavior showed by various types of organismindividuals in the nature during survival collaborationand evolution Application research is conducted for theswarm intelligence algorithm in optimization solutions ofengineering problems such as economic analysis and forecaststructural damage positioning and inspecting command and

dispatch of communication and transportation evacuationroute planning target identifying and tracking factory siteselection and evaluation communication network planningand route plan preparation [4] The swarm intelligencealgorithmhas such advantages as distributed control indirectinformation transfer and simple individuals and swarm intel-ligence As a classic swarm intelligence algorithm the particleswarm optimization also has the above characteristics

Centralizedmanagement of the alarms in the informationcommunication network is an important part of operationmaintenance of the information communication networkThe alarm correlation directly influences the quantity andquality of the alarm work orders An analysis on thelarge amounts of alarm data through an efficient algorithmbecomes the critical technical means The APPSO discussedin the paper incorporates the Apriori algorithm and swarmoptimization algorithms and applies swarm optimizationalgorithms in the information communication field

Section 2 in the paper elaborates such basic conceptsof faults in the information communication network net-work alarms alarm standardization and so forth Section 3discusses the data characteristics of network alarms andthe alarm correlation logical relationships within andbetween network devices Section 4 describes achieving qual-ity improvement of the data source of the network alarms bypre-processing of the network alarmdata Section 51 presentsthe concepts of support and confidence coefficient and min-ing analysis process inApriori algorithm in combinationwithexamples Section 52 describes the swarm intelligencemodeland basic flow of the PSO algorithm Section 53 discussesthe creation of APPSO association rule mining algorithmwhich deducts on the basis of the Apriori and PSO algorithmcharacteristics Besides combining with the characteristicsof the network alarm data the section puts forward theimprovement of the performance of the APPSO associationrule mining algorithm by sequencing code sliding windowsparse linked list and nature of the Apriori algorithmIt conducts a performance test for the algorithm throughthe alarm data in the information communication networkfrom different angles At the end of the section an indexevaluation of the alarm association rate is put forward whichis used for application of the alarm correlation relationshipderived from the APPSO algorithm mining into the actualnetwork

2 Concepts Pertinent to Alarms in theInformation Communication Network

Concepts pertinent to the data analysis on the alarms in theinformation communication network are defined as follows[5 6]

Definition 1 A network fault refers to an event where theinformation communication network is not able to operatenormally and efficiently due to some reasons and even noservice can be provided The reasons causing network faultscan be divided into network device faults communicationlink abnormality inappropriate operation and maintenance

Mathematical Problems in Engineering 3

energy power and room environment abnormality andnetwork system faults (affecting monitoring instead of thecommunication service)

Definition 2 A network alarm is a message triggered duringabnormal operation of communication device and eachalarm message represents its unique running status Nouniform standard specification is applicable to the networkdevices in the whole industry due to the difference inmechanism and connotation of the alarmmessages of devicesof different types from various manufacturers However thestandardization can be achieved by specific standardizedfields

Definition 3 Alarm standardization redefines the level clas-sification influence and so forth of the full professionalalarms which achieving the target on achieve mapping defi-nition normative classification and centralizedmanagementof professional alarms of different manufacturers

Definition 4 Thealarm standardization fields include profes-sion manufacturer device type alarm title auxiliary fieldsof alarm explanation manufacturer alarm level applicablemanufacturer version number network management alarmlevel network management alarm ID alarm explanationalarm class alarm logic class alarm logic subclass effect ofsuch an event on the device effect of such an event on theservice and standard name of the alarm

Definition 5 The alarm standardization fields of the networkmanagement system refer to the other alarm standardizationfields of the networkmanagement system excluding the alarmstandardization fields for example citycountydistrict net-work element name number of network element board cardlocal port information of the alarm remote port informationof the alarm occurrence time of the network element alarmdiscovery time of the network management alarm elimina-tion time of the alarm and so forth

3 Data Characteristics and Association Logicof Network Alarms

The information communication network has such charac-teristics as complex hierarchical and full end-to-end net-working These network elements have certain physical andlogical association and the independent network elementfailure will result in ldquoclick alarm multiclick disseminationrdquoeffect on related network element However there is asso-ciation of occurrence time and logical name between thesealarms Thus association classification and combinationof such alarms can substantially improve the efficiency ofcentralized monitoring [7]

31 Data Characteristics of Network Alarms Informationcommunication network alarm is characterized by huge datavolume alarm fluctuation network communication effectaccumulative and lagging effects and redundancy of faultmessages and so forth The analysis of these characteristics

will contribute to mining analysis on rules of associationamong alarms

(1) Huge Data Volume The number of alarms and faults inthe current network is huge due to such characteristics asdiversification of types of information communication net-work services network scale expansion topological structuretightness and centralization of network monitoring and soforth

(2) Alarm Fluctuation From the perspective of monitoringmanagement the equipment failure alarms have certainunpredictability The crash of critical equipment will causethe whole network paralysis leading to a sharply increasingnumber of alarms inevitably Similarly the alarms can beeliminated if the failures are maintained and handled timelyFor instance the block of central transmission lines will affectlocal lines lines across cities and relative network equipmentthus all relevant equipment exhibits alarm conditions If thecentral lines are dealt with appropriately the alarm will beremoved rapidly

(3) Network Communication Effect The alarm does notspread through some concrete networks but relies on theindependent ldquomanagement networkrdquo [8] Take SDH networkalarm for example LAN regenerator section LOS alarm rarrmultiplex section MIS rarr AIS alarm rarr remote device MS-FERF alarm connected to local devices andAU-AIS alarm rarrlocal HO-VCHP-AIS alarm rarr local TU-AIS alarm and HP-FERFRDI alarm

(4) Accumulative and Lagging Effect The abnormality ofsome network equipment would degrade the relative networkquality If this condition has accumulated to an extent thatexceeds the limits the connected network equipment wouldalarm Besides these features may be caused by clock syn-chronous exception among communication equipment NMfor manufacturerrsquos equipment and NM for multidisciplinaryor abnormal network management data

(5) Redundancy of FaultMessages Fault points on single panelwould cause the associated devices parts to alarm and thefailure of network convergence nodes can trigger a large-scale network alarm For example the failure of MSC server(mobile switching center) will lead some devices to stay inan alarm state such as MGW (media gateway) BSC (basestation controller) and RNC (radio network controller) Andthis phenomenon will lead to a sudden ldquoalarm stormrdquo

(6) Abundant Property Field Each alarm corresponds tosome recognized information combination Different prop-erty fields reveal certain relevant logic

(7) Abnormal Alarm It can be divided into waste alarmultrashort alarm and overlength alarm The waste alarm isnot caused by the filter clear of network access test and devicedata in time The ultrashort alarm points the alarm lasts forless than one minute And the overlength alarm refers to thealarms which are not removed after a long time


Network equipment alarm

Derivative correlation

Topology correlation

Timing correlation

Causal correlation

Linkcorrelation


Alarm

Compressing Filtering mechanism

Calculating accumulatively

Suppressing shielding

Boolean operation Universalization Specialization Temporal

relation

Alarm

Alarm





relation

Alarm

Figure 1 Association logic of network alarms

32 Association Logic of Network Alarms The networkassociation logic can be divided into two levels that isalarm association logic within network device and alarmassociation logic among network device as shown in Figure 1

The alarm logical association on the network equipmentitself is as follows [9] (1) alarm compressing taking thesimultaneous multialarm which has the same attributes(adjacent cells same network element or light path etc)into an alarm (2) filtering mechanism alarm which doesnot conform to the attribute association will be deleted (3)calculating accumulatively a number of concurrent alarmswill be converted to an alarmwith new name (4) suppressingshielding low priority alarms will be suppressed when theyare of high priority to be generated (5) boolean operationmaking a group of alarms in conformity with some rules ofBoolean operation into an alarm (6) generalization networkelement is to be a more general alarm (7) specializationthe more detailed alarm information will replace networkelement alarms (8) temporal relation the different alarms areto be generated as per certain time sequence

Alarmassociation among groups of network equipment isas follows (1) derivative association the network equipmentalarms are divided into root alarm and derivative alarm(2) topological association the network equipment alarmcontains home terminal alarm and opposite end (3) timingassociation the same fault point generates alarms withthe same time trigger characteristic (4) causal associationOccurrence of Alarm A causes Alarm B that is elementmanagement system has been out of management as a resultof optical cable break (5) link association convergence line

fault will trigger the network equipment alarm on the entirepath and send unification orders

