Soft Computing, Machine Intelligence and Data Mining

Sankar K. PalSankar K. Pal

Machine Intelligence UnitMachine Intelligence Unit

Indian Statistical Institute, CalcuttaIndian Statistical Institute, Calcutta

http://www.isical.ac.in/~sankarhttp://www.isical.ac.in/~sankar

MIU Activities

Pattern Recognition and Image ProcessingPattern Recognition and Image Processing Color Image ProcessingColor Image Processing

Data MiningData Mining Data Condensation, Feature SelectionData Condensation, Feature Selection Support Vector MachineSupport Vector Machine Case GenerationCase Generation

Soft ComputingSoft Computing Fuzzy Logic, Neural Networks, Genetic Algorithms, Rough SetsFuzzy Logic, Neural Networks, Genetic Algorithms, Rough Sets HybridizationHybridization Case Based ReasoningCase Based Reasoning

Fractals/WaveletsFractals/Wavelets Image CompressionImage Compression Digital WatermarkingDigital Watermarking Wavelet + ANNWavelet + ANN

BioinformaticsBioinformatics

(Formed in March 1993)

Externally Funded ProjectsExternally Funded Projects INTELINTEL CSIRCSIR SilicogeneSilicogene

Center for Excellence in Soft Computing ResearchCenter for Excellence in Soft Computing Research Foreign CollaborationsForeign Collaborations

(Japan, France, Poland, Honk Kong, Australia)(Japan, France, Poland, Honk Kong, Australia)

Editorial ActivitiesEditorial Activities Journals, Special IssuesJournals, Special Issues BooksBooks

Achievements/RecognitionsAchievements/Recognitions

Faculty: 10Research Scholar/Associate: 8

Contents

What is Soft Computing ?What is Soft Computing ?

- - Computational Theory of PerceptionComputational Theory of Perception Pattern Recognition and Machine Pattern Recognition and Machine

IntelligenceIntelligence Relevance of Soft Computing ToolsRelevance of Soft Computing Tools Different IntegrationsDifferent Integrations

Emergence of Data MiningEmergence of Data Mining NeedNeed KDD ProcessKDD Process Relevance of Soft Computing ToolsRelevance of Soft Computing Tools Rule Generation/EvaluationRule Generation/Evaluation

• Modular Evolutionary Rough Fuzzy MLP

– Modular Network

– Rough Sets, Granules & Rule Generation

– Variable Mutation Operations

– Knowledge Flow

– Example and Merits

Rough-fuzzy Case GenerationRough-fuzzy Case Generation Granular ComputingGranular Computing Fuzzy GranulationFuzzy Granulation Mapping Dependency Rules to CasesMapping Dependency Rules to Cases Case RetrievalCase Retrieval Examples and MeritsExamples and Merits

ConclusionsConclusions

SOFT COMPUTING (L. A. Zadeh)

Aim :

• To exploit the tolerance for imprecision uncertainty, approximate reasoning and partial truth to achieve tractability, robustness, low solution cost, and close resemblance with human like decision making

• To find an approximate solution to an imprecisely/precisely formulated problem.

Parking a Car

Generally, a car can be parked rather easily because the final position of the car is not specified exactly. It it were specified to within, say, a fraction of a millimeter and a few seconds of arc, it would take hours or days of maneuvering and precise measurements of distance and angular position to solve the problem.

High precision carries a high cost.

The challenge is to exploit the tolerance for The challenge is to exploit the tolerance for imprecision by devising methods of imprecision by devising methods of computation which lead to an acceptable computation which lead to an acceptable solution at low cost. solution at low cost. This, in essence, is the This, in essence, is the guiding principle of soft computing.guiding principle of soft computing.

• Soft Computing is a collection of methodologies (working synergistically, not competitively) which, in one form or another, reflect its guiding principle: Exploit the tolerance for imprecision, uncertainty, approximate reasoning and partial truth to achieve Tractability, Robustness, and close resemblance with human like decision making.

Foundation for the conception and design of high MIQ (Machine IQ) systems.

Provides Provides Flexible Information Processing Flexible Information Processing CapabilityCapability for representation and evaluation of for representation and evaluation of various real life ambiguous and uncertain various real life ambiguous and uncertain situations.situations.

Real World ComputingReal World Computing

•• •• It may be argued that it isIt may be argued that it is soft computing rather soft computing rather than hard computingthan hard computing that should be viewed as that should be viewed as the foundation for Artificial Intelligence.the foundation for Artificial Intelligence.

