This example shows how to use a custom kernel function, such as the sigmoid kernel, to train SVM classifiers, and adjust custom kernel function parameters.
Generate a random set of points within the unit circle. Label points in the first and third quadrants as belonging to the positive class, and those in the second and fourth quadrants in the negative class.
rng(1); % For reproducibility n = 100; % Number of points per quadrant r1 = sqrt(rand(2*n,1)); % Random radii t1 = [pi/2*rand(n,1); (pi/2*rand(n,1)+pi)]; % Random angles for Q1 and Q3 X1 = [r1.*cos(t1) r1.*sin(t1)]; % Polar-to-Cartesian conversion r2 = sqrt(rand(2*n,1)); t2 = [pi/2*rand(n,1)+pi/2; (pi/2*rand(n,1)-pi/2)]; % Random angles for Q2 and Q4 X2 = [r2.*cos(t2) r2.*sin(t2)]; X = [X1; X2]; % Predictors Y = ones(4*n,1); Y(2*n + 1:end) = -1; % Labels
Plot the data.
figure;
gscatter(X(:,1),X(:,2),Y);
title('Scatter Diagram of Simulated Data')
Write a function that accepts two matrices in the feature space as inputs, and transforms them into a Gram matrix using the sigmoid kernel.
function G = mysigmoid(U,V) % Sigmoid kernel function with slope gamma and intercept c gamma = 1; c = -1; G = tanh(gamma*U*V' + c); end
Save this code as a file named mysigmoid on your MATLAB® path.
Train an SVM classifier using the sigmoid kernel function. It is good practice to standardize the data.
Mdl1 = fitcsvm(X,Y,'KernelFunction','mysigmoid','Standardize',true);
Mdl1 is a ClassificationSVM classifier containing the estimated parameters.
Plot the data, and identify the support vectors and the decision boundary.
% Compute the scores over a grid
d = 0.02; % Step size of the grid
[x1Grid,x2Grid] = meshgrid(min(X(:,1)):d:max(X(:,1)),...
min(X(:,2)):d:max(X(:,2)));
xGrid = [x1Grid(:),x2Grid(:)]; % The grid
[~,scores1] = predict(Mdl1,xGrid); % The scores
figure;
h(1:2) = gscatter(X(:,1),X(:,2),Y);
hold on
h(3) = plot(X(Mdl1.IsSupportVector,1),...
X(Mdl1.IsSupportVector,2),'ko','MarkerSize',10);
% Support vectors
contour(x1Grid,x2Grid,reshape(scores1(:,2),size(x1Grid)),[0 0],'k');
% Decision boundary
title('Scatter Diagram with the Decision Boundary')
legend({'-1','1','Support Vectors'},'Location','Best');
hold off
You can adjust the kernel parameters in an attempt to improve the shape of the decision boundary. This might also decrease the within-sample misclassification rate, but, you should first determine the out-of-sample misclassification rate.
Determine the out-of-sample misclassification rate by using 10-fold cross validation.
CVMdl1 = crossval(Mdl1); misclass1 = kfoldLoss(CVMdl1); misclass1
misclass1 =
0.1350
The out-of-sample misclassification rate is 13.5%.
Write another sigmoid function, but Set gamma = 0.5;.
function G = mysigmoid2(U,V) % Sigmoid kernel function with slope gamma and intercept c gamma = 0.5; c = -1; G = tanh(gamma*U*V' + c); end
Save this code as a file named mysigmoid2 on your MATLAB® path.
Train another SVM classifier using the adjusted sigmoid kernel. Plot the data and the decision region, and determine the out-of-sample misclassification rate.
Mdl2 = fitcsvm(X,Y,'KernelFunction','mysigmoid2','Standardize',true);
[~,scores2] = predict(Mdl2,xGrid);
figure;
h(1:2) = gscatter(X(:,1),X(:,2),Y);
hold on
h(3) = plot(X(Mdl2.IsSupportVector,1),...
X(Mdl2.IsSupportVector,2),'ko','MarkerSize',10);
title('Scatter Diagram with the Decision Boundary')
contour(x1Grid,x2Grid,reshape(scores2(:,2),size(x1Grid)),[0 0],'k');
legend({'-1','1','Support Vectors'},'Location','Best');
hold off
CVMdl2 = crossval(Mdl2);
misclass2 = kfoldLoss(CVMdl2);
misclass2
misclass2 =
0.0450
After the sigmoid slope adjustment, the new decision boundary seems to provide a better within-sample fit, and the cross-validation rate contracts by more than 66%.
more page 4
Matlabsolutions.com provides guaranteed satisfaction with a
commitment to complete the work within time. Combined with our meticulous work ethics and extensive domain
experience, We are the ideal partner for all your homework/assignment needs. We pledge to provide 24*7 support
to dissolve all your academic doubts. We are composed of 300+ esteemed Matlab and other experts who have been
empanelled after extensive research and quality check.
