Data classification based on tolerant rough set

reporter: yanan yean

Abstract

• Similarity measure between two data is described by a distance function of all constituent attributes.

• Optimal similarity threshold value –GA• Two-stage classification method

– Lower approximation– Rough membership functions obtained from the

upper approximation

• BPNN,OFUNN,FCM

Outline

• Introduction

• Tolerant rough set

• Determination of similarity thresholds

• Data classification based on the tolerant rough set

• Simulation results and discussion

• conclusion

• Carpenter and Grossberg– Fuzzy adaptive resonance theory (ART)

• Lin and Lee– A general neural-network model for fuzzy logic control and d

ecision systems

• Simpson– A fuzzy min-max classification neural network

• Banzan et al.– Multi-modal logics for automatic feature extraction– Rough-set-based induct reasoning for discovering optimal feature s

et.• Nguyen et al.

– The tolerance relation among the objects for pattern classification.

1.Introduction

2.Tolerant rough set

• Some objects have an indiscernibility relation I from each other with the given attributes.

• A tolerance relation that satisfies only the reflexive and symmetric property.

• A tolerance set

• Define a similarity measure that quantifies the closeness between attribute values of objects.– t(a) is a similarity threshold value

• We can relate the tolerance relation with the similarity measure as

• One of the most important tasks in the data classification using the similarity measure defined above is the optimal determination of the similarity threshold

• Apply the GA to solve this optimization problem

3.Determination of similarity thresholds• 3-1. Chromosome representation

– The Inputs: the information table– The similarity measure– The output: a set of optimal similarity threshold

values– An object is represented by n attributes– The chromosome for the GA consists of n+1

consecutive real numbers of the similarity thresholds

– t(A) : the similarity threshold that defines the tolerance relation when all attributes A are considered together.

3-2. Initial population generation

• The initial gene values in the chromosome are obtained by generating n+1 real-valued random numbers in the interval of [0.5,1.0]

3-3.Fitness function

• If ,then we can say that there is a connection between two objects x and y.

• When two objects are tolerant and contained in the same class, they have good connection.

• Some objects that are tolerant of each other are included in the same class as many as possible.

• A quality of approximation of classification that express the ratio of all classified objects to all objects.

• A set of objects contained in the same class

• The tolerance set of an object x whose all elements in TS(x) is contained in the same class di

• A quality of approximation of classification that express the ratio of all classified objects to all objects.

• ; the size of tolerant sets ;similarity thresholds

• The ratio of good connection– Express a ration of good connections to all possible

connections as

• ;the size of tolerant sets ;the similarity thresholds• The fitness function F in order to balance two coefficients

• The first term makes some tolerant objects to be contained in the same class

• The second term makes the objects in the same class to be tolerant.

3-4. Genetic operations

• Reproduction– First selection method : F – Second selection method: a modified k-tournamen

t method.• F , k chromosomes selected from the upper class of fit

ness values randomly is chosen => reproduction

– Choromosomes : C1.C2 =>Cc+m

• Crossover– (C1,t1(ai),F1) (C2,t2(ai),F2)

– The new chromosome Cc created by the chromosome operation is computed by an average weighted by fitness value as

• Mutation

4.Data classification based on the tolerant rough set

• We define a rough membership function udi (x)– Express the degree of inclusion of the sample x in the decision clas

s di as

• 1st stage: Classification using the lower approximation set– A tolerant set of a test sample x,

• 2nd stage: Classification using the upper approximation set

5.Simulation results and discussion