• At this junction, the principal constituents of soft computing are Fuzzy Logic , Neurocomputing , Genetic Algorithms and Rough Sets .RS

• Within Soft Computing FL, NC, GA, RS are Complementary rather than Competitive

FLNC GA

FL : the algorithms for dealing with imprecision and uncertainty NC : the machinery for learning and curve fitting GA : the algorithms for search and optimization

RSRShandling uncertainty arising fromthe granularity in the domain of discourse

Role of

Referring back to example:“Parking a Car’’

Do we use any measurement and Do we use any measurement and computation while performing the tasks in computation while performing the tasks in Soft Computing?Soft Computing?

We use We use Computational Theory of Computational Theory of Perceptions (CTP)Perceptions (CTP)

Computational Theory of Perceptions (CTP)

ExampleExample: Car parking, driving in city, : Car parking, driving in city, cooking meal, summarizing storycooking meal, summarizing story

Humans have remarkable capability to Humans have remarkable capability to perform a wide variety of physical and perform a wide variety of physical and mental tasks without any measurement mental tasks without any measurement and computationsand computations

AI Magazine, 22(1), 73-84, 2001

Provides capability to compute and reason with perception based information

They use perceptions of time, direction, speed, They use perceptions of time, direction, speed, shape, possibility, likelihood, truth, and other shape, possibility, likelihood, truth, and other attributes of physical and mental objectsattributes of physical and mental objects

Reflecting the finite ability of the sensory Reflecting the finite ability of the sensory organs and (finally the brain) to resolve details, organs and (finally the brain) to resolve details, Perceptions are inherently imprecisePerceptions are inherently imprecise

Perceptions are Perceptions are fuzzy (F) – granularfuzzy (F) – granular

(both fuzzy and granular)(both fuzzy and granular)

Boundaries of perceived classes are unsharpBoundaries of perceived classes are unsharp Values of attributes are granulated.Values of attributes are granulated.

(a clump of indistinguishable points/objects)(a clump of indistinguishable points/objects)

Example:Example:

Granules in age: Granules in age: very young, young, not so old,…very young, young, not so old,…

Granules in direction: Granules in direction: slightly left, sharp right,…slightly left, sharp right,…

MachineMachineIntelligenceIntelligence

Knowledge-basedSystems

Probabilistic reasoning Approximate reasoning Case based reasoning

Fuzzy logic

Rough sets

Pattern recognition and learning

Hybrid Systems

Neuro-fuzzy Genetic neural Fuzzy genetic Fuzzy neuro genetic

Non-linear Dynamics

Chaos theory Rescaled range analysis (wavelet) Fractal analysis

Data Driven Systems

Neural network system Evolutionary computing

Machine Intelligence: A core concept for grouping various advanced technologies with Pattern Recognition and Learning

Relevance of FL, ANN, GAs Individually

to PR Problems is Established

In late eighties scientists thought –

Why NOT Integrations ?

Fuzzy Logic + ANNANN + GAFuzzy Logic + ANN + GAFuzzy Logic + ANN + GA + Rough Set

Neuro-fuzzy hybridization is the most visibleintegration realized so far.

Why Fusion

Fuzzy Set theoretic models try to mimic human reasoningand the capability of handling uncertainty – (SW)

Neural Network models attempt to emulate architectureand information representation scheme of human brain – (HW)

NEURO-FUZZY Computing(for More Intelligent System)

FUZZY SYSTEM

ANN used for learning and Adaptation NFS

ANN

Fuzzy Sets used to Augment its Application domain

FNN

MERITS

GENERICGENERIC

APPLICATION SPECIFICAPPLICATION SPECIFIC

Rough Fuzzy Hybridization: A New Trend in Decision Making,S. K. Pal and A. Skowron (eds), Springer-Verlag, Singapore, 1999

Incorporate Domain Knowledge using Rough SetsIncorporate Domain Knowledge using Rough Sets

IEEE TNN, .9, 1203-1216, 1998

1

2 3

L M H

FjL

FjM

FjH

1

2

3

GA Tuning

Fj

X X | 0 0 0 | X X

0 0 | X X X | 00

Integrating of ANN, FL, Gas and Rough Sets

Before we describe

• Modular Evolutionary Rough-fuzzy MLP

• Rough-fuzzy Case Generation System

We explain Data Mining and the significanceof Pattern Recognition, Image Processing andMachine Intelligence.

