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【数据分析】基于MATLAB实现SVDD决策边界可视化

2022-08-03 02:08:00 【matlab_dingdang】

1 内容介绍

在现实世界中，万事万物都有着其特征，这样的特征或多或少、或重要或不重要。人们通过事物的特征可以确定其所属分类，但是当事物的特征都很多时，如果人们依靠传统的方法对事物进行分类就显得耗时耗力，并且分类的精确性不高。而分类作为一种预测模型，如果分类的精确性低或用时长，则这种预测将变得毫无价值。因此人们提出了各种分类模型来对事物进行预测，其中支持向量机和支持向量描述数据在对高维数据进行预测时有着一定的优势，并且根据不同的要求，对这两种算法的改进应用到了现实生活中的许多领域。首先，本文研究了数据挖掘分类算法中的支持向量机的背景和理论，分析并总结了SVM各种改进方法的研究现状。

2 仿真代码

function x_range = grid_range(x, varargin) %{ % DESCRIPTION Compute the range of grid

x_range = grid_range(x) x_range = grid_range(x, 'r', 0.5) x_range = grid_range(x, 'n', 200) x_range = grid_range(x, 'r', 0.5, 'n', 200)

INPUT x Training inputs (N*1) N: number of samples r Radio of expansion (0<r<1) n Number of grids

OUTPUT x_range range of grid

Created on 18th October 2019, by Kepeng Qiu. -------------------------------------------------------------% %}

% Default Parameters setting r = 0.5; % radio of expansion (0<r<1) n = 2*size(x, 1); % number of grids

% Parameters setting if ~rem(nargin, 2) error('Parameters to rvm_train should be pairs') end numParameters = (nargin-1)/2; if numParameters ~= 0 for i =1:numParameters Parameters = varargin{(i-1)*2+1}; value = varargin{(i-1)*2+2}; switch Parameters % case 'r' r = value; % case 'n' n = value; end end end

% xlim_1 = min(x); xlim_2 = max(x);

% min if xlim_1<0 xlim_1 = xlim_1*(1+r); else xlim_1 = xlim_1*(1-r); end

% max if xlim_2<0 xlim_2 = xlim_2*(1-r); else xlim_2 = xlim_2*(1+r); end

% range of grid x_range = linspace(xlim_1, xlim_2, n); end

function [traindata, testdata, trainlabel, testlabel] = prepareData %{ % DESCRIPTION Prepare the data for SVDD_WOA

[traindata, testdata, trainlabel, testlabel] = prepareData

OUTPUT traindata Training data testdata Testing data trainlabel Training label trainlabel Training label

Created on 18th October 2019, by Kepeng Qiu. -------------------------------------------------------------% %}

load .\data\banana.mat

traindata(:, 1) = banana(1:2:500, 1); traindata(:, 2) = banana(1:2:500, 2);

testdata(:, 1) = banana(501:2:1000, 1); testdata(:, 2) = banana(501:2:1000, 2);

trainlabel = ones(size(traindata, 1), 1); testlabel = -ones(size(testdata, 1), 1); end

function [rho, X1, X2] = decision_boundary(model, traindata)

%{ % DESCRIPTION Computation of decision boundary

[rho, X1, X2] = decision_boundary(model, traindata)

INPUT model SVDD model N: number of samples traindata Training data

OUTPUT rho Bias term X1, X2 Grid range

Created on 18th October 2019, by Kepeng Qiu. -------------------------------------------------------------% %}

% Compute the range of grid x1_range = grid_range(traindata(:, 1)); x2_range = grid_range(traindata(:, 2));

% grid [X1, X2] = meshgrid(x1_range, x2_range); X_Grid = [X1(:), X2(:)];

% the grid label is only for the input of the function 'libsvmpredict' grid_label = ones(size(X_Grid, 1), 1);

% Predict the label of each grid point [~, ~, rho_0] = libsvmpredict(grid_label, X_Grid, model); rho = reshape(rho_0, size(X1, 1), size(X1, 2)); end