支持向量机matlab实例及理论.docx

支持向量机 matlab 分类实例及理论

线性支持向量机可对线性可分的样本群进行分类，此时不需要借助于核函数就可较为理想地解

决问题。非线性支持向量机将低维的非线性分类问题转化为高维的线性分类问题，然后采用线性支

持向量机的求解方法求解。此时需要借助于核函数，避免线性分类问题转化为非线性分类问题时出

现的维数爆炸难题，从而避免由于维数太多而无法进行求解。

第 O 层：Matlab 的 SVM 函数求解分类问题实例

0.1 Linear classification

%Two Dimension Linear-SVM Problem, Two Class and Separable Situation

clear all;

close all

clc;

sp=[3,7; 6,6; 4,6;5,6.5] % positive sample points

nsp=size(sp);

sn=[1,2; 3,5;7,3;3,4;6,2.7] % negative sample points

nsn=size(sn)

sd=[sp;sn]

lsd=[true true true true false false false false false]

plot(sn(1:nsn,1),sn(1:nsn,2),'c*');

subplot(1,2,2)

svmStruct = svmtrain(sd,Y,'showplot',true);

0.2 NonLinear classification

clear all;

close all

clc;

sp=[3,7; 6,6; 4,6; 5,6.5] % positive sample points

nsp=size(sp);

figure(1);

subplot(1,2,1)

plot(sp(1:nsp,1),sp(1:nsp,2),'m+');

hold on

plot(sn(1:nsn,1),sn(1:nsn,2),'c*');

subplot(1,2,2)

% svmStruct = svmtrain(sd,Y,'Kernel_Function','linear',

'showplot',true);

svmStruct = svmtrain(sd,Y,'Kernel_Function','quadratic',

'showplot',true);

clear all;

close all

sp=[5,4.5;3,7; 6,6; 4,6; 5,6.5] % positive sample points

false]

Y = nominal(lsd)

figure(1);

subplot(1,2,1)

plot(sp(1:nsp,1),sp(1:nsp,2),'m+');

hold on

plot(sn(1:nsn,1),sn(1:nsn,2),'c*');

subplot(1,2,2)

svmStruct =

svmtrain(sd,Y,'Kernel_Function','rbf','rbf_sigma',0.6,'method','SMO',

'showplot',true);

% svmStruct = svmtrain(sd,Y,'Kernel_Function','quadratic',

'showplot',true);

svmtrain(sd,Y,'Kernel_Function','rbf','rbf_sigma',0.2,'method','SM

O','showplot',true);

0.4 Svmtrain Function

svmtrain Train a support vector machine classifier

SVMSTRUCT = svmtrain(TRAINING, Y) trains a support vector machine

(SVM)

classifier on data taken from two groups. TRAINING is a numeric

matrix

of predictor data. Rows of TRAINING correspond to observations;

columns

correspond to features. Y is a column vector that contains the

categorical, numeric, or logical vector; a cell vector of

strings; or a character matrix with each row representing a class

label (see help for

groupingvariable). Each element of Y specifies the group the

for classification. svmtrain treats NaNs, empty strings or

'undefined'

values as missing values and ignores the corresponding rows in

TRAINING and Y.

SVMSTRUCT = svmtrain(TRAINING, Y, 'PARAM1',val1,

'PARAM2',val2, ...)

specifies one or more of the following name/value pairs:

'kernel_function' A string or a function handle specifying

the

(default). In this case,

svmtrain

finds the optimal separating

plane

in the original space.

'quadratic' - Quadratic kernel

'polynomial' - Polynomial kernel with

default

order 3. To specify another

order,

use the 'polyorder'

argument.

'rbf' - Gaussian Radial Basis

Function

factor,