分类中基于代价的特征选择的多目标粒子群优化方法

#引用

##Latex

@ARTICLE{7243331,
author={Y. Zhang and D. w. Gong and J. Cheng},
journal={IEEE/ACM Transactions on Computational Biology and Bioinformatics},
title={Multi-Objective Particle Swarm Optimization Approach for Cost-Based Feature Selection in Classification},
year={2017},
volume={14},
number={1},
pages={64-75},
keywords={bioinformatics;decision making;encoding;feature selection;particle swarm optimisation;probability;signal processing;PSO-based multiobjective feature selection algorithm;Pareto domination relationship;Pareto front;bioinformatics;classification performance;classification problems;cost-based feature selection problems;crowding distance;data-preprocessing technique;decision-makers;effective hybrid operator;external archive;feature subsets;multiobjective feature selection algorithms;multiobjective particle swarm optimization;nondominated solutions;probability-based encoding technology;signal processing;single-objective optimization problem;Bioinformatics;Classification algorithms;Genetic algorithms;IEEE transactions;Optimization;Particle swarm optimization;Search problems;Feature selection;cost;multi-objective;particle swarm optimization},
doi={10.1109/TCBB.2015.2476796},
ISSN={1545-5963},
month={Jan},}

##Normal

Y. Zhang, D. w. Gong and J. Cheng, “Multi-Objective Particle Swarm Optimization Approach for Cost-Based Feature Selection in Classification,” in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 14, no. 1, pp. 64-75, Jan.-Feb. 1 2017.
doi: 10.1109/TCBB.2015.2476796
keywords: {bioinformatics;decision making;encoding;feature selection;particle swarm optimisation;probability;signal processing;PSO-based multiobjective feature selection algorithm;Pareto domination relationship;Pareto front;bioinformatics;classification performance;classification problems;cost-based feature selection problems;crowding distance;data-preprocessing technique;decision-makers;effective hybrid operator;external archive;feature subsets;multiobjective feature selection algorithms;multiobjective particle swarm optimization;nondominated solutions;probability-based encoding technology;signal processing;single-objective optimization problem;Bioinformatics;Classification algorithms;Genetic algorithms;IEEE transactions;Optimization;Particle swarm optimization;Search problems;Feature selection;cost;multi-objective;particle swarm optimization},
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7243331&isnumber=7842713

#摘要

Feature selection is an important data-preprocessing technique in classification problems — bioinformatics and signal processing

maximizing the classification performance
minimizing the cost that may be associated with features

cost-based feature selection

multi-objective particle swarm optimization (PSO)

a probability-based encoding technology
an effective hybrid operator
the ideas of the crowding distance, the external archive, and the Pareto domination relationship

compared with：several multi-objective feature selection algorithms

5 benchmark datasets

#主要内容

##PSO

##FS

filter
wrapper

###多目标

the number of features
the classification performance

support vector machine classifier

chaotic mappings：

logistic
tent

##算法

###A 编码粒子

解码：

###B 适应度评估

成本：

总成本：

the classification error rate：
the leave-oneout cross-validation (LOOCV) of k-NN

the one nearest neighbor (1-NN) method：
In this method, a datum from the original dataset is selected as a testing sample, and the rest constitute the training samples. Then the 1-NN classifier predicts the class of the testing sample by calculating and sorting the distances between the testing sample and the training ones.
— repeated for each datum

###C 外部存档更新

the crowding distance

the Pareto dominated comparison

###D 更新Gbest and Pbest

a domination-based strategy — Pbest

archive — Gbest ：
the diversity of non-dominated solutions — the crowding distance
the binary tournament — crowding distances

###E 混合变异

trapped in local optima

the re-initialization operator — reinitialize the fly velocities in each generation （10%）
the jumping mutation — uniformly jump in any dimensional space with the probability of pmp_mpm（a partial re-initialization）

the two operators does not add much computational burden

###F 算法框架

acceleration coefficients 加速度系数：

###G 收敛性分析

###H 复杂度分析

Space Complexity
the archive memorizer — KaTeX parse error: Unexpected character: '' at position 6: O(Na ̲\times D)
memorizer for the particles — KaTeX parse error: Unexpected character: '' at position 12: O(Ns \times̲ D)
total — KaTeX parse error: Unexpected character: '' at position 22: …(Na, Ns) \times̲ D)

Computational Complexity — main time complexity
the Pareto comparison — KaTeX parse error: Unexpected character: '' at position 11: O(M \times̲ Ns \times Na) basic operation
the crowding distance metric — KaTeX parse error: Unexpected character: '' at position 11: O(M \times̲ Na \times \…
the Pbest update — KaTeX parse error: Unexpected character: '' at position 11: O(M \times̲ Ns)
the Gbest update — O(Ns)O(Ns)O(Ns)
the worst case time complexity — KaTeX parse error: Unexpected character: '' at position 11: O(M \times̲ Ns \times Na)

##试验

###A 数据集

###B 比较的算法及参数

DE-based multi-objective feature selection algorithm (DEMOFS)
the NSGA-based feature selection algorithm (NSGAFS)
the SPEA2-based feature selection algorithm (SPEAFS)
NSGAFS — based on the idea of NSGA-II
本文的HMPSOFS

All the algorithms are wrapper approaches

K-nearest neighbor (KNN)

the jumping probability is set to 0.01

###C 性能度量

the hyper-volume (HV) metric
the two-set coverage (SC) — the degree of convergence of two Pareto optimal sets
the SP metric — To estimate the distribution of solutions throughout the Pareto optimal set

###D 混合变异分析

HMPSOFS/J — HMPSOFS without the jumping mutation
HMPSOFS/JR — HMPSOFS without the two operators

the re-initialization proportion

###E

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