Why Data Mining ? Digital revolution has made digitized information Digital revolution has made digitized information

easyeasy to capture and fairly to capture and fairly inexpensiveinexpensive to store. to store. With the development of computer hardware and With the development of computer hardware and

software and the rapid computerization of software and the rapid computerization of business, huge amount of data have been collected business, huge amount of data have been collected and stored in and stored in centralizedcentralized or or distributeddistributed databases. databases.

• Data is heterogeneous (mixture of text, symbolic, numeric, texture, image), huge (both in dimension and size) and scattered.

• The rate at which such data is stored is growing at a phenomenal rate.

As a result, traditional As a result, traditional ad hocad hoc mixtures of mixtures of statistical techniques and data management statistical techniques and data management tools are tools are no longerno longer adequate for analyzing adequate for analyzing this vast collection of data.this vast collection of data.

Pattern RecognitionPattern Recognition and and Machine LearningMachine Learningprinciples applied to a very large (both in size principles applied to a very large (both in size and dimension) heterogeneous database and dimension) heterogeneous database Data MiningData Mining

Data MiningData Mining + + KnowledgeKnowledge Interpretation Interpretation Knowledge DiscoveryKnowledge Discovery

Process of identifying valid, novel, potentiallyProcess of identifying valid, novel, potentiallyuseful, and ultimately understandable patternsuseful, and ultimately understandable patternsin datain data

HugeRawData

•DataCleaning

•DataCondensation

•DimensionalityReduction

•Data Wrapping/ Description

Machine Learning

•Classification•Clustering•RuleGeneration

KnowledgeInterpretation

•KnowledgeExtraction•KnowledgeEvaluation

UsefulKnowledge

Preprocessed

Data

Mathe-maticalModel of

Data(Patterns)

Data Mining (DM)

Knowledge Discovery in Database (KDD)

Pattern Recognition, World Scientific, 2001

Why Growth of Interest ?

Falling costFalling cost of large storage devices and of large storage devices and increasing ease increasing ease

of collecting data over networks.of collecting data over networks.

AvailabilityAvailability of Robust/Efficient machine learning of Robust/Efficient machine learning

algorithms to process data.algorithms to process data.

Falling costFalling cost of computational power of computational power enabling use of enabling use of

computationally intensivecomputationally intensive methods for data analysis. methods for data analysis.

Example : Medical Data

Numeric and textual information may be Numeric and textual information may be interspersedinterspersed

Different symbols can be used with Different symbols can be used with same meaningsame meaning Redundancy Redundancy often existsoften exists Erroneous/misspelledErroneous/misspelled medical terms are common medical terms are common Data is often Data is often sparselysparsely distributed distributed

Robust preprocessingRobust preprocessing system is required to system is required to extract any kind of knowledge from even extract any kind of knowledge from even medium-sized medical data setsmedium-sized medical data sets

The data must not only be cleaned of errors The data must not only be cleaned of errors and redundancy, but and redundancy, but organizedorganized in a fashion in a fashion that makes sense for the problemthat makes sense for the problem

So, We NEEDSo, We NEED

EfficientEfficient RobustRobust FlexibleFlexible

Machine Learning AlgorithmsMachine Learning Algorithms

NEED for NEED for Soft Computing ParadigmSoft Computing Paradigm

Without “Soft Computing” Machine Intelligence Research Remains Incomplete.

Modular Neural Networks

Task: Split a learning task into several subtasks, train a Subnetwork for each subtask, integrate the subnetworks to generate the final solution.

Strategy: ‘Divide and Conquer’

The approach involves

• Effective decomposition of the problems s.t. the Subproblems could be solved with compact networks.

• Effective combination and training of the subnetworks s.t. there is Gain in terms of both total training time, network size and accuracy of solution.

Advantages

• Accelerated training

• The final solution network has more structured components

• Representation of individual clusters (irrespective of size/importance) is better preserved in the final solution network.

• The catastrophic interference problem of neural network learning (in case of overlapped regions) is reduced.

Class 1 Subnetwork Class 2 Subnetwork Class 3 Subnetwork

I

Integrate Subnetwork Modules

3-class problem 3 (2-class problem)

Links to be grown

Links with values preserved

Final Training Phase

Final Network Inter-module

links grown

Modular Rough Fuzzy MLP?

A modular network designed using four different Soft Computing tools.

