Hidden community mining under the RST/POSL framework

Hong Feng Lai Department of Business Management, National United University

walden.lai@msa.hinet.net

Abstract

The social network analysis (SNA) attempts to find explicit similarities between actors in the network. Traditional clustering methods are based on the attributes between actors in the network that lacks for logic foundation. In this paper we apply rough set theory to SNA. Objects are partitioned into equivalence classes interpreting the hidden community. This paper proposes a framework to find the implicit social network based on RST (rough set theory) and POSL to extract and express the social structure and relationship in diverse databases. The interface of different level is a mapping from a source model to a target model using a set of transformation rules. Finally, the validation is supported by OO jDREW to evaluate the correctness and the adequacy of the model. This paper will apply an example of a virtual team to validate the feasibility of the RST/POSL framework.Keywords: social network analysis, rough set theory, Hidden community mining, implicit social network

1. Introduction As market and customer requirement changes rapidly,

it is important for business to form a dynamic project team catering to market requirements. How to form a project team is still a challenging issue [1-3]. Social network supports some useful cues. A social network is a set of actors that may have relationships with one another [4]. Social network analysis (SNA) is a methodology applied extensively in various fields. The SNA is to explore the social relations among a set of actors in a distinct community. The SNA supports a useful way for quantitative analysis of interaction patterns that disclose the hidden role between the actors. Recently, more and more social network data has been investigated for the purpose of further application such as team formation and community mining [5].

Social network analysis is traditionally based on the explicit relationship. Instead of constructing explicit social relationship, we explore to retrieve those implicit relationships in a member database [6]. While studying complex systems, data collection phase is difficult for

social networks compared to other networks such as the internet [7]. To formulate the internet information of social networks, we have to consider the attributes and the relationships between individuals.

Social networks are likely to change over time. Most of the traditional tools and measures for SNA cannot handle dynamic data. The data collection for SNA is often still created manually unsupported by real time computer systems due to intrinsic complexity. Moreover, the data collected by questionnaire or interviewing for SNA do not reflect the newly updated information. Since the social network is under developing, it is important to collect the real time data for reflecting real situation.

To find an expert within a social network dynamically, in [8] integrating RDF-based FOAF (Friend Of A Friend) project and OO jDREW (java Deductive Reasoning Engine for Web) with RuleML and POSL (Positional-Slotted Language). The scenarios of expert finding and collaboration decision are implemented by POSL that combines Prolog’s positional and POSL’s slotted syntaxes for expressing the knowledge base including facts and rules in the semantic web.

However, how to construct hidden community by rough set theory is rarely emphasized by past studies. The research for offering the deductive rules of forming the community or team in internet is an insufficient research field. In this paper, we propose a development framework based on rough set with POSL to find the implicit social network.

In real social networks, there are various types of relations. Each object’s relation can be taken as a network [9]. An object-oriented and attribute based logic POSL is suitable. Moreover, logical specifications describe system requirements formally. Through formal semantics, it supports deductive capabilities that make specifications executable [10]. Since the social network lacks for logic foundation, in this study we aim at constructing sufficient formality to allow formal analysis and to verify the properties of a social network. To embed deductive capability, we transform the rough set data model into a logical specification language, POSL[11]. How to transform the rough set into formal specifications is investigated in this study. An example of a project team

Symposia and Workshops on Ubiquitous, Autonomic and Trusted Computing

978-0-7695-3737-5/09 $25.00 © 2009 IEEE

DOI 10.1109/UIC-ATC.2009.97

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Symposia and Workshops on Ubiquitous, Autonomic and Trusted Computing

978-0-7695-3737-5/09 $25.00 © 2009 IEEE

DOI 10.1109/UIC-ATC.2009.97

440

Symposia and Workshops on Ubiquitous, Autonomic and Trusted Computing

978-0-7695-3737-5/09 $25.00 © 2009 IEEE

DOI 10.1109/UIC-ATC.2009.97

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formation will be exploited to validate the feasibility of the RST/POSL framework.

2 The RST/POSL framework In this study, we take the implicit social network as

hidden community, and represented by the equivalent class of an indiscernibility relation in rough set theory (RST). The rough set with POSL development framework will be expressed in this section as follows.

2.1. The RST/POSL development framework The RST/POSL framework (in Fig. 1) is to find the

implicit social network based on RST and POSL to extract and express the social structure and relationship in diverse member databases.

Fig. 1. The RST/POSL development framework.

The logic model of this framework is based on RST and POSL. The interface of different level is a mapping from a source model to a target model using a set of transformation rules. Finally, the validation level is supported by OO jDREW to evaluate the correctness and the adequacy of the model.

