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

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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

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主要内容

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PSO

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FS

1. filter
2. wrapper

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多目标

1. the number of features
2. the classification performance

support vector machine classifier

chaotic mappings：

• logistic
• tent

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算法

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A 编码粒子

解码：

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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

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C 外部存档更新

the crowding distance

the Pareto dominated comparison

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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

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E 混合变异

trapped in local optima

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

the two operators does not add much computational burden

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F 算法框架

acceleration coefficients 加速度系数：

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G 收敛性分析

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H 复杂度分析

Space Complexity
the archive memorizer — $O(Na \times D)$
memorizer for the particles — $O(Ns \times D)$
total — $O(\max(Na, Ns) \times D)$

Computational Complexity — main time complexity
the Pareto comparison — $O(M \times Ns \times Na)$ basic operation
the crowding distance metric — $O(M \times Na \times \log{Na})$
the Pbest update — $O(M \times Ns)$
the Gbest update — $O(Ns)$
the worst case time complexity — $O(M \times Ns \times Na)$

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试验

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A 数据集

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B 比较的算法及参数

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

All the algorithms are wrapper approaches

K-nearest neighbor (KNN)

the jumping probability is set to 0.01

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C 性能度量

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

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D 混合变异分析

1. HMPSOFS/J — HMPSOFS without the jumping mutation
2. HMPSOFS/JR — HMPSOFS without the two operators

the re-initialization proportion

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E