Basic Network Model: Fuzzy MLP

Rough Set theory is used to generate Crude decision rules Representing each of the classes from the Discernibility Matrix.

(There may be multiple rules for each class multiple subnetworks for each class)

The Knowledge based subnetworks are concatenated to form a population of initial solution networks.

The final solution network is evolved using a GA with variable mutation operator. The bits corresponding to the Intra-module links (already evolved) have low mutation probability, while Inter-module links have high mutation probability.

Rough Sets

. x

UpperApproximation BX

Set X

LowerApproximation BX

[x]B (Granules)

[x]B = set of all points belonging to the same granule as of the point x in feature space B.

[x]B is the set of all points which are indiscernible with point xin terms of feature subset B.

UB

Approximations of the set UX

B-lower: BX = }][:{ XxUx B

B-upper: BX = }][:{ XxUx B

If BX = BX, X is B-exact or B-definable

Otherwise it is Roughly definable

Granules definitelybelonging to X

w.r.t feature subset B

Granules definitelyand possibly belongingto X

Rough SetsRough Sets

UncertaintyHandling

GranularComputing

(Using lower & upper approximations) (Using information granules)

Information compression

Computational gain

Granular Computing: Computation is performed using

information granules and not the data points (objects)

low medium high

low

med

ium

high

F1

F2

Rule 21 MM • Rule provides crude description of the class using granule

Information Granules and Rough Set Theoretic Rules

Rough Set Rule Generation

Decision Table:Object F1 F2 F3 F4 F5 Decision

x1 1 0 1 0 1 Class 1x2 0 0 0 0 1 Class 1x3 1 1 1 1 1 Class 1x4 0 1 0 1 0 Class 2

x5 1 1 1 0 0 Class 2

Discernibility Matrix (c) for Class 1:

},1)},()(:{ pjijxaixaaijc

ObjectsObjects xx11 xx22 xx33

xx11 FF11, F, F33 FF22, F, F44

xx2 2 FF11,F,F22,F,F33,F,F44

xx33

Discernibility function: },,1:)({ kjckjpjkjcjxf k

Discernibility function considering the object x1 belonging to Class 1= Discernibility of x1 w.r.t x2 (and) Discernibility of x1 w.r.t x3

= )42()31( FFFF

Similarly, Discernibility function considering object 43212 FFFFx

Dependency Rules (AND-OR form):

)43()23()41()21( 1 Class FFFFFFFF

43211 Class FFFF

(SN1)

Network Mapping

R1 (Subnet 1) R2 (Subnet 2) R3 (Subnet 3)

Partial Training with Ordinary GA

(SN2) (SN3)

Partially Refined Subnetworks

Rough Set Rules(R1) )()( 21211 HMMLc R3)( (R2) 122122 LLcHMc

Feature Space

Feature Space

F1

F2

F1

F2

C1

C1

(R1)

C2(R2)

C2(R3)

SN1

SN2

SN3

IEEE Trans. Knowledge Data Engg., 15(1), 14-25, 2003

Knowledge Flow in Modular Rough Fuzzy MLP

Concatenation of Subnetworks

Evolution of the Population of Concatenated networks with GA having variable mutation operator

Final Solution Network

Feature Space

C1

C2

F1

F2

high mutation prob.

low mutation prob.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

Train (20%) Test (80%)

MLP

FMLP

MFMLP

RFMLP

MRFMLP

Classification Accuracy

Speech Data: 3 Features, 6 Classes

0

50

100

150

200

250

MLP

FMLP

MFMLP

RFMLP

MRFML

Network Size (No. of Links)

0.00

0.50

1.00

1.50

2.00

2.50

3.00

MLPFMLPMFMLPRFMLPMRFMLP

Training Time (hrs)DEC Alpha Workstation @400MHz

1. MLP 4. Rough Fuzzy MLP2. Fuzzy MLP 5. Modular Rough Fuzzy MLP3. Modular Fuzzy MLP

Network Structure: IEEE Trans. Knowledge Data Engg., 15(1), 14-25, 2003

Structured (# of links few)

Unstructured (# of links more)

Modular Rough Fuzzy MLP

Fuzzy MLP

Histogram of weight values

Connectivity of the network obtained using Modular Rough Fuzzy MLP

Rule Evaluation AccuracyAccuracy FidelityFidelity (Number of times network and rule (Number of times network and rule

base output agree)base output agree) ConfusionConfusion (should be restricted within (should be restricted within

minimum no. of classes)minimum no. of classes)• Coverage (a rule base with smaller

uncovered region i.e., % test set for which no rules are fired, is better)