4 Preprocessing of Network Alarm Data

The transmission network device alarm data is used asthe analytical data for association rules for the informationcommunication network alarms and the link of data prepro-cessing is as follows (Figure 2)

(1) Data Extraction All transmission alarms within a specifictime interval are extracted through the network manage-ment system (including engineering cutover and devicealarms arising from network adjustment) and the data fieldsextracted include alarm standardization field and networksystem alarm standardization field

(2) Data Cleaning Special data affecting the algorithm analy-sis quality is cleaned from the alarm data extracted and suchdata includes

A abnormal data junk alarm ultrashort alarm ultra-long alarm and abnormal and special alarm dataB incomplete data alarm data with a null alarmdeterminant attribute fieldC erroneous data alarm data with a large differencebetween the time field of the network managementalarm and the time field of the device alarm due totime synchronization abnormality


Alarm informationstandardization fields

District

Ne_clear_time

Vendor Device_type Native_object_name Title System_alarm_idSeverity Event_class Event_type Event_sub_type

Affect_businessAffect_device

Alarm standardization fields of the network management Alarm standardization fields

Dataextraction

Preprocessing of network alarm data

Datacleaning

Datascreening

Dataintegration

Divisionclass

Device_typeNative_object_name

TitleSystem_alarm_id

Severity

Ne_time

Affect_businessAffect_deviceWeight

class

City System_levelSite

Management_domain Ne_time

Figure 2 Preprocessing of network alarm data

D duplicated data duplicated alarm data due tomerging or removing flashes

(3) Data Screening A Interference data screen and rejectthe interference alarm data for example uncorrelated alarms(alarms such as access control enabling and mismatching ofthe main and standby sing board versions) in a number ofsignal alarms (alarms such as signal degradation indicationand output signal loss) are rejected During screening theduplicated alarms should not be deleted blindly and theyshould be analyzed and discriminated based on the actualfault conditions considering that the duplicated alarms maybe caused by different faults during different periods [10]

B Alarm information standardization field main infor-mation fields are screened from the standardization fields ofthe network management alarms and alarm standardizationfields for subsequent mining of association rules Theseinformation fields are set as two classes division class andweight class The alarm information fields of division classare mainly used to describe attribution relation and attributeparameters of alarms The alarm information fields of weightclass are mainly used to describe importance difference andinfluence and assign differentiated weight to the data of theassociation rule mining algorithm

(4) Data Integration The alarm processed in the above linkand its corresponding information standardization fields areresorted out eventually and generate network alarm datasources with high information amount

5 Mining Algorithm for Association Rules forthe Network Alarm Data

The Apriori algorithm has been widely used by researchersas a classic mining algorithm for association rules Whilethe swarm intelligence algorithm has been studied deeplyand applied in various fields due to its characteristics suchas distributed control low communication overhead simplebehavior rule and strong self-organization The APPSO

algorithm is exactly an efficient algorithm for it incorporatesthe above two algorithm thoughts and combineswith the datacharacteristics of the alarms in the information communica-tion network

51 Example Analysis for Apriori Algorithm On the ICDM(IEEE International Conference on Data Mining) held inDecember 2006 the top ten classical algorithmswere selectedfrom the 18 candidate algorithms after three links of nom-ination review and voting that is C45 (classification) K-Meams (statistical learning) SVM (statistical learning) Apri-ori (association analysis) EM (statistical learning) PageRank(link mining) AdaBoost (bagging and boosting) kNN (clas-sification) Naive Bayes (classification) andCART (classifica-tion) The Apriori algorithm formulated by Wu and Vipin in2009 ranks fourth among the ten top classical algorithms fordata mining which also sufficiently shows its importance indata mining algorithm [11]

The association rules mining algorithm exactly obtainsthe association relationship among terms from data setsthrough mathematical logic The market basket analysissufficiently embodies the industrial application value ofthe association rules mining algorithm The Apriori is anassociation rules mining algorithm based on characteristicsof frequent item sets (a priori knowledge) whose core conceptis a layer-wise iterative search of the theory of frequent itemsets

In combination with the examples of fault alarms ofthe information communication network the application ofconcept and flow of the Apriori algorithm are discussed asfollows

511 Concept of the Apriori Algorithm

(1) All item sets all alarm item sets of the examples thatis Alarm1ndashAlarm5

(2) item set concurrent item combination for exampleAlarm1Alarm2 Alarm2Alarm3Alarm4


(3) support describes universality and frequency of asso-ciation rules and the association rule of high supportreflects that it may be applicable to most events of thedata sets

(4) support count the number of alarm affairs containedin a group of item sets

(5) confidence describes reliability and accuracy of theassociation rules that is probability of Alarm2 occur-rence on the premise of Alarm1 occurrence (condi-tional probability)

As for the mining association rules of the Apriori algo-rithm high support and low confidence of the associationrule indicate the reliability of the association rule is poor lowsupport and high confidence of the association rule indicatethe applicability of the association rule is poor Minimumsupport count and minimum confidence are set manuallyby users An association rule is deemed to be concernedif it satisfies both parameters above [12] The matchingrelation between the support and the confidence should beset rationally in combination with the value demand forindustrial rules in practical application

The generation process of association rules is also the pro-cess where joining pruning and enumerating are performedthrough support and confidenceThe association rules are notable to be applied directly through the algorithm besides theapplication value requires analyzing and screening by experts

512 Flow of the Apriori Algorithm The flow the Apriorialgorithm can be reduced to the following steps [13] (1)analysing the frequent item sets that is obtaining all itemsets no less than the preset minimum support count fromthe iteration of the full database (joining pruning andenumerating) (2) obtaining the strong association rules thatis extracting the association rules from the frequent item setsbased on theminimum support andminimumconfidence Incombination with instances the analysis and explanation arepresented in Table 1

Table 1 shows the corresponding alarm items generatedon the network device when the information network failsThe network fault events are successively defined as Fault 1ndashFault 5 The alarm item class corresponding to each fault isdefined as Alarm1ndashAlarm5 (reduced to A1ndashA5) The networkfaults arising from different reasons will generate differentcombinations of alarm item classes (Table 1)

(1) All alarm item sets are scanned and the support of eachalarm item is calculated in Table 2

(2) The minimum support count is 2 and the candidateitem set C1 will form after screening (eliminating A5) of thealarm item combinations in L1 (see Table 3)

(3) All alarm item sets are scanned again to form thesupport calculation L2 based on the candidate item set C1 (seeTable 4)

(4) The minimum support count is 2 and the candidateitem set C2 will form after screening (eliminating A1A4and A3A4) of the alarm item combinations in L2 (seeTable 5)

Table 1 Fault alarms of information communication network

Network fault event (fault ID) Alarm item sets (alarm items)Fault 1 A1 A2 A3 A5Fault 2 A2 A4Fault 3 A2 A3Fault 4 A1 A2 A3 A4Fault 5 A1 A3

Table 2 Calculation of support of all alarm item sets L1

Alarm item Support countA1 3A2 4A3 4A4 2A5 1

Table 3 Support of alarm item sets C1

Alarm item Support countA1 3A2 4A3 4A4 2

Table 4 Support of alarm item sets L2

Alarm item Support countA1 A2 2A1 A3 3A1 A4 1A2 A3 3A2 A4 2A3 A4 1

Table 5 Support of Alarm Item Sets C2

Alarm item Support countA1 A2 2A1 A3 3A2 A3 3A2 A4 2


Alarm item Support countA1 A2 A3 2A1 A2 A4lowast 1A1 A3 A4lowast 1A2 A3 A4lowast 1

(5) All alarm item sets are scanned again to form thesupport calculation L3 based on the candidate item set C2(see Table 6) Based on the nature of the Apriori algorithm(all subsets of the item sets are frequent necessarily) A1A4


and A3A4 are not frequent item sets Thus A1A2A4lowastA1A3A4lowast and A2A3A4lowast in Table 6 are not frequentitem sets and can be excluded directly

(6)Theminimum support count is 2 and the final item setC3 will form after screening of the alarm item combinationsin L2 (see Table 7)

The nonvoid proper subsets of A1A2A3 includeA1A2 A1A3 A2A3 A1 A2 and A3 and it canbe inferred that the confidence coefficients are as presentedin Table 8

They meet the confidence coefficient confidence = 60and the association rules are obtained A1A2 rarr A3A1A3 rarr A2 A2A3 rarr A1 A1 rarr A2A3 thatis Alarm3 will necessarily appear when Alarm1 and Alarm2occur concurrently the probability of concurrent occurrenceof Alarm2 and Alarm3 is 67 when Alarm1 occurs the rulesfor others are similar