Through formal semantics of logic, it supports deductive capabilities that make specifications executable [10]. Since the specification of hidden community lacks for logic foundation, in this study we aim at constructing sufficient formality to allow formal analysis and to verify the properties of the implicit social network, through transforming the RST into a logical specification language, POSL.

How to transform the RST into formal specifications is investigated in this study. The deductive RST consists of three components: member object set (a set of object), list operation rules (a set of list operation rules in POSL form), and the deductive rough set theory (a set of rules for determining rough set operation). Since POSL is not set-oriented, the set operations such as set union, intersection, and difference are defined by list structure and its relation.

2.2. The rough set theory

Rough set theory was proposed by Pawlak [12]. The rough set approach is an induction method to explore the relations that exist amongst a set of numeric and non-numeric variables. The rough set theory has been taken as a useful tool for knowledge discovery in databases, which could deal with the classificatory analysis of vague, incomplete, uncertain, or imprecise data. In rough set theory, the objects are described in the form of an information table, whose rows denote distinct objects and whose columns refer to the different attributes. An information table is formally expressed by the 4-tuple S = (U, Q, V, f), where U is a finite set of objects, Q = {qi,q2,... ,qm} is a finite set of attributes, Vq is the domain of the attribute q, V = q Q Vq and f : U * Q V is a total function such that f(x,q) Vq for each q Q, x U,called the information function.

For every subset of attributes A of Q we define an indiscernibility relation on U, denoted Ind(A) and expressed as follows.

Ind(A) = {(x,y) U× U| f(x,a) = f(y,a), a A} (1)

The family of all equivalence classes of the relation Ind(A) will be denoted by U/Ind(A), in short U/A. If (x,y) belongs to an equivalence class Ind(A) we will say that x and y are A-indiscernible. An equivalence class including an element x will be expressed as Ind(A)(x), in short A(x) [12].

The approximation answers the question how to describe a set (concept) in terms of attributes set. In rough set theory a concept is expressed by its lower and upperapproximations based on some indiscernibility relation. For a subset X of U, and subset A of attributes Q, the lower (lower_app) and upper approximation (upper_app) is defined as follows.

lower_app(X,A) = {x U|A(x) X} (2) upper_app(X,A) = {x U| A(x) X } (3)

These two sets lower_app(X,A) and upper_app(X,A) are called the lower and the upper approximation of X, respectively.

The difference between upper_app(X,A) and lower_app(X,A) is called boundary defined as follows,

boundary(X,A)=upper_app(X,A)-lower_app(X,A) (4)

, where “-“ denoting the set difference, which refers to as the A-boundary region of X. If the boundary region of X is the empty set, then the set X will be called exact with respect to A; if boundary(X) , the set X will be referred to as rough in terms of A.

The accuracy of approximation can be characterized numerically by the following coefficient:

accuracy(X,A)=|lower_app(X,A)|/|upper_app(X,A)| (5)

, where |S| denotes the cardinality of a set S.

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3 POSL and transformation rules POSL is a human-readable logic language for

Semantic Web Knowledge that combines Prolog’s positional and POSL’s slotted syntaxes for representing knowledge (facts and rules) in the Semantic Web [11].

3.1 POSL syntax RuleML is an XML based standard for rule

specification and sharing data between smart environments. RuleML is an open standard for which researchers can propose changes and develop tools. One of the reasons for adopting RuleML to explore hidden community is that the standard is expected to be deployed in many smart environments around the world. Hence, this should simplify the integration in the existing smart environments. Additionally, several useful tools are being developed for this standard. For conciseness we use its shorthand counterpart Positional-Slotted Language (POSL) [11] here to express rules; whereas RuleML can be used for communication with other parties. POSL is interchangeable with RuleML through the existing converter that contributes to be user friendly [13].

The POSL has been proposed that merges the concrete syntax, abstract syntax, and unification algorithms of Prolog and F-logic. A term consists of constructor and variable, similar to terms in first-order logic. For instance, f (?X, ?Y, a) is a term, where f is a predicate or object constructor, ‘a’ is a constant, and ?X and ?Y are variables. A ground POSL-term is a term not containing variables (?-variable-free). A term that contains a question mark letter denotes a term that may be non-ground.

A term is defined as one of the following statements, which denote objects or predicates.

(1) A predicate term as p(comma separated list of expressions), where p refers to a predicate name.

(2) A object term is expressed as O[semicolon-separated list of expressions], where O signifies an object constructor, and an expression can be a scalar data expression: Ai ->Ri, where Ai, Ri is an term.

