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### 基于混沌粒子群优化与最小二乘支持向量机的新数据分类方法 #### 摘要本文提出了一种新的数据分类方法——基于混沌粒子群优化（Chaotic Particle Swarm Optimization, CPSO）与最小二乘支持向量机（Least Square-Support Vector Machine, LS-SVM）的数据分类方法（CPL-SVM）。该方法旨在提高化学位计数据的分类准确性。通过将混沌优化算法（COA）和粒子群优化算法（PSO）引入到LS-SVM模型中，可以构建出一个经过优化的LS-SVM模型及一种新颖的数据分类方法。 #### 引言在机器学习领域，支持向量机因其强大的泛化能力而在数据分类问题中得到了广泛应用。然而，在实际应用中，如何选择合适的参数是支持向量机面临的一个重要挑战。传统的交叉验证方法虽然可以用于参数选择，但耗时且容易陷入盲目性。因此，本文结合混沌优化算法和粒子群优化算法的优势，提出了一种能够有效解决上述问题的方法。 #### 方法介绍 1. **混沌优化算法（COA）**：混沌优化算法是一种基于混沌理论的全局优化算法。它利用混沌运动的随机性和遍历性来搜索最优解，具有较好的全局搜索能力。 2. **粒子群优化算法（PSO）**：粒子群优化算法是一种启发式优化方法，模拟了鸟群觅食的行为。每个粒子代表解空间中的一个潜在解决方案，通过粒子之间的协作和信息共享来寻找全局最优解。 3. **最小二乘支持向量机（LS-SVM）**：LS-SVM是一种基于支持向量机原理的分类器，通过引入等式约束代替不等式约束，简化了计算过程，提高了求解效率。 #### CPL-SVM方法流程 - **混沌粒子群优化算法（CPSO）**：利用混沌优化算法处理粒子群优化算法中的初始位置和局部最优位置，以增强搜索能力并避免局部最优陷阱。 - **参数优化**：利用CPSO算法对LS-SVM的关键参数进行优化，包括惩罚因子和核函数参数等，从而获得更优的分类模型。 - **分类模型构建**：使用优化后的参数训练LS-SVM模型，并应用于新数据集的分类任务。 #### 实验验证为了验证CPL-SVM方法的有效性，作者选择了二元分类数据、鸢尾花数据以及与药物药效学特性相关的三个数据集进行了实验。实验结果表明，CPL-SVM方法不仅具有良好的学习性能和较强的泛化能力，而且在处理小样本数据方面也表现出了优势。 #### 结论本文提出了一种结合混沌优化算法和粒子群优化算法的最小二乘支持向量机分类方法。该方法不仅克服了传统交叉验证方法耗时和盲目性的缺点，还有效提高了分类准确率和模型的泛化能力。通过对不同数据集的实验分析，验证了所提出方法的有效性和优越性。未来的研究方向可以考虑进一步探索混沌优化算法和粒子群优化算法的组合方式，以期得到更高效的优化策略和更好的分类效果。

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A new data classiﬁcation method based on chaotic particle swarm

optimization and least square-support vector machine

Fang Liu

a,b,c,d,

⁎

, Zhiguang Zhou

Institute of information, Zhejiang University of Finance & Economics, Hangzhou 310018, China

The State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China

Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning 530006, China

The Provincial Key Laboratory for Computer Information Processing Technology, Soochow University, Suzhou 215006, China

abstractarticle info

Article history:

Received 3 June 2015

Received in revised form 28 July 2015

Accepted 17 August 2015

Available online 23 August 2015

Keywords:

Chaotic optimization algorithm

Particle swarm optimization algorithm

Least square-support vector machine (LS-SVM)

Data classiﬁcation

Generalization ability

Classiﬁcation accuracy

In order to improve the classiﬁcation accuracy in chemometrics data, chaotic optimization algorithm (COA) and

particle swarm optimization (PSO) algorithm are introduced into least square-support vector machine (LS-SVM)

model in order to propose an optimized LS-SVM model and a novel data classiﬁcation (CPL-SVM) method in this

paper. In the proposed CPL-SVM method, the COA with the randomness and ergodicity is used to chaotically

process the initial position and local extreme position of particle in the PSO algorithm in order to obtain a chaotic

particle swarm optimization (CPSO) algorithm, and the CPSO is used to select and optimize the important param-

eters of LS-SVM, then the optimized parameters are used to obtain a better CPL-SVM classiﬁcation method. The

choice randomness of parameters is avoided and the selection workload of parameters is reduced. And this meth-

od can not only overcome the time-consuming and blindness of cross validation method, but also reﬂect small

sample learning ability. In order to verify the effectiveness of CPL-SVM method, binary classiﬁcation data, IRIS

ﬂower data and three relevant data sets with pharmacodynamic properties of drug are selected in this paper.

The experiment results show that the proposed CPL-SVM method takes on the better learning performance,

strong generalization ability, best sensitivity, Matthews correlation coefﬁcient and classiﬁcation accuracy. And

it can effectively avoid the isolated effects of sample in the learning process.