Based on the thinking of the Apriori algorithm flowabove the characteristics are as follows

(1) Advantages the algorithmic logic is clear withoutany complex mathematical derivation process with the dualparameter values of the support and confidence coefficient asthe interest indicator for weighing the association rules

(2) Disadvantages frequent repeated scans of the infor-mation in the sample database lead to a heavy load on thesystem IO the number of the candidate frequent item setsincreases sharply and the operation time increases signifi-cantly when the item sets are large the attribute differenceand importance of the set elements is ignored and high-value information is lost when the support and confidencecoefficient serve as the sole criterion for weighing the itemsets the single-dimensional Boolean type association rulesmining mode is used and multidimensional multilevel andnumeric type association rules need to be improved

In response to disadvantages of the Apriori algorithmresearchers compress the database samples by random sam-pling formulate hash functions to the size of the candidateitem set reduce the number of scanning of the database bythe method of dynamic item set counting quickly establishfrequent item sets utilizing the relation of ldquolocal-overallrdquooptimize the event database to reduce the quantity of the itemsets in combination with the nature of the Apriori algorithmuse parallel computation and so forth [14ndash16]

Based on the Apriori algorithm thought Han et al aprofessor from Simon Fraser University adopted a partitionsearchmethod combining expandedprefix tree data structureand branch-like local growth that is FP-growth (frequentpattern-growth) algorithm in 2000 [17] which avoids theproblem of repeating an ergodic database in the Apriorialgorithm and substantially improves the mining efficiencyof association rules

52 Particle Swarm Intelligence Algorithm Theadaptivity andhigh-efficiency characteristics of group system consisting ofthe natural ecosystem and various kinds of organisms inresponse to complex problems (eg community cooperationbiological evolution immune system nerve conduction etc)provide new research directions and application schemes

Table 7 Final item set of alarm item sets C3

Alarm item Support countA1 A2 A3 2

for complex scientific problems for example ant colonyalgorithm bat algorithm bee algorithm firefly algorithmcuckoo search algorithm particle swarm optimization algo-rithm and so forth [18] In 1987 the zoologist Reynoldssimulated the process of aggregating and flying of bird flockself-organization by establishing flight rules for individuals ofthe bird flock that is collision avoidance velocity matchingand flock centering [19] In 1995 Kennedy and Eberhartanalysed the process of aggregating scattering andmigratingof birds that is when a bird flock searches for specific foodin a certain unknown area at random all individuals of thebird flock do not known their locations but they know thedistance between their locations and the food The simplestand efficient strategy is to search for the peripheral regionof the bird closest to the food [20] The whole foragingprocess achieved information sharing and competitive col-laboration among individuals of the low-intelligence birdflock In addition the process embodies the value of the groupintelligence evolving from unordered to ordered in obtainingthe optimum solution Kennedy considered the individuals ofthe birds as single particles and proposed the particle swarmoptimization (PSO)The whole process follows the principlesof environmental stimulus evaluation adjacent individualscomparison and learning adjacent advanced individual [21]

The PSO algorithm first initializes the particle swarmthat is random location and velocity are assigned to theparticle swarm in the feasible solution space Each particle is afeasible solution in the optimization problem A fitness valueis determined by an optimization function then each particlewill move in the solution space and the particle velocitywill determine its motion direction and distance Usuallyparticles approximate the current optimal particle until theoptimal solution by means of iteration and each particlewill approximate two optimal solutions during iteration thatis particle optimum solution (POS) and global optimumsolution (GOS)

521 Fundamental Principles of PSO Assume a 119889-dimen-sional target search space there is a group of particle swarmsconsisting of 119898 particles with potential problem solution119878 119904 = 997888119909

19978881199092 997888119909119898 among which 997888119883

119894= (119909

1198941

1199091198942 119909

119894119889) 119894 = 1 2 119898 indicates a vector point of 119894th

in the 119889-dimensional solving space 997888119909119894is substituted into

the objective function pertinent to solving problem and thematched fitness value can be obtained 997888119875

119894= (1199011198941 1199011198942 119901

119894119889)

is used and 119894 = 1 2 119898 indicates the optimum valuepoint of the 119894th particle obtained by self-search (the optimumvalue means that its corresponding fitness value is the mini-mum) in the particle swarm 119878 there is an overall optimumparticle which is calculated as 997888119866

119894= (119892

1198941 1198921198942 119892

119894119889)

119894 = 1 2 119898 each particle also has a velocity variable


Table 8 Calculation of confidence coefficient of C3 alarm item set

Logical relationship among alarms Analytical calculation of confidence coefficientA1 A2 rarrA3 Confidence = 22 = 100A1 A3 rarrA2 Confidence = 23 asymp 67A2 A3 rarrA1 Confidence = 23 asymp 67A1rarr A2 A3 Confidence = 23 asymp 67A2rarr A1 A3 Confidence = 24 = 50A3rarr A1 A2 Confidence = 24 = 50

Pi

Pi

Vi

Vi

Gi

Gi

Xk+1i

Xki

Xki

Figure 3 Particle migration of PSO

997888

119881119894= (V1198941 V1198942 V

119894119889) 119894 = 1 2 119898 indicating the velocity

of the 119894th particleIn the PSO algorithm the following formulae are used for

recursive calculation of particle movement

997888

119881

119896+1

119894=

997888

119881

119896

119894+ 1198881lowast 1199031lowast (

997888

119875

119896

119894minus

997888

119883

119896

119894) + 1198882lowast 1199032lowast (

997888

119866

119896

119894minus

997888

119883

119896

119894)

(1a)

997888

119883

119896+1

119894=

997888

119883

119896

119894+

997888

119881

119896+1

119894

(1b)

where the particle number is 119894 = 1 2 119898 119896 is the numberof iterations learning factors 119888

1and 1198882are positive constants

to which 2 is usually assigned 1199031and 1199032are random numbers

distributed between [0 1] In order to maintain the values of997888

119881

119896

119894and997888119883

119896

119894within a reasonable regional range997888119881max and

997888

119883maxshould be set rationally

Formula (1a) encompasses three facets of information

when calculating the newvelocity997888119881119896+1

119894of the particle 119894 firstly

velocity 997888119881119896

119894is the speed of the particle 119894 at the previous

moment secondly information on distance between thecurrent position of the particle 119894 and the optimum positionof the individual particle and thirdly the information on thecurrent position of the particle 119894 and the optimum positionof the overall particle swarm Formula (1a) is deployed tocalculate the new position coordinates of particles Formula(1a) and formula (1b) jointly determine the next motionposition of the particle 119894 Taking a two-dimensional space asan example Figure 3 describes the process where a particlemoves from its initial position to its new position based onformula (1a) and formula (1b)

From the social dynamics an analysis is conducted thefirst part of formula (1a) is the memory term reflectingthe velocity vector of particle in the previous step the

second part is self-recognition term a vector pointing tothe optimum point of the particle from the current pointreflecting self-learning judgment of the particle under theeffect of ambient particle swarm the third part is the group-recognition term a vector pointing to the optimum point ofthe overall particle swarm from the current point reflectingexperience sharing and collaboration among particles Theprocess reflects the basic learning development rules forbiotic communities in the nature that is the process wherecompanion knowledge learning and self-cognitive decision-making are integrating under constant action of externalenvironmental information

53 Optimization Algorithm for Mining of Particle SwarmAssociation Rules Based on an analysis of the flow for theApriori algorithm and particle swarm optimization it hasbeen discovered that the process of searching for the frequentitems in the Apriori algorithm is actually a global searchprocess while the particle swarmoptimization is an algorithmfinding the optimal global solution with excellent optimalperformanceTherefore the global optimum characteristic ofthe Apriori algorithm and the high efficiency of seeking theglobal optimal solution of the particle swarm optimizationare needed for combing to achieve the optimization algo-rithm for association rules mining-APPSO algorithm

531 Basic Flow of the APPSO Algorithm The Apriori algo-rithm includes two stages and its overall performance isprimarily determined by the first link which aims at findingall frequent item sets meeting the minimum support in thedatabase the second link refers to finding the associationrules meeting the minimum confidence coefficient from thefrequent item sets

Create three particle swarms in APPSO algorithm (seeFigure 4) that is the sample particle swarm the candidate


Start

Parameter settingParticle swarm scale iterative times T

minimum support minimum confidence

Alarm code of the database

The time window generates sample particle swarm A

Generate candidate particle swarm B rule particle swarm C at random

Create sparse list

Calculate the support of particle Bi in eachcandidate particle swarm and update the

optimum value with sample particle swarm A

Perform logical operation and rule extraction for thecandidate particle swarm particle