Matlabsolutions.com provides undivided attention to each Matlab
assignment order with a methodical approach to solution. Our network span is not restricted to US, UK and Australia rather extends to countries like Singapore, Canada and UAE. Our Matlab assignment help services
include Image Processing Assignments, Electrical Engineering Assignments, Matlab homework help, Matlab Research Paper help, Matlab Simulink help. Get your work
done at the best price in industry.
Desktop Basics - MATLAB & Simulink
Array Indexing - MATLAB & Simulink
Workspace Variables - MATLAB & Simulink
Text and Characters - MATLAB & Simulink
Calling Functions - MATLAB & Simulink
2-D and 3-D Plots - MATLAB & Simulink
Programming and Scripts - MATLAB & Simulink
Help and Documentation - MATLAB & Simulink
Creating, Concatenating, and Expanding Matrices - MATLAB & Simulink
Removing Rows or Columns from a Matrix
Reshaping and Rearranging Arrays
Add Title and Axis Labels to Chart
Change Color Scheme Using a Colormap
How Surface Plot Data Relates to a Colormap
How Image Data Relates to a Colormap
Time-Domain Response Data and Plots
Time-Domain Responses of Discrete-Time Model
Time-Domain Responses of MIMO Model
Time-Domain Responses of Multiple Models
Introduction: PID Controller Design
Introduction: Root Locus Controller Design
Introduction: Frequency Domain Methods for Controller Design
DC Motor Speed: PID Controller Design
DC Motor Position: PID Controller Design
Cruise Control: PID Controller Design
Suspension: Root Locus Controller Design
Aircraft Pitch: Root Locus Controller Design
Inverted Pendulum: Root Locus Controller Design
Get Started with Deep Network Designer
Create Simple Image Classification Network Using Deep Network Designer
Build Networks with Deep Network Designer
Classify Image Using GoogLeNet
Classify Webcam Images Using Deep Learning
Transfer Learning with Deep Network Designer
Train Deep Learning Network to Classify New Images
Deep Learning Processor Customization and IP Generation
Prototype Deep Learning Networks on FPGA
Deep Learning Processor Architecture
Deep Learning INT8 Quantization
Quantization of Deep Neural Networks
Custom Processor Configuration Workflow
Estimate Performance of Deep Learning Network by Using Custom Processor Configuration
Preprocess Images for Deep Learning
Preprocess Volumes for Deep Learning
Transfer Learning Using AlexNet
Time Series Forecasting Using Deep Learning
Create Simple Sequence Classification Network Using Deep Network Designer
Classify Image Using Pretrained Network
Train Classification Models in Classification Learner App
Train Regression Models in Regression Learner App
Explore the Random Number Generation UI
Logistic regression create generalized linear regression model - MATLAB fitglm 2
Support Vector Machines for Binary Classification
Support Vector Machines for Binary Classification 2
Support Vector Machines for Binary Classification 3
Support Vector Machines for Binary Classification 4
Support Vector Machines for Binary Classification 5
Assess Neural Network Classifier Performance
Discriminant Analysis Classification
Train Generalized Additive Model for Binary Classification
Train Generalized Additive Model for Binary Classification 2
Classification Using Nearest Neighbors
Classification Using Nearest Neighbors 2
Classification Using Nearest Neighbors 3
Classification Using Nearest Neighbors 4
Classification Using Nearest Neighbors 5
Gaussian Process Regression Models
Gaussian Process Regression Models 2
Understanding Support Vector Machine Regression
Extract Voices from Music Signal
Align Signals with Different Start Times
Find a Signal in a Measurement
Extract Features of a Clock Signal
Filtering Data With Signal Processing Toolbox Software
Find Periodicity Using Frequency Analysis
Find and Track Ridges Using Reassigned Spectrogram
Classify ECG Signals Using Long Short-Term Memory Networks
Waveform Segmentation Using Deep Learning
Label Signal Attributes, Regions of Interest, and Points
Introduction to Streaming Signal Processing in MATLAB
Filter Frames of a Noisy Sine Wave Signal in MATLAB
Filter Frames of a Noisy Sine Wave Signal in Simulink
Lowpass Filter Design in MATLAB
Tunable Lowpass Filtering of Noisy Input in Simulink
Signal Processing Acceleration Through Code Generation
Signal Visualization and Measurements in MATLAB
Estimate the Power Spectrum in MATLAB
Design of Decimators and Interpolators
Multirate Filtering in MATLAB and Simulink
Australia
UK
UAE
Singapore
Canada
New
Zealand
Malaysia
USA
India
South Africa
Ireland
Saudi
Arab
Qatar
Kuwait
Hongkong
Copyright 2016-2024 www.matlabsolutions.com - All Rights Reserved.
Disclaimer : Any type of help and guidance service given by us is just for reference purpose. We never ask any of our clients to submit our solution guide as it is, anywhere.