• Rule base size (smaller the no. of rules, more compact is the rule base)

• Certainty (confidence of rules)

66%

68%

70%

72%

74%

76%

78%

80%

82%

84%

Accuracy User'sAccuracy

Kappa

PROPOSED

Subset

MofN

X2R

C4.5

Comparison of Rules obtained for Speech data

IEEE Trans. Knowledge Data Engg., 15(1), 14-25, 2003

0%

5%

10%

15%

20%

25%

30%

35%

ProposedSubsetMofNX2RC4.5

Uncovered Region (Sample)0

2

4

6

8

10

12

14

16

ProposedSubsetMofNX2RC4.5

Number of Rules

0

0.2

0.4

0.6

0.8

1

1.2

1.4

(sec)

Proposed

Subset

MofN

X2R

C4.5

CPU Time

0

0.5

1

1.5

2

Proposed

Subset

MofN

X2R

C4.5

Confusion

Case Based Reasoning (CBR)

CBR CBR involves involves adaptingadapting old solutions to meet new demands old solutions to meet new demands— usingusing old cases to explain new situations or to old cases to explain new situations or to

justify new solutionsjustify new solutions

— reasoningreasoning from precedents to interpret new from precedents to interpret new situations.situations.

• Cases : some typical situations, already experienced by the system.

conceptualized piece of knowledge representing an experience that teaches a lesson for achieving the goals of the system.

learnslearns and becomes moreand becomes more efficientefficient as a byproduct as a byproduct of its reasoning activity.of its reasoning activity.

• Example : Medical diagnosis and Law interpretation where the knowledge available is incomplete and/or evidence is sparse.

Case SelectionCase Selection Cases belong to the set Cases belong to the set of examples encountered.of examples encountered.

Case GenerationCase Generation Constructed ‘Cases’ Constructed ‘Cases’ need not be any of the examples.need not be any of the examples.

Rough SetsRough Sets

UncertaintyHandling

GranularComputing

(Using lower & upper approximations) (Using information granules)

Granular Computing and Case Generation

Information Granules: A group of similar objects clubbed together by an indiscernibility relation.

Granular Computing: Computation is performed using information granules and not the data points (objects)

– Information compression

– Computational gain

IEEE Trans. Knowledge Data Engg., to appear

Cases – Informative patterns (prototypes) characterizing the problems.

• In rough set theoretic framework:

Cases Information Granules

• In rough-fuzzy framework:

Cases Fuzzy Information Granules

• Cases are cluster granules, not sample points

• Involves only reduced number of relevant features with variable size

•• Less storage requirements •• Fast retrieval

Suitable for mining data with large dimension and size

Characteristics and Merits

How to Achieve?How to Achieve?

Fuzzy sets help in Fuzzy sets help in linguistic representationlinguistic representation of of patterns, providing a patterns, providing a fuzzy granulationfuzzy granulation of the feature of the feature spacespace

Rough sets help in generating Rough sets help in generating dependency rulesdependency rules to to model ‘informative/representative regions’ in the model ‘informative/representative regions’ in the granulated feature space.granulated feature space.

Fuzzy membership functionsFuzzy membership functions corresponding to the corresponding to the ‘representative regions’ are stored as ‘representative regions’ are stored as Cases.Cases.

Fuzzy (F)-Granulation:

1

0.5

Feature j

Mem

bers

hip

valu

e

low medium high

cLcM cH

L M

function

Example IEEE Trans. Knowledge Data Engg., to appear

F2

X X X X X X

X X X

0.9

0.4

0.2

0.1 0.5 0.7 F1

CASE 2

211C HL

212C LH

CASE 1

Parameters of fuzzy linguistic sets low, medium, high4.0,7.0,7.0,5.0,5.0,1.0 :1 Feature HHcMMcLLc

5.0,9.0,7.0,4.0,5.0,2.0 :2 Feature HHcMMcLLc

Dependency Rules and Cases Obtained:

212

211

LHClass

HLClass

Case 1:

Feature No: 1, fuzzset (L): c = 0.1, = 0.5

Feature No: 2, fuzzset (H): c = 0.9, = 0.5

Class=1

Case 2:

Feature No: 1, fuzzset (H): c = 0.7, = 0.4

Feature No: 2, fuzzset (L): c = 0.2, = 0.5

Class=2

Case Retrieval

Similarity Similarity (sim(x,c))(sim(x,c)) between a pattern between a pattern xx and a case and a case cc is defined as: is defined as:

nn: number of features present in case : number of features present in case cc

2

1

))((1

),( xn

cxsim jfuzzset

n

j

: the degree of belongingness of : the degree of belongingness of pattern pattern xx to fuzzy linguistic set to fuzzy linguistic set fuzzsetfuzzset for for feature feature jj..