Incorporate the subset of the candidate particleswarm particle Bi into the candidate particle

swarm B and initialize candidate particle

Calculate confidencecoefficient (fitness function)

Update the historical optimumvalue of the particle

Update the historical optimumvalue of the particle swarm C

Is the optimum rulevalid

Candidate particle swarm Bmoves once based on theoccurrence probability of

item set

Finish

Number of iterationsNumber of iterations

Rule particle swarmC moves once

Outputassociation rules

No

Yes

Yes

Yes

No

No

No

Yes

t1lt iterative times T


t2 = t2 + 1

t1 = t1 + 1

Bi and candidate particle swarm Ci

Initialize t2 = 0

swarm C

Support ge minimumsupport

Initialize t1 = 0

Figure 4 Basic flow of the APPSO algorithm


particle swarm and the rule particle swarm The sampleparticle swarms are entity particle swarms taking four-dimensional alarm data as an example the sample particlesare (A1A3A2) (A1A2A4) the candidate particle swarmand the rule particle swarm are logical particle swarms forexample (1110) and (1101) The eligibility of the particlesin the candidate particle swarm for candidate particles isdetermined by calculating and determining whether theparticles in the sample particle swarm satisfy the minimumsupport The particles in the candidate particle swarm andthe rule particle swarm are judged logically to generate pre-liminary association ruleThe association rules will be outputif each preliminary association rule satisfies the minimumconfidence otherwise they will be discarded The creatingprocess is as follows

(i) Sample particle swarm the alarm data source ispartitioned to create sample particle swarm A (SPS-A forshort) by sliding the time window For instance after thenumber119873 timewindow capturing the natural time the alarmsequence is shown in A1 A3 and A4 namely the particle isA1 A3 and A4

(ii) Candidate particle swarm B particle swarm is createdrandomly in the APPSO algorithm (corresponding to thefirst link in the Apriori algorithm) such that each particle ofthe candidate particle swarm represents a certain candidateitem set and all candidate particles of the whole candidateparticle swarm represent a collection of all existing differentcandidate item sets The support of the item set representedby each candidate particle is calculated to judge whetherit meets the minimum support count value (calculationmethod see Section 512) Such a particle swarm is referredto as candidate particle swarm B (Particle swarm CPS-B)

It is assumed that there are 4 types of alarms in the alarmdatabase and they are AlarmA1 A2 A3 and A4 respectivelyEach alarm is expressed with 0 or 1 0 indicates that the alarmis not in the candidate particle currently while 1 indicates thatthe alarm is in the candidate particle currently It is assumedthat the value of a candidate particle is 1100 that is AlarmA3 and Alarm A4 are not in the candidate particle and theparticle represents a 2-item set consisting of A1 and A2 Ifthe 2-item set meets the minimum support count value forsample particle swarm the certain candidate particle wouldbe reserved or removed conversely

(iii) Rule particle swarm in the APPSO algorithm aparticle swarm is randomly created (corresponding to thesecond link in the Apriori algorithm) such that each particleof the particle swarm represents a potential association ruleThe length of each particle is equal to the length of eachparticle in the candidate particle swarm Each alarm isexpressed with 0 or 1 1 indicates the corresponding alarm isthe antecedent of the association rule while 0 indicates thatthe corresponding alarm is the consequent of the associationrule Such a particle swarm is referred to as rule particleswarm C (RPS-C)

Assume the value of a certain particle 119887 in particle swarmC is 111000 and then the rule represented is (A1A2A3) rArr(A4A5A6)

After creating of candidate particle swarm B and ruleparticle swarmC the operational method for the two particle

swarms is as follows (particle 119886 belongs to candidate particleswarm B and particle 119887 belongs to rule particle swarm C)

The logic operation of ldquoandrdquo is performed for each particleof candidate particle swarm B and each particle of ruleparticle swarmCand the operational result is used to estimatethe relation between the antecedent and consequent of therule For example 119886 = 110011 119887 = 111000 and 119886 cap 119887 =111000 indicate that Alarm A3 and Alarm A4 are not in theassociation rulesThefield value ofA2 andA2 is 1 and the fieldvalue of A4 and A6 is 0 We can obtain that the associationrule represented by 119886 and 119887 is (A1A2) rArr (A5A6)

532 APPSO Algorithm Optimization Link During miningof association rules based on swarm intelligence the particleergodic method is usually used to obtain the support of theitem set represented by the particle The particle supportobtained by scanning the whole database is accurate inresult However some shortcomings exist that is the actualanalysis efficiency is low and no data source characteristicsand basic algorithm characteristics are combined Thereforedata source sequencing coding and sliding window valueassignment are used based on the data characteristics of thenetwork alarms the sparse linked list algorithm is deployedto calculate the support of the item set

(1) Sequencing Code As alarm names are usually describedwith English character string or digit combined number suchan identification method would bring about a large amountof combined data (eg MPLS TUNNEL MISMERGE and007-061-00-800446) resolution consumption to data pro-cessing and analysing Therefore we employ the methodby sequencing codes to reduce resolution consumption inwhich all alarmnames or networkmanagement alarm IDs aresequenced on the basis of the sequence of letters and figuresIt targets on avoiding two or more integral values beingassigned to the same alarm subsequently (Figure 5) differen-tiated values are assigned on the basis of data sequence

(2) SlidingWindowDue to the combination of time-type dataand relationship type in alarms the time-type alarm datais sequenced on the basis of time length the size of slidingtime window and sliding step length and the relationshiptype alarm data is converted and combined into differenttransactional data item sets

(3) Sparse Linked List Compared with the overall alarmdatabase after division each of the alarm data item sets onlycontains partial alarm data types The efficiency of databasescanning by the APPSO algorithm is further improvedusing the thought of sparse linked list based on the datacharacteristics The algorithm process is as follows

A linked list header is created for each item of the wholedatabase For example if there are 200 alarmcode integer datatypes consisting in 10000 item sets 200 linked list headerswill be created and the integral value of each item is thenumber of its corresponding linked list

The item sets are scanned in sequence and the items ofeach item set are added to the end of the corresponding linkedlist For example If the 119899th item set in the database is (50 108


Alarm1 Alarm3Initial permutation

1 2 3 4 5 6 7 Encoding

Permutation schedule

1 2 3 3 3 4 5Natural coding darr Sequencing coding darr

rarrAlarm2 Alarm1 Alarm1 Alarm5Alarm4 Alarm2 Alarm1Alarm3 Alarm1 Alarm4 Alarm5Alarm1

Figure 5 Natural coding and sequencing coding

1

17

50

108

200

50 108 17

middot middot middotmiddot middot middot

middot middot middot




50ndash1

108ndash1

1ndash1

17ndash1

200ndash1

108ndash88

17ndash24

50ndash64

Figure 6 Examples of sparse linked list

17) then the 119899th item set is added to the end of the linked list50 and the end of the linked list 108 and so forth 200 linkedlists are created finally that is sparse linked list The numberof the alarm code integers saved in each linked list is muchless than the 10000 item sets of the whole database (Figure 6)

(4) Calculation of the Particle Support Based on the SparseLinked List Take the 119899th item set in the database (50 108 17)and 200 linked list headers as examples (Figure 7)

Starting with the linked list 50 it is assumed to becontaining the item ldquo50rdquo through searching the 64th itemset Similarly the linked lists 108 and 17 correspond to 88and 24 respectively that is all item sets before the 88th itemset do not contain the corresponding item of the particleAfter searching in the 88th item set 1 will be added to theparticle support if it contains (50 108 17) (Step 1) otherwisecontinually searching in the linked list (50 108 17) in order tofind the next data respectively Assume that they correspondto 121 90 and 65 respectively and directly search in the 121stitem set 1 will be added to the particle support if it contains(50 108 17) (Step 2) otherwise continue to search in thelinked list (50 108 17) and find the next data Suppose thatthey correspond to 121 184 and 121 respectively and directlysearch in the 184th item set 1 will be added to the particlesupport if it contains (50 108 17) (Step 3) otherwise keep onsearchingThe overall linked list would finish searching when50 has been sorted out in (50 108 17) (Step 4)