1. Introduction

Chemometrics has been deﬁned as the chemical discipline that uses

mathematic al and statistical methods to design and select optimal

procedures and experiments, and provide the maximum chemical in-

formation based on analyzing chemical data. The most prominent part

of chemometrics is data classiﬁcation by using some intelligent methods

for all obtained data. The chemometrics has mainly involved the infor-

mation extraction from these obtained data. The available data and

desired information often exist the hidden relationship, the analysi s

goal of chemometrics is to ﬁnd out some relationship s and classify

these data by using new intelligent methods. These intelligent methods

include neural networks (NN), genetic algorithm (GA), simulated an-

nealing (SA), particle swarm optimization (PSO) algorithm, statistical

analysis, support vector machine (SVM) and so on. However, the data

of chemometrics have mostly multi-factors, high noise, nonlinear and

irregular, so these complex data are classiﬁed in order to discovery the

interdependent relationships and extract data model among these

features. The SVM model [1] is a machine learning method based on

the minimum structural risk principle for data classiﬁcation by Vapnik.

This model is a convex optimization problem to ﬁnd out the global op-

timiz ation s olution. It can effectively solve these complex problems

with the small sample, nonlinear, local minimum, avoid the slow

convergence speed, and easily fall into the local minimum value. On

the basis of SVM model, Suykens et al. [2,3] proposed a least square-

support vector mac hine (LS-SVM) method. The LS-SVM model is to

transform the SVM from the quadratic programming problem into the

linear equations in order to reduce the computational complexity and

improve the calculation speed in processing large sample. The LS-SVM

has been widely applied in the pattern recognition, data mi ning,

image analysis, network security and so on. However, the optimization

parameters of LS-SVM model have an important inﬂuence on its optimi-

zation performance and learning precision. So how to optimize param-

eters of LS-SVM model is an important research problem in machine

learning.

Chaotic optimization algorithm (COA) with the randomness and er-

godicity is introduced into the PSO algorithm in order to make up for the

low convergence speed, the late time oscillation and easy falling local

minimum value in this paper. And a chaotic particle swarm optimiza-

tion (CPSO) algorithm based on combining the COA and PSO is pro-

posed. In LS-SVM model, the regularization par ameter γ and radial

basis kernel width parameter σ are very important for the optimization

performance. It is an open problem in the ﬁeld of LS-SVM how to ﬁnd

Chemometrics and Intelligent Laboratory Systems 147 (2015) 147–156

⁎ Corresponding author. Tel.:+86 571 8755 7136.

E-mail address: puigpuig2010@gmail.com (F. Liu).

http://dx.doi.org/10.1016/j.chemolab.2015.08.015

Contents lists available at ScienceDirect

Chemometrics and Intelligent Laboratory Systems

journal homepage: www.elsevier.com/locate/chemolab

the optimal values of regularization parameter γ and radial basis kernel

width parameter σ. The common selection method is the cross valida-

tion method, but this method will not only consume a lot of computing

time, but also take on certain blindness. So the proposed CPSO algorithm

with global optimization ability is used to optimize the parameters of

LS-SVM model. This can not only overcome the time-consuming and

blindness of the cross validation method, but also reﬂect small sample

learning ability, so as to improve the learning performance, generaliza-

tion ability and robustness. Finally, a new data classiﬁcat ion method

based on the CPSO algorithm and LS-SVM model (CPL-SVM) is proposed

in this paper. The binary classiﬁcation data, IRIS ﬂower data and three

relevant data sets with pharmacodynamic properties of drug are select-

ed to verify the effectiveness of the proposed CPL-SVM method.

The rest of this paper is organized as follows. Section 2 brieﬂy intro-

duces the related works about SVM, LS-SVM and their improve d

methods in the classiﬁcation. Section 3 brieﬂy introduces the related

basic methods, including the COA, PSO algorithm, LS-SVM model and

diversity-guided mutation strategy. Section 4 presents a chaotic particle

swarm optimization algorithm, named the CPSO algorithm. Section 5

presents a novel data classiﬁcation (CPL-SVM) method. In this section,

the thoughts, model and the steps of the CPL-SVM method are intro-

duced in detail. Section 6 applies and analyzes the CPL-SVM method

in solving data classiﬁ cation problem. Finally, the conclusions are

discussed in Section 7.

2. Related works

In recent years, in allusion to the optimization parameters of the

SVM model or LS-SVM model, many researchers have deeply studied

and explored from the different views in optimizing these parameters.

They have proposed some optimization methods of parameters of the

SVM model or LS-SVM model, such as empirical selection method, gra-

dient descent method, cross validation method, GA, PSO algorithm and

so on [4–8].Temkoaetal.[9] proposed a fuzzy integral based combining

different information sources to classify a small set of highly confusable

human non-speech sounds. Devos et al. [10] proposed a methodological

approach to guide the optimization parameters of SVM based on a grid

search f or minimizing the classiﬁcation error rate . Tao et al. [11]

proposed a new fast pruning algorithm for chemical pattern classiﬁca-

tion. Ghorbanzad'e and Fatemi [12] proposed a classiﬁcation method

of central nervous syste m agents by using LS-SVM based on their

structural descriptors. Li et al. [13] proposed a novel automatic speaker

age and gender identiﬁcation approach based on combin ing seven

different m ethods in order to improve the baseline performance.

