Particle swarm optimization for parameter determination and feature selection of support vector machines

Shih-Wei Lin, Kuo-Ching Ying,

Shih-Chieh Chen, Zne-Jung Lee

Expert Systems with Applications 2008

Introduction

Classification problems have been extensively studied.

Support vector machine (SVM) is a popular pattern classification method with many diverse applications.

Kernel parameter setting in the SVM training procedure, along with the feature selection, significantly influences the classification accuracy.

Introduction

How to choose the optimal input feature subset for SVM?How to set the best kernel parameters?

Hybridizing the particle swarm optimization (PSO) and SVM to improve the classification accuracy with a small and appropriate feature subset.

This makes the optimal separating hyper-plane obtainable in both linear and non-linear classification problems

1.

2.

Support Vector Machine (SVM)

Support vector machine (SVM) is a new technique for data classification were first suggested by Vapnik in 1995.

SVM is using Separating Hyperplane to distinguish the data of two or several different Class that deal with the data mining problem of classification.

Kernel Function

Several kernel functions help the SVM in obtaining the optimal solution. For example: Linear, Polynomial, RBF, Sigmoid

The RBF is generally applied most frequently, because it can classify multi-dimensional data, unlike a linear kernel function.

The RBF has fewer parameters to set than other kernel.

RBF is an effective option for kernel function.

SVM Parameters Setting

Proper parameters setting can improve the classification accuracy of SVM.

The parameters that should be optimized include penalty parameter C and the parameters with different kernel function (gamma of RBF).

Grid Algorithm is an alternative to find the best C and the gamma parameter, however it is time consuming and does not perform well.

Feature Selection

Feature selection is used to identify a powerfully predictive subset of fields within the database and to reduce the number of fields presented to the mining process.

Affects several aspects of pattern classification: 1.The accuracy of classification algorithm learned 2.The time needed for learning a classification function 3.The number of examples needed for learning 4.The cost associated with feature

Feature Selection

Filter Wrapper

FeatureGeneration

LearningAlgorithm

TestingLearning

Algorithm

Good ?

Phase 1

Phase 2

Subset

Classifier Best Subset

TrainingData

TrainingData

TestingData

Accuracy

Yes

No

AccuracyFull Set

Particle swarm optimization

Particle swarm optimization (PSO) (Kennedy & Eberhart,1995) is an emerging population-based meta-heuristic

The new position of a particle is calculated using the following formula:

Particle swarm optimization

rnd( ) is a random function in the range[0, 1] Positive constant c1 and c2 are personal and social learni

ng factors. w is the inertia weight and inertia weight balances the glo

bal exploration and local exploitation. Pi,d denote the best previous position encountered by the i

th particle. Pg,d denotes the global best position thus far. t denotes the iteration counter.

Search concept of PSO.

Grid-Search Algorithm

Particle representation

The flowchart of PSO algorithm.

Fitness = Accuracy

Platform

The platform adopted to develop the

PSO + SVM approach is a PC with the following features:

Intel Pentium IV 3.0 GHz CPU 512 MB RAM Windows XP operating system Visual C++ 6.0 development environment

Dataset

Cross-Validation

To guarantee that the present results are valid and can be generalized for making predictions regarding new data

Using k-fold-cross-validation This study used k = 10, meaning that all of

the data will be divided into ten parts, each of which will take turns at being the testing data set.

PSO-based parameters determinationand feature selection approach for SVM

Comparison between the PSO + SVM, NSVM, SVM, LSVM

Fung & Mangasarian (2003) and Liao et al (2004)

PSO+SVM VS PSO+GA

PSO + SVM approach with and without feature selection and grid search

PSO + SVM approach with and without feature selection

Conclusions

We proposed a PSO-based strategy to select features subset and to set the parameters for SVM classification.

We have conducted two experiments to evaluate the classification accuracy of the proposed PSO-based approach with RBF kernel and the grid search method on 17 real-world datasets from UCI database.

Generally, compared with the grid search approach, the proposed PSO-based approach has good accuracy performance with fewer features.

Future research

Other kernel parameters can also be optimized using the same approach.

Experimental results obtained from UCI datasets, other public datasets and real-world problems can be tested in the future to verify and extend this approach.

Thank YouQ & A