(5) Nature of the Apriori Algorithm Based on the nature ofthe Apriori algorithm ldquothe subset of the known frequent itemset 119896 is also frequentrdquo the nature is used to optimize the

search rule for the particle swarm that is all subsets of theparticle are also frequent if the corresponding candidate itemset of a certain particle is a frequent item set For exampleif the particle 119886 (110011) belongs to a frequent item set thenany subset of the value of 119886 such as 110000 000011 100001010010 100010 and 010001 are frequent and these subsets aredirectly incorporated into candidate particle swarmA as newparticles

In conclusion themain principle of theAPPSOalgorithmis to estimate whether each particle in candidate particleswarmA (CPS-A) is frequent or notThe subset of the particlewill be added to A if the particle is frequent Then the logicaloperation of ldquoandrdquo is performed for the particle and eachparticle of rule particle swarm B (RPS-B) to judge whetherthe corresponding rule of the result obtained is an associationrule meeting the conditions or not In accordance with acertain sequence A and B are constantly updated until alliterative processes terminate

533 APPSOAlgorithmTest A comparison test is conductedon the test platform with the APPSO algorithm and Apriorialgorithm (hardware CPU Intel Core i5 33 GHz 8G RAM1 T hard disk software operating system window7 devel-opment platform Qt470 single-thread development) Thealarm data (21084 pieces) of the networkmanagement systemPTN device is extracted at random as the data The data isgenerated into item sets with 5-seconds (5 s) time windowand the data set containing only a single item (1-item sets)is rejected Finally 4753 item sets in total are obtained Thescales of candidate particle swarmand the rule particle swarmare identical

(i) Test 1 relation between the support and numberof association rules the scale of the particle swarm is 40number of iterations is 100 and confidence coefficient is 30

Analysis on Test 1 Apriori algorithm is a global searchalgorithm Therefore the number of the association rulesmined by the APPSO algorithm is less than the number ofthe association rules mined by the Apriori algorithm Morethan 60 of the main association rules is obtained with theAPPSO algorithm as shown in Figure 8

(ii) Test 2 relation between the confidence coefficient andnumber of association rules the scale of the particle swarm is40 number of iterations is 100 and confidence coefficient is5

Analysis on Test 2 under the condition of a constantnumber of iterations and minimum support the numberof alarms obtained by the two algorithms will necessarilydecrease with increasing of confidence coefficient indexcompared with the Apriori algorithm when the confidence


50 108 17

50ndash1

108ndash1

1ndash1

17ndash1

200ndash1

108ndash88

17ndash24

50ndash64

17ndash65 17ndash121 17ndash188

108ndash121

50ndash184

108ndash90 108ndash195

50ndash121

Step1 Step2 Step3 Step4

End50

108

1

17

200



Figure 7 Examples of calculation of the particle support based on the sparse linked list

35

19 1611

5

43

2822

158

8168 73 73

63

0

10

20

30

40

50

60

5 10 20 40 50

Num

ber o

f ass

ocia

tion

rule

s

Support ()

APPSOAprioriProportion of rule number

Figure 8 Relation between the support and number of associationrules

coefficient value is within the discrete interval [30 60]the number of the association rules obtained with the APPSOalgorithm accounts for approximately 80 as shown inFigure 9

(iii) Test 3 relation between the scale of the particleswarm and the number of association rules the number ofiterations is 100 the minimum support is 5 and confidencecoefficient is 30

Analysis on Test 3 under the condition of a constantnumber of iterations minimum support and confidencecoefficient the larger the particle swarm is the more thenumber of the association rules will be The number ofthe association rules will approach the number of the rulesobtained by the global search of the Apriori algorithm asshown in Figure 10

(iv) Test 4 relation between the number of iterationsand operation time the scale of the particle swarm is 40minimum support is 5 and the confidence coefficient is30

Analysis on Test 4 under the condition of a constantparticle swarm scale minimum support and confidencecoefficient the time for the APPSO algorithm is prolonged

3529

1711

2

4335

2114

5

81 83 81 79

40

0102030405060

30 40 50 60 70Num

ber o

f ass

ocia

tion

rule

s

Confidence coefficient ()


Figure 9 Relation between the confidence coefficient and numberof association rules

16

35 3842 4243 43 43 43 43

37 81 88 98 98

0

10

20

30

40

50

60

20 40 60 80 100

Num

ber o

f ass

ocia

tion

rule

s

Particle swarm scale


Figure 10 Relation between the scale of the particle swarm and thenumber of association rules

with increase of the number of iterations but the number ofassociation rules obtained significantly increases comparedwith the Apriori algorithm the efficiency of the APPSOalgorithm significantly increases for example the numberof iterations is 120 the time for the APPSO algorithm only


Table 9 Distribution of training data sets

Item sets 1-itemsets

2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets

10-itemsets

Number ofitem sets 136342 91787 36780 10141 2578 626 206 109 188 204


12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets

20-itemsets

100-itemsets


Table 10 Distribution of test data sets


2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets

Number ofitem sets 15455 8649 1386 232 33 5 5 4 8


11-itemsets

12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets


Table 11 Statistics on association rate of test data

Minimum support count 001 001 001Minimum confidence 001 005 009Number of rules from training data sets 185 149 154Alarm association rate from test data sets 8123 8121 8122

accounts for 17 of the time for the Apriori algorithm yet thenumber of the rules obtained accounts for 88 of the totalnumber of rules as shown in Figure 11

On the premise of desired demand for the number ofrules the APPSO algorithm is able to control the operational

precision and decrease the computation time and mem-ory consumption by reasonably setting the particle swarmparameters

(v) Engineering test the network alarm data over the fourof the 8 consecutive weeks is used as rdquotraining datardquo Thealarm association rules are mined by the APPSO algorithmand the data over the other 4 weeks is used as ldquotest datardquoto calculate the alarm correlation rate Specific method allalarms are intercepted as per the fixed flow time window andall of the non-1-item sets are included in the calculation of thealarm correlation rate (the 1-item sets themselves do not havea correlation relationship) The algorithm is as follows

Alarm association rate = (number of non-1-item sets meeting the association rules

number of all non-1-item sets) times 100 (1c)

For example the alarm sequence is (A1A2A3A1A4A2A3A4A4A2) and becomes A1A2 A3 A1A4A2 A3A4 A4A2 after being intercepted in accordancewith the fixed flow time window among which the non-1-item sets involving in the calculation of the alarm correlationrate are A1A2 A1A4A2 A3A4 and A4A2 Theassociation rate of the alarm data is 50 if the association ruleis A1rarrA2

Analysis on engineering test The alarm association rulesobtained through the training data over the first 4 weeks isapplied in the test data over the last 4 weeks The trainingdata over the first 4 weeks contains the equipment types BSCBTS CELL and 516271 alarms of which the alarm types are131The timewindow is set to 2 s and the sliding step length to1 s the test data over the last 4 weeks contains the equipmenttypes BSC BTS CELL and 39470 alarms of which the alarmtypes are 89 In combination with the requirements for actual

conditions of the engineering operating environment thetime window is set to 3 s 10420 non-1-item sets are obtainedafter interception of data

FromTables 9 10 and 11 it is obtained that all of the alarmassociation rates are higher than 80TheAPPSOassociationmining algorithm provides an effective analytic method forthe alarm association analysis

6 Conclusion

The association rules for the alarm data in the informationcommunication network should be analysed in conjunctionwith the data characteristics to perform a design specificallyto achieve a corresponding algorithm flow Compared withthe Apriori algorithm the mining efficiency of the APPSOalgorithm is significantly enhanced but a small number of


42 61 79 97 115

664 664 664 664 664

6 9 12 15 1742

56 70 81 88

0

100

200

300

400

500

600

700

40 60 80 100 120

Tim

e (s)

Number of iterations

APPSOApriori

Time proportionProportion of rule number

Figure 11 Relation between the number of iterations and operationtime

association rules are lost to some extent due to the charac-teristics of the PSO algorithm The value of the associationrules lies in quick acquisition and subsequent high-valueevaluation of association logic instead of sole acquisitionof all association rules From this perspective the APPSOalgorithm improves in both mining efficiency and algorithmconcept

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported by a grant from the NationalNatural Science Foundation of China (no 51205274) theScience and Technology Major Project of the Shanxi Scienceand Technology Department (20121101004) the Key Disci-plines Construction in Colleges and Universities of ShanXi([2012]45) the Shanxi Scholarship Council of China (no2013-035) the China Postdoctoral Science Foundation (no2013M530894) and the Innovation Project of the Postgradu-ate Education in Shanxi Province (no 20123027)

References

[1] E Kiciman and A Fox ldquoDetecting and localizing anomalousbehavior to discover failures in component-based internetservicesrdquo Tech Rep The Stanford Computer Science (CS)Department Stanford Calif USA 2004