Huang et al. [14] proposed an informative novel tree kernel SVM classi-

ﬁer to model the relationship between bioacti vity and molecular

descriptors. Dong and Luo

[15] p

roposed a new method to achieve bear-

ing

degradation classi ﬁcation based on principal component analysis

(PCA) and optimized LS-SVM method. Lou'i et al. [16] proposed two

new multisensor data fusion algorithms to reduce the rate of false

detection and obtain reliable decisions on the presence of target objects.

Zhang [17] proposed an improved data classiﬁcation method based on

SVM applying rational sample data selection and GA-controlled training

parameters optimization. Yao and Yi [18] proposed a new License Plate

(LP) detection technique based on multistage information fusion. Sung

and Chung [19] proposed a distributed energy monitoring network

system based on da ta fusion via improved PSO algorithm. He et al.

[20] proposed a new method for classifying electronic nose data in

rats wound infection detection based on SVM an d wavelet analysis.

Subha jit et al. [21] proposed a PSO method al ong with adaptive K-

nearest neighborhood based gene selection technique to distinguish a

small subset of useful genes.

For the optimization parameters of SVM model and LS-SVM model,

although these scholars have done the in-depth study and discussion

by using the various optimization methods from the different angle

degree in order to obtain some good results, each proposed method

has its own defect in optimizing parameters of SVM model and LS-

SVM model, such as the low classiﬁcation accuracy, weak generalization

ability, slow convergence speed, and so on. So the CPSO algorithm based

on COA and PSO is proposed to select and optimize the parameters of

LS-SVM model in order to improve the classiﬁcation accuracy, learning

performance and generalization ability.

3. Basic methods

3.1. Chaotic optimization algorithm (COA)

Chaos often exists in the nonlinear system. It is a kind of characteris-

tic that has a bounded unstable dynamic behavior and exhibits sensitive

dependence on the initial conditions. Chaotic optimization algorithm

(COA) [22] is a population-based stochastic optimization algorithm by

using the chaotic mapping. The basic procedure of the COA is divided

into two steps. First, the COA searches all the points in turn within the

changing range of variables, and selects the better point as the current

optimum point by using chaotic ergodicity, regularity, initial sensitivity

and topological transitivity. Then the current optimum point is regarded

as the center, a tiny chaotic disturbance is imposed and a careful search

is performed in order to ﬁnd out the global optimum point with the

higher probability. Due to the chaotic non-repetition, the COA can

carry out the overall search with the higher speed. So the COA takes

on the characteristics of the easy implementation, short execution

time and robust mechanism.

Currently, there have been several kinds of the COA based on chaotic

characteristics, such as adaptive mutative scale COA [23], a mutative

scale COA [24], chaotic harmony search algorithm [25], multi-objective

chaotic ant swarm optimization [26] and so on. Because the adaptive

mutative scale COA has the reﬁned search space, better search speed

and higher search accuracy [23], it is used to optimize the particle

swarm optimization (PSO) algorithm in this paper. Generally, the main

problem of the COA is to obtain chaotic variables. So the Logistic chaotic

model is used to generate the chaotic variable. The mapping equation of

the Logistic model is described:

nþ1

¼ L μ; X

ðÞ

¼ μZ

1−X

ðÞ

μ ∈ 0 ; 4

½

; n ¼ 0 ; 1; 2; 3; ⋯ ð1Þ

where control variable (μ ∈ [0, 4]) is the parameter of the Logistic. It has

shown, when Z

∈ [0, 1], the Logistic mapping is in the chaotic state. That

is, the generated sequences under Logistic mapping function (the initial

condition Z

) are not periodic and conve rge. But the generated

sequences must converge to one speciﬁc value outside the given range.

3.2. Particle swarm optimization (PSO)

The PSO algorithm [27] is a search algorithm based on simulating the

social behavior of birds within a ﬂock. In the PSO algorithm, individuals,

referred to as particles, are “ﬂown” through hyper dimensional search

space. The positions of particles within the search space are changed

based on the social-psychological tendency of individuals in order to

delete the success of other individuals. The changing of particle within

the population is inﬂuenced by the expe rience, or knowledge. The

consequenc e of modeling for the social behavior is that the search is

processed in order to return toward previously successful regions in

the search space. Namely, the velocity (v) and position (x) of each

particle will be changed according to the following expressions:

t þ 1ðÞ¼wv

tðÞþc

tðÞ−x

tðÞ



þ c

tðÞ−x

tðÞ



ð2Þ

t þ 1ðÞ¼x

tðÞþv

t þ 1ðÞ ð3Þ

where v

(t + 1) is the velocity of particle i

at iteration j

(t + 1) is

the position of particle i

at iteration j

. w is inertia weight to be

employed to control the impact of the velocity of previous histo ry.

148 F. Liu, Z. Zhou / Chemometrics and Intelligent Laboratory Systems 147 (2015) 147–156

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