(3). A term with mixed form combines case (1) and (2). The application of POSL can be found in several

studies [8, 11]. OO JDREW is a deductive engine for POSL. In [8] OO JDREWwith is used to extract, restructure and manage the friend of a friend (FOAF), and provide expert recommendation. The deductive engine of OO JDREW is an Object Oriented extension to jDREW. OO jDREW implements deductive engine for RuleML [13]. In this study, we apply POSL to express the classification of diverse member database, and to infer the implicit community.

3.2 RST/POSL transformation rules To extract the implicit social network by rough set and

POSL involves a process of model transformation. Model

transformation is a mapping from a source model to a target model using a set of transformation rules [10]. There is a natural correspondence between the rough set and POSL. The transformation rules from rough set into POSL specifications are listed below.

The following two transformation rules express how to define rough set objects in POSL form. Rule1. Each member can be defined by POSL as follows.

member(object_name->x1; expertise ->system_A_D; department-> IT; publish->paper[Y2006->[pp001,pp002]; Y2007-

>[pp004,pp007]; Y2008->pp011]; execute->project[Y2006->pj015; Y2007->pj020;

Y2008->pj010]; post->thread[Y2006->[thread001, thread003];

Y2007->thread012;Y2008->[thread031,thread0032]];

decision->group_a).

By generalizing the definition of objects, we can extend the analysis for tabulated data to social network data. The following transformation rules express how to transform the rough set theory in POSL form. Rule2. The following rule is to find all of the indiscernibility set of each object. The predicate find_ind is defined by recursive relation: (attribute set, object set, from remaining set, power set of indiscernibility relation).

find_ind(?P_name, ?L, [], []). find_ind(?P_name,[?Xi|?Tx],?From,[?Res|?ResTx]):

- ind_set(?P_name, ?Xi, ?From, ?Res), remainlist(?Res,?Rem,?From),find_ind(?P_name, ?Rem, ?Rem, ?ResTx).

Rule3. The following rule is to find the lower approximation of an object set ?S. The predicate lower_app is defined by recursive relation: (object set, power set of indiscernibility relation, lower approximation set).

lower_app(?S, [], []). lower_app(?S, [?Hres|?Tres], [?Hres | ?Lapp]) :-

object_set(set_name->?S; element->?Oset), contained_in(?Hres,?Oset),lower_app(?S, ?Tres, ?Lapp).

Rule4. The following rule is to find the lower approximation of an object set ?S. The predicate upper_app is defined by recursive relation: (object set, power set of indiscernibility relation, upper approximation set).

upper_app(?S, [], []). upper_app(?S, [?Hres|?Tres], [?Hres | ?Uapp]) :-

object_set(set_name->?S; element->?Oset),

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intersect(?Hres,?Oset),upper_app(?S, ?Tres, ?Uapp).

Rule5. The following rule is to find the boundary region of RST by the difference operation between the upper_app and lower_app set. The predicate remainlist is to find the boundary that is defined by recursive relation: (lower_app, boundary, upper_app).

remainlist([],?L,?L).remainlist ([?H|?T],?L,?L1) :-

deletelist(?H,?L1,?L2), remainlist(?T,?L,?L2).

Rule6. The following rule is to find the accuracy of the rough set. The cardinality of a set is defined as the length of a list.

length([],0:Integer).length([?Head|?Tail],?N) :- length(?Tail,?M),

add(?N, ?M:Integer, 1:Integer). accuracy(?Low,?Up, ?Acc) :- length(?Low,?nL),

length(?Up,?nU),divide(?Acc,?nL:Integer,?nU:Integer).

4 Application of RST/POSL framework 4.1 Introduction to the example

To demonstrate the feasibility of the proposed development framework, in this section we apply RST/POSL to an example for forming a virtual team, which refers to an equivalent class in RST. RST is used to expose the most discriminate attributes required for classification. The searching and partition process will be deduced by POSL.

To find the hidden community, the rough set approach pays attention to the categorical attributes such as member features. The resource data is taken from the member collaboration information and interaction between members on the forum of a practice community that includes the collaboration information for our study, such as the publishing paper, executing project, expertise, and forum posting records.

The example is a practice community’s forum of an auto maintenance incorporated. The main purpose of practice community’s forum is to provide a platform where started threads can be discussed, i.e. to integrate members who think differently about a topic via the internet [14]. A member can search for forums based on keywords which can be the topic of the community. An example of an auto practice community could be a group discussing a specific topic together. In case of mechanical and electrical breakdown, failure or breakage, the experts may post their opinions on the forum from various viewpoints of car body, chassis, engine, internal combustion engine, fuel injection, carburetor, electrical system, headlights, cooling system, fuel and lubrication etc.

The discussing information in practice community’s forum might be suitable for members of different departments such as market, R&D, production, and quality assurance. For example, in the thread of a newest car’s maintenance case, the R&D engineer might be interested in the performance of newest equipment and function; the market salesman might be interested in how to response the customer querying about the newest product; the QC or production engineer might be interested in how the design and manufacturing specification to be realized.