[2] L L Huang G G Su and Y J Jiang Operation Support SystemTechnology and Practice Posts amp Telecom Press Beijing China2012 (Chinese)

[3] D T Li Researches on data mining based alarm correlationanalysis in communication networks [PhD thesis] University ofElectronic Science and Technology of China Chengdu China2010 (Chinese)

[4] B Z Yao RMu and B Yu ldquoSwarm intelligence in engineeringrdquoMathematical Problems in Engineering vol 2013 Article ID835251 3 pages 2013

[5] Y Wang G C Li and Y K Xu ldquoResearch on managementmethod classification and correlation of alarm in informationcommunication networkrdquo Telecommunications Science vol 29no 8 pp 132ndash135 2013 (Chinese)

[6] X BWangW Li andHWXu ldquoManagement analysis of alarmstandardization in centralized operational moderdquo Telecommu-nications Technology no 4 pp 39ndash42 2009 (Chinese)

[7] T-Y Li and X-M Li ldquoPreprocessing expert system for miningassociation rules in telecommunication networksrdquo Expert Sys-tems with Applications vol 38 no 3 pp 1709ndash1715 2011

[8] H Mannila H Toivonen and I Verkamo ldquoDiscovery of fre-quent episodes in event sequencesrdquoDataMining andKnowledgeDiscovery vol 1 no 3 pp 259ndash289 1997

[9] R Sterritt D Bustard and A McCrea ldquoAutonomic computingcorrelation for fault management system evolutionrdquo in Proceed-ings of the IEEE International Conference Industrial Informatics(INDIN rsquo03) pp 240ndash247 Alberta Canada

[10] A A Amaral B Z Zarpelao L M Mendes et al ldquoInferenceof network anomaly propagation using spatio-temporal corre-lationrdquo Journal of Network and Computer Applications vol 35no 6 pp 1781ndash1792 2012

[11] X D Wu and K VipinThe Top Ten Algorithms in Data MiningChapman and HallCRC Boca Raton Fla USA 2009

[12] R Agrawal and R Srikant ldquoFast algorithms for mining asso-ciation rules in large databasesrdquo in Proceedings of the 20thInternational Conference onVery Large Data Bases pp 487ndash499Santiago de Chile Chile 1994

[13] S Y Jiang X Li and Q Zheng Principles and Practice ofDataMining PublishingHouse of Electronics Industry BeijingChina 2011 (Chinese)

[14] T Calders N Dexters J J M Gillis and B Goethals ldquoMiningfrequent itemsets in a streamrdquo Information Systems vol 39 pp233ndash255 2012

[15] V D Mabonzo Study on new approach for effective miningassociation rules from huge databases [PhD thesis] DalianMaritime University Dalian China 2012

[16] K Z Ziauddin K T Shahid and Z K Khaiuz ldquoResearch onassociation rule miningrdquo Advances in Computational Mathe-matics and Its Applications vol 2 no 1 pp 226ndash236 2012

[17] J W Han J Pei and Y W Yin ldquoMining frequent patternswithout candidate generationrdquo in Proceedings of the ACMSIGMOD International Conference on Management of Data(SIGMOD rsquo00) pp 1ndash12 Dallas Tex USA 2000

[18] X S Yang Z H Cui R B Xiao et al Swarm Intelligence andBio-Inspired Computation Theory and Applications ElsevierAmsterdam The Netherlands 2013

[19] C W Reynolds ldquoFlocks herds and schools a distributedbehavioral modelrdquo Computer Graphics vol 21 no 4 pp 25ndash341987

[20] J Kennedy and R C Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks pp 1942ndash1948 December 1995

[21] G Veysel and M P Kevin Swarm Stability and OptimizationSpringer Berlin Germany 2011

Submit your manuscripts athttpwwwhindawicom

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Algebra

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Stochastic AnalysisInternational Journal of


operation management will make problems exhibit a sharpfull data increasing including network faults device alarmsand customer complaints

As the information communication system consists ofvarious medium interlinked network devices and operatingsystems implicit and complex-correlated logic is ubiquitousamong network elements that is a certain fault point maytrigger numerous alarms in the whole network The suddenintensive alarms not only consume the resources of thenetwork management system but also obscure the positionof the network fault source points thus severely impedingtrouble shooting by the network operation and maintenancepersonnel Several alarms are incorporated into a single alarmor source alarm with a large amount of information bysuch links as paraphrasing and explaining eliminating andfiltering information integration and correlating and trans-forming and so forth It aims at assisting the operation andmaintenance personnel to analyse fault messages and locatefaults quickly that is mining analysis on alarm associationrules

Mining of alarm association rules refers to a processof analysis on the association between the attributive char-acteristic logic of the alarms within devices and the topo-logical hierarchy of network devices It aims at achievingclear critical alarms accurate fault location and trouble-shooting and intelligent fault prediction and evaluationThemining of alarm association rules can be divided into threelevels analysis on alarm association in the device within theprofession analysis on topological alarm association of thenetwork device within the profession and analysis on inter-professional topological alarm association of the networkdevice but their core ismining algorithm for association rules[3]

The centralized management of information communi-cation network brings about large amounts of alarm dataA rapid mining analysis on the network alarm associationrules is achieved by the classic Apriori association miningalgorithm and PSO algorithm under the context of big dataThe alarm association relationship can be used to add andmerge the fault alarms maintain the work order improvethe centralized monitoring efficiency and reduce the cost ofnetwork maintenance

The Apriori is an association rules mining algorithmbased on characteristics of frequent item sets (priori knowl-edge) whose core concept is a layer-wise iterative search of thetheory of frequent item sets However the Apriori algorithmthought also presents some inevitable problems For instancefrequent repeated scans of the information in the sampledatabase lead to a heavy load on the system IO large itemsets lead to a sharp increase in the number of the candidatefrequent item sets and a significant increase in operation timeand so forth

Swarm intelligence refers to the macroscopic intelli-gent group behavior showed by various types of organismindividuals in the nature during survival collaborationand evolution Application research is conducted for theswarm intelligence algorithm in optimization solutions ofengineering problems such as economic analysis and forecaststructural damage positioning and inspecting command and

dispatch of communication and transportation evacuationroute planning target identifying and tracking factory siteselection and evaluation communication network planningand route plan preparation [4] The swarm intelligencealgorithmhas such advantages as distributed control indirectinformation transfer and simple individuals and swarm intel-ligence As a classic swarm intelligence algorithm the particleswarm optimization also has the above characteristics

Centralizedmanagement of the alarms in the informationcommunication network is an important part of operationmaintenance of the information communication networkThe alarm correlation directly influences the quantity andquality of the alarm work orders An analysis on thelarge amounts of alarm data through an efficient algorithmbecomes the critical technical means The APPSO discussedin the paper incorporates the Apriori algorithm and swarmoptimization algorithms and applies swarm optimizationalgorithms in the information communication field

Section 2 in the paper elaborates such basic conceptsof faults in the information communication network net-work alarms alarm standardization and so forth Section 3discusses the data characteristics of network alarms andthe alarm correlation logical relationships within andbetween network devices Section 4 describes achieving qual-ity improvement of the data source of the network alarms bypre-processing of the network alarmdata Section 51 presentsthe concepts of support and confidence coefficient and min-ing analysis process inApriori algorithm in combinationwithexamples Section 52 describes the swarm intelligencemodeland basic flow of the PSO algorithm Section 53 discussesthe creation of APPSO association rule mining algorithmwhich deducts on the basis of the Apriori and PSO algorithmcharacteristics Besides combining with the characteristicsof the network alarm data the section puts forward theimprovement of the performance of the APPSO associationrule mining algorithm by sequencing code sliding windowsparse linked list and nature of the Apriori algorithmIt conducts a performance test for the algorithm throughthe alarm data in the information communication networkfrom different angles At the end of the section an indexevaluation of the alarm association rate is put forward whichis used for application of the alarm correlation relationshipderived from the APPSO algorithm mining into the actualnetwork

2 Concepts Pertinent to Alarms in theInformation Communication Network

Concepts pertinent to the data analysis on the alarms in theinformation communication network are defined as follows[5 6]

Definition 1 A network fault refers to an event where theinformation communication network is not able to operatenormally and efficiently due to some reasons and even noservice can be provided The reasons causing network faultscan be divided into network device faults communicationlink abnormality inappropriate operation and maintenance






