For classifying an unknown pattern, the For classifying an unknown pattern, the case closest to the pattern in terms of case closest to the pattern in terms of sim(x,c)sim(x,c) is retrieved and its class is assigned is retrieved and its class is assigned to the pattern.to the pattern.

)(xjfuzzset

Evaluation in terms of:

a)a) 1-NN classification accuracy using the 1-NN classification accuracy using the cases. Training set 10% for case cases. Training set 10% for case generation, and Test set 90% generation, and Test set 90%

b)b) Number of cases stored in the case base.Number of cases stored in the case base.

c)c) Average number of features required to Average number of features required to store a case store a case (n(navgavg).).

d) CPU time required for case generation (tgen).

e) Average CPU time required to retrieve a case (tret). (on a Sun UltraSparc @350 MHz Workstation)

Iris Flowers: 4 features, 3 classes, 150 samples

0

0.5

1

1.5

2

2.5

3

3.5

4

avg. feature/case

Rough-fuzzy

IB3

IB4

Random

Number of cases = 3 (for all methods)

80%82%84%86%88%90%92%94%96%98%

100%

Classification Accuracy (1-NN)

Rough-fuzzy

IB3

IB4

Random

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

tgen(sec)

Rough-fuzzy

IB3

IB4

Random

0

0.002

0.004

0.006

0.008

0.01

tret(sec)

Rough-fuzzy

IB3

IB4

Random

Forest Cover Types: 10 features, 7 classes, 5,86,012 samples

0

2

4

6

8

10

avg. feature/case

Rough-fuzzy

IB3

IB4

Random

Number of cases = 545 (for all methods)

0%

10%

20%

30%

40%

50%

60%

70%

Classification Accuracy (1-NN)

Rough-fuzzy

IB3

IB4

Random

0

1000

2000

3000

4000

5000

6000

7000

8000

tgen(sec)

Rough-fuzzy

IB3

IB4

Random

0

10

20

30

40

50

60

tret(sec)

Rough-fuzzy

IB3

IB4

Random

Hand Written Numerals: 649 features, 10 classes, 2000 samples

0

100

200

300

400

500

600

700

avg. feature/case

Rough-fuzzy

IB3

IB4

Random

Number of cases = 50 (for all methods)

0%

10%

20%

30%

40%

50%

60%

70%

80%

Classification Accuracy (1-NN)

Rough-fuzzy

IB3

IB4

Random

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

tgen(sec)

Rough-fuzzy

IB3

IB4

Random

0

100

200

300

400

500

600

tret(sec)

Rough-fuzzy

IB3

IB4

Random

For same number of cases

Accuracy: Proposed method much superior to random selection and IB4, close IB3.

Average Number of Features Stored: Proposed method stores much less than the original data dimension.

Case Generation Time: Proposed method requires much less compared to IB3 and IB4.

Case Retrieval Time: Several orders less for proposed method compared to IB3 and random selection. Also less than IB4.

Conclusions

• Relation between Soft Computing, Machine Intelligence and Pattern Recognition is explained.

• Emergence of Data Mining and Knowledge Discovery from PR point of view is explained.

• Significance of Hybridization in Soft Computing paradigm is illustrated.

• Modular concept enhances performance, accelerates training and makes the network structured with less no. of links.

• Rules generated are superior to other related methods in terms of accuracy, coverage, fidelity, confusion, size and certainty.

• Rough sets used for generating information granules.

• Fuzzy sets provide efficient granulation of feature space (F -granulation).

• Reduced and variable feature subset representation of cases is a unique feature of the scheme.

• Rough-fuzzy case generation method is suitable for CBR systems involving datasets large both in dimension and size.

• Unsupervised case generation, Rough-SOM (Applied intelligence, to appear)

• Application to multi-spectral image segmentation

(IEEE Trans. Geoscience and Remote Sensing, 40(11), 2495-2501, 2002)

• Significance in Computational Theory of Perception (CTP)

Thank You!!