The development processes of RST/POSL are described as follows. In conceptual level, we identify the basic personal data in web list, and collaboration attributes for evaluating the virtual team formation. In logical level, the member database is expressed by information table of RST. Then the information table is transformed into POSL by transformation rules as described in section 3.2. The deductive results will be indicated in next section.

4.2The query of the RST/POSL framework After implementing the deductive system, the logic-

based practice community consists of a set of members, a set of attributes, and some deductive rules about these elements. The overall system of the example in OO JDREW is expressed in Fig. 2.

Fig. 2.The social network result.

Various types of queries can be evaluated and answered by OO JDREW. The query process and results are displayed as follows.

% Answer to query : ind_set(p2, x1, [x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16], ?Ind).

?Ind = .

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% Answer to query the virtual team in Y2006: find_ind(p2, [x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15,x16], [x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,x15, x16], ?Powerset ).

?Powerset =.

% Answer to query the virtual team in Y2008: : find_ind(p8, [x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15,x16], [x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14,x15, x16], ?Powerset ).

?Powerset = [[x1, x3, x5, x11, x13], [x2, x4, x6, x9, x14], [x7, x8, x10, x12], [x15, x16]] . The above two queries indicate that the virtual team

evolves dynamically as time elapses, i.e. the virtual team in Y2008 differing from the virtual team in Y2006.

% Answer to query: report(p2,s2,?Ind_class,?Low, ?Up, ?Boun,?Acc).

?Ind_class=.

?Low= [x2, x4, x10, x12, x14]. ?Up=[x2, x4, x10, x12, x14, x5, x6, x9, x11, x13, x15] ?Boun=[x5, x6, x9, x11, x13, x15]. ?Acc=0.45454545454545453 : Real

The logic-based RST can provide more information, e.g. finding the RuleML form (as indicated in Fig. 3) which is portable for heterogeneous platforms.

Fig. 3. Converter between RuleML and POSL.

5 Related works To express and investigate the implicit social network,

three types of approaches have been proposed: heuristic-based, probability-based and logic-based approaches. The heuristic-based approaches apply a set of heuristics to extract the implicit social network. The probability-based approaches include Bayes rule and regression approach.

The logic-based using logic for inferring the implicit social network includes: first order logic and description logic.

The heuristic-based approaches could not find the complete solution, whereas provide feasible answers. In [15, 16] they exploit web pages to create the referral chain, , an interactive tool on the web that helps people find short referral chains and explore the social networks in which they participate. The referral Web system extracts hidden relationships between people through co-authorship. In [17] they apply three techniques namely web mining, tagging behavior analysis and social network analysis to construct implicit social network and recommended experts.

The probability-based approaches are based on the possibility of events occurring. In [18], to find the implicit social network and to locate potential insiders, their algorithm using an extended version of Probabilistic Latent Semantic Indexing PLSI is based on Bayes Rule. The conditional probability is determined firstly. Then, a small manageable number of individuals are generated. In [9] they apply regression method to find the hidden community from multi-relational networks. The labeled values between multi-objects are expressed by the possibility that denotes two objects in the same community.

The logic-based approaches using rules and declarations define the interaction and relationship between objects. From object-oriented viewpoint, the social network systems could be taken as a set of interacting objects. To verify the definability of objects’ roles, in [19] using first order logic to express the social position. To protect personal privacy in tabulated data under the disclosure of social network data, in [5] adopts description logic (DL) to represent formalism and the metrics of anonymity. To model the rules in business collaboration, In [20] they introduce the Business Collaboration Development Framework (BCDF), which provides business with the rule-based framework to express their business activity and collaboration agreements.

The above related work illustrates the various types of approaches for presenting implicit social network. In our approach, RST/POSL can be taken as a schema transformation.

6 Conclusions The method of inputting the data for social network

analysis is often still performed manually because of intrinsic complexity. In this paper, we propose a deductive template based on rough set with POSL to support the virtual team formation based on implicit social relation.

We apply a practice community example to validate the RST/POSL methodology. With the help of OO

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JDREW, the complexity of social network analysis is reduced. With temporal attribute the RST/POSL could interpret dynamical evolvement of virtual team formation.Moreover, the extracting process and result can be investigated and validated by top-down and bottom-up simulation.

The future work will include rule extraction from information tables by POSL. Moreover, how to implement the extension of rough set substituting the indiscernibility relation by a dominance relation in OO JDREW deserves further exploration [21].

Acknowledgment. Financial support for this work was provided by the National Science Council Taiwan, under the contract NSC 95-2815-C-239 -013 -H.

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