Timing correlation

Causal correlation

Linkcorrelation


Alarm





relation

Alarm

Alarm





relation

Alarm













District

Ne_clear_time




Dataextraction


Datacleaning

Datascreening

Dataintegration

Divisionclass



Severity

Ne_time


class


























































19978881199092 997888119909119898 among which 997888119883

119894= (119909

1198941

1199091198942 119909




119894= (1199011198941 1199011198942 119901

119894119889)


119894= (119892

1198941 1198921198942 119892

119894119889)





Pi

Pi

Vi

Vi

Gi

Gi

Xk+1i

Xki

Xki


997888

119881119894= (V1198941 V1198942 V




997888

119881

119896+1

119894=

997888

119881

119896

119894+ 1198881lowast 1199031lowast (

997888

119875

119896

119894minus

997888

119883

119896

119894) + 1198882lowast 1199032lowast (

997888

119866

119896

119894minus

997888

119883

119896

119894)

(1a)

997888

119883

119896+1

119894=

997888

119883

119896

119894+

997888

119881

119896+1

119894

(1b)





119881

119896

119894and997888119883

119896


997888





velocity 997888119881119896









Start






Create sparse list











item set

Finish




No

Yes

Yes

Yes

No

No

No

Yes



t2 = t2 + 1

t1 = t1 + 1


Initialize t2 = 0

swarm C


Initialize t1 = 0




















1 2 3 4 5 6 7 Encoding





1

17

50

108

200

50 108 17






50ndash1

108ndash1

1ndash1

17ndash1

200ndash1

108ndash88

17ndash24

50ndash64














50 108 17

50ndash1

108ndash1

1ndash1

17ndash1

200ndash1

108ndash88

17ndash24

50ndash64


108ndash121

50ndash184


50ndash121


End50

108

1

17

200




35

19 1611

5

43

2822

158

8168 73 73

63

0

10

20

30

40

50

60

5 10 20 40 50

Num

ber o

f ass

ocia

tion

rule

s

Support ()








3529

1711

2

4335

2114

5

81 83 81 79

40

0102030405060

30 40 50 60 70Num

ber o

f ass

ocia

tion

rule

s




16

35 3842 4243 43 43 43 43

37 81 88 98 98

0

10

20

30

40

50

60

20 40 60 80 100

Num

ber o

f ass

ocia

tion

rule

s








2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets

10-itemsets



12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets

20-itemsets

100-itemsets




2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets



11-itemsets

12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets














6 Conclusion



42 61 79 97 115

664 664 664 664 664

6 9 12 15 1742

56 70 81 88

0

100

200

300

400

500

600

700

40 60 80 100 120

Tim

e (s)


APPSOApriori






Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra






























Timing correlation

Causal correlation

Linkcorrelation


Alarm





relation

Alarm

Alarm





relation

Alarm













District

Ne_clear_time




Dataextraction


Datacleaning

Datascreening

Dataintegration

Divisionclass



Severity

Ne_time


class


























































19978881199092 997888119909119898 among which 997888119883

119894= (119909

1198941

1199091198942 119909




119894= (1199011198941 1199011198942 119901

119894119889)


119894= (119892

1198941 1198921198942 119892

119894119889)





Pi

Pi

Vi

Vi

Gi

Gi

Xk+1i

Xki

Xki


997888

119881119894= (V1198941 V1198942 V




997888

119881

119896+1

119894=

997888

119881

119896

119894+ 1198881lowast 1199031lowast (

997888

119875

119896

119894minus

997888

119883

119896

119894) + 1198882lowast 1199032lowast (

997888

119866

119896

119894minus

997888

119883

119896

119894)

(1a)

997888

119883

119896+1

119894=

997888

119883

119896

119894+

997888

119881

119896+1

119894

(1b)





119881

119896

119894and997888119883

119896


997888





velocity 997888119881119896









Start






Create sparse list











item set

Finish




No

Yes

Yes

Yes

No

No

No

Yes



t2 = t2 + 1

t1 = t1 + 1


Initialize t2 = 0

swarm C


Initialize t1 = 0




















1 2 3 4 5 6 7 Encoding





1

17

50

108

200

50 108 17






50ndash1

108ndash1

1ndash1

17ndash1

200ndash1

108ndash88

17ndash24

50ndash64














50 108 17

50ndash1

108ndash1

1ndash1

17ndash1

200ndash1

108ndash88

17ndash24

50ndash64


108ndash121

50ndash184


50ndash121


End50

108

1

17

200




35

19 1611

5

43

2822

158

8168 73 73

63

0

10

20

30

40

50

60

5 10 20 40 50

Num

ber o

f ass

ocia

tion

rule

s

Support ()








3529

1711

2

4335

2114

5

81 83 81 79

40

0102030405060

30 40 50 60 70Num

ber o

f ass

ocia

tion

rule

s




16

35 3842 4243 43 43 43 43

37 81 88 98 98

0

10

20

30

40

50

60

20 40 60 80 100

Num

ber o

f ass

ocia

tion

rule

s








2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets

10-itemsets



12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets

20-itemsets

100-itemsets




2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets



11-itemsets

12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets














6 Conclusion



42 61 79 97 115

664 664 664 664 664

6 9 12 15 1742

56 70 81 88

0

100

200

300

400

500

600

700

40 60 80 100 120

Tim

e (s)


APPSOApriori






Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











District

Ne_clear_time




Dataextraction


Datacleaning

Datascreening

Dataintegration

Divisionclass



Severity

Ne_time


class


























































19978881199092 997888119909119898 among which 997888119883

119894= (119909

1198941

1199091198942 119909




119894= (1199011198941 1199011198942 119901

119894119889)


119894= (119892

1198941 1198921198942 119892

119894119889)





Pi

Pi

Vi

Vi

Gi

Gi

Xk+1i

Xki

Xki


997888

119881119894= (V1198941 V1198942 V




997888

119881

119896+1

119894=

997888

119881

119896

119894+ 1198881lowast 1199031lowast (

997888

119875

119896

119894minus

997888

119883

119896

119894) + 1198882lowast 1199032lowast (

997888

119866

119896

119894minus

997888

119883

119896

119894)

(1a)

997888

119883

119896+1

119894=

997888

119883

119896

119894+

997888

119881

119896+1

119894

(1b)





119881

119896

119894and997888119883

119896


997888





velocity 997888119881119896









Start






Create sparse list











item set

Finish




No

Yes

Yes

Yes

No

No

No

Yes



t2 = t2 + 1

t1 = t1 + 1


Initialize t2 = 0

swarm C


Initialize t1 = 0




















1 2 3 4 5 6 7 Encoding





1

17

50

108

200

50 108 17






50ndash1

108ndash1

1ndash1

17ndash1

200ndash1

108ndash88

17ndash24

50ndash64














50 108 17

50ndash1

108ndash1

1ndash1

17ndash1

200ndash1

108ndash88

17ndash24

50ndash64


108ndash121

50ndash184


50ndash121


End50

108

1

17

200




35

19 1611

5

43

2822

158

8168 73 73

63

0

10

20

30

40

50

60

5 10 20 40 50

Num

ber o

f ass

ocia

tion

rule

s

Support ()








3529

1711

2

4335

2114

5

81 83 81 79

40

0102030405060

30 40 50 60 70Num

ber o

f ass

ocia

tion

rule

s




16

35 3842 4243 43 43 43 43

37 81 88 98 98

0

10

20

30

40

50

60

20 40 60 80 100

Num

ber o

f ass

ocia

tion

rule

s








2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets

10-itemsets



12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets

20-itemsets

100-itemsets




2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets



11-itemsets

12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets














6 Conclusion



42 61 79 97 115

664 664 664 664 664

6 9 12 15 1742

56 70 81 88

0

100

200

300

400

500

600

700

40 60 80 100 120

Tim

e (s)


APPSOApriori






Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra


















































19978881199092 997888119909119898 among which 997888119883

119894= (119909

1198941

1199091198942 119909




119894= (1199011198941 1199011198942 119901

119894119889)


119894= (119892

1198941 1198921198942 119892

119894119889)





Pi

Pi

Vi

Vi

Gi

Gi

Xk+1i

Xki

Xki


997888

119881119894= (V1198941 V1198942 V




997888

119881

119896+1

119894=

997888

119881

119896

119894+ 1198881lowast 1199031lowast (

997888

119875

119896

119894minus

997888

119883

119896

119894) + 1198882lowast 1199032lowast (

997888

119866

119896

119894minus

997888

119883

119896

119894)

(1a)

997888

119883

119896+1

119894=

997888

119883

119896

119894+

997888

119881

119896+1

119894

(1b)





119881

119896

119894and997888119883

119896


997888





velocity 997888119881119896









Start






Create sparse list











item set

Finish




No

Yes

Yes

Yes

No

No

No

Yes



t2 = t2 + 1

t1 = t1 + 1


Initialize t2 = 0

swarm C


Initialize t1 = 0




















1 2 3 4 5 6 7 Encoding





1

17

50

108

200

50 108 17






50ndash1

108ndash1

1ndash1

17ndash1

200ndash1

108ndash88

17ndash24

50ndash64














50 108 17

50ndash1

108ndash1

1ndash1

17ndash1

200ndash1

108ndash88

17ndash24

50ndash64


108ndash121

50ndash184


50ndash121


End50

108

1

17

200




35

19 1611

5

43

2822

158

8168 73 73

63

0

10

20

30

40

50

60

5 10 20 40 50

Num

ber o

f ass

ocia

tion

rule

s

Support ()








3529

1711

2

4335

2114

5

81 83 81 79

40

0102030405060

30 40 50 60 70Num

ber o

f ass

ocia

tion

rule

s




16

35 3842 4243 43 43 43 43

37 81 88 98 98

0

10

20

30

40

50

60

20 40 60 80 100

Num

ber o

f ass

ocia

tion

rule

s








2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets

10-itemsets



12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets

20-itemsets

100-itemsets




2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets



11-itemsets

12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets














6 Conclusion



42 61 79 97 115

664 664 664 664 664

6 9 12 15 1742

56 70 81 88

0

100

200

300

400

500

600

700

40 60 80 100 120

Tim

e (s)


APPSOApriori






Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Pi

Pi

Vi

Vi

Gi

Gi

Xk+1i

Xki

Xki


997888

119881119894= (V1198941 V1198942 V




997888

119881

119896+1

119894=

997888

119881

119896

119894+ 1198881lowast 1199031lowast (

997888

119875

119896

119894minus

997888

119883

119896

119894) + 1198882lowast 1199032lowast (

997888

119866

119896

119894minus

997888

119883

119896

119894)

(1a)

997888

119883

119896+1

119894=

997888

119883

119896

119894+

997888

119881

119896+1

119894

(1b)





119881

119896

119894and997888119883

119896


997888





velocity 997888119881119896









Start






Create sparse list











item set

Finish




No

Yes

Yes

Yes

No

No

No

Yes



t2 = t2 + 1

t1 = t1 + 1


Initialize t2 = 0

swarm C


Initialize t1 = 0




















1 2 3 4 5 6 7 Encoding





1

17

50

108

200

50 108 17






50ndash1

108ndash1

1ndash1

17ndash1

200ndash1

108ndash88

17ndash24

50ndash64














50 108 17

50ndash1

108ndash1

1ndash1

17ndash1

200ndash1

108ndash88

17ndash24

50ndash64


108ndash121

50ndash184


50ndash121


End50

108

1

17

200




35

19 1611

5

43

2822

158

8168 73 73

63

0

10

20

30

40

50

60

5 10 20 40 50

Num

ber o

f ass

ocia

tion

rule

s

Support ()








3529

1711

2

4335

2114

5

81 83 81 79

40

0102030405060

30 40 50 60 70Num

ber o

f ass

ocia

tion

rule

s




16

35 3842 4243 43 43 43 43

37 81 88 98 98

0

10

20

30

40

50

60

20 40 60 80 100

Num

ber o

f ass

ocia

tion

rule

s








2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets

10-itemsets



12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets

20-itemsets

100-itemsets




2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets



11-itemsets

12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets














6 Conclusion



42 61 79 97 115

664 664 664 664 664

6 9 12 15 1742

56 70 81 88

0

100

200

300

400

500

600

700

40 60 80 100 120

Tim

e (s)


APPSOApriori






Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Start






Create sparse list











item set

Finish




No

Yes

Yes

Yes

No

No

No

Yes



t2 = t2 + 1

t1 = t1 + 1


Initialize t2 = 0

swarm C


Initialize t1 = 0




















1 2 3 4 5 6 7 Encoding





1

17

50

108

200

50 108 17






50ndash1

108ndash1

1ndash1

17ndash1

200ndash1

108ndash88

17ndash24

50ndash64














50 108 17

50ndash1

108ndash1

1ndash1

17ndash1

200ndash1

108ndash88

17ndash24

50ndash64


108ndash121

50ndash184


50ndash121


End50

108

1

17

200




35

19 1611

5

43

2822

158

8168 73 73

63

0

10

20

30

40

50

60

5 10 20 40 50

Num

ber o

f ass

ocia

tion

rule

s

Support ()








3529

1711

2

4335

2114

5

81 83 81 79

40

0102030405060

30 40 50 60 70Num

ber o

f ass

ocia

tion

rule

s




16

35 3842 4243 43 43 43 43

37 81 88 98 98

0

10

20

30

40

50

60

20 40 60 80 100

Num

ber o

f ass

ocia

tion

rule

s








2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets

10-itemsets



12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets

20-itemsets

100-itemsets




2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets



11-itemsets

12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets














6 Conclusion



42 61 79 97 115

664 664 664 664 664

6 9 12 15 1742

56 70 81 88

0

100

200

300

400

500

600

700

40 60 80 100 120

Tim

e (s)


APPSOApriori






Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra



























1 2 3 4 5 6 7 Encoding





1

17

50

108

200

50 108 17






50ndash1

108ndash1

1ndash1

17ndash1

200ndash1

108ndash88

17ndash24

50ndash64














50 108 17

50ndash1

108ndash1

1ndash1

17ndash1

200ndash1

108ndash88

17ndash24

50ndash64


108ndash121

50ndash184


50ndash121


End50

108

1

17

200




35

19 1611

5

43

2822

158

8168 73 73

63

0

10

20

30

40

50

60

5 10 20 40 50

Num

ber o

f ass

ocia

tion

rule

s

Support ()








3529

1711

2

4335

2114

5

81 83 81 79

40

0102030405060

30 40 50 60 70Num

ber o

f ass

ocia

tion

rule

s




16

35 3842 4243 43 43 43 43

37 81 88 98 98

0

10

20

30

40

50

60

20 40 60 80 100

Num

ber o

f ass

ocia

tion

rule

s








2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets

10-itemsets



12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets

20-itemsets

100-itemsets




2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets



11-itemsets

12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets














6 Conclusion



42 61 79 97 115

664 664 664 664 664

6 9 12 15 1742

56 70 81 88

0

100

200

300

400

500

600

700

40 60 80 100 120

Tim

e (s)


APPSOApriori






Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










50 108 17

50ndash1

108ndash1

1ndash1

17ndash1

200ndash1

108ndash88

17ndash24

50ndash64


108ndash121

50ndash184


50ndash121


End50

108

1

17

200




35

19 1611

5

43

2822

158

8168 73 73

63

0

10

20

30

40

50

60

5 10 20 40 50

Num

ber o

f ass

ocia

tion

rule

s

Support ()








3529

1711

2

4335

2114

5

81 83 81 79

40

0102030405060

30 40 50 60 70Num

ber o

f ass

ocia

tion

rule

s




16

35 3842 4243 43 43 43 43

37 81 88 98 98

0

10

20

30

40

50

60

20 40 60 80 100

Num

ber o

f ass

ocia

tion

rule

s








2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets

10-itemsets



12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets

20-itemsets

100-itemsets




2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets



11-itemsets

12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets














6 Conclusion



42 61 79 97 115

664 664 664 664 664

6 9 12 15 1742

56 70 81 88

0

100

200

300

400

500

600

700

40 60 80 100 120

Tim

e (s)


APPSOApriori






Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets

10-itemsets



12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets

20-itemsets

100-itemsets




2-itemsets

3-itemsets

4-itemsets

5-itemsets

6-itemsets

7-itemsets

8-itemsets

9-itemsets



11-itemsets

12-itemsets

13-itemsets

14-itemsets

15-itemsets

16-itemsets

17-itemsets

18-itemsets














6 Conclusion



42 61 79 97 115

664 664 664 664 664

6 9 12 15 1742

56 70 81 88

0

100

200

300

400

500

600

700

40 60 80 100 120

Tim

e (s)


APPSOApriori






Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










42 61 79 97 115

664 664 664 664 664

6 9 12 15 1742

56 70 81 88

0

100

200

300

400

500

600

700

40 60 80 100 120

Tim

e (s)


APPSOApriori






Acknowledgments


References





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article an algorithm for mining of association...

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