UNIVERSITY OF SOUTHAMPTON
Support Vector Machines
for
语法讲义Classification and Regression
by
Steve R.Gunn
Technical Report
Faculty of Engineering,Science and Mathematics School of Electronics and Computer Science
10May1998
Contents
Nomenclature xi
无师自通韩国语
1Introduction1
1.1Statistical Learning Theory (2)
1.1.1VC Dimension (3)
1.1.2Structural Risk Minimisation (4)
2Support Vector Classification5
2.1The Optimal Separating Hyperplane (5)
2.1.1Linearly Separable Example (10)
2.2The Generalid Optimal Separating Hyperplane (10)
2.2.1Linearly Non-Separable Example (13)
2.3Generalisation in High Dimensional Feature Space (14)
2.3.1Polynomial Mapping Example (16)
2.4Discussion (16)
gc课程3Feature Space19
3.1Kernel Functions (19)
3.1.1Polynomial (20)
3.1.2Gaussian Radial Basis Function (20)
贫煤
3.1.3Exponential Radial Basis Function (20)
3.1.4Multi-Layer Perceptron (20)
swana3.1.5Fourier Series (21)
3.1.6Splines (21)
3.1.7B splines (21)
3.1.8Additive Kernels (22)
3.1.9Tensor Product (22)
3.2Implicit vs.Explicit Bias (22)
2013六级作文>south是什么意思3.3Data Normalisation (23)
3.4Kernel Selection (23)
4Classification Example:IRIS data25
4.1Applications (28)
5Support Vector Regression29
5.1Linear Regression (30)
5.1.1 -innsitive Loss Function (30)
5.1.2Quadratic Loss Function (31)
iii
iv CONTENTS
5.1.3Huber Loss Function (32)
5.1.4Example (33)
5.2Non Linear Regression (33)
probably5.2.1Examples (34)
5.2.2Comments (36)
6Regression Example:Titanium Data39
6.1Applications (42)
7Conclusions43
A Implementation Issues45
A.1Support Vector Classification (45)
A.2Support Vector Regression (47)
B MATLAB SVM Toolbox51 Bibliography53
List of Figures
1.1Modelling Errors (2)
1.2VC Dimension Illustration (3)
2.1Optimal Separating Hyperplane (5)
2.2Canonical Hyperplanes (6)
2.3Constraining the Canonical Hyperplanes (7)
2.4Optimal Separating Hyperplane (10)
2.5Generalid Optimal Separating Hyperplane (11)
2.6Generalid Optimal Separating Hyperplane Example(C=1) (13)features是什么意思
2.7Generalid Optimal Separating Hyperplane Example(C=105) (14)
2.8Generalid Optimal Separating Hyperplane Example(C=10−8) (14)
2.9Mapping the Input Space into a High Dimensional Feature Space (14)
2.10Mapping input space into Polynomial Feature Space (16)
3.1Comparison between Implicit and Explicit bias for a linear kernel (22)
4.1Iris data t (25)
4.2Separating Setosa with a linear SVC(C=∞) (26)
4.3Separating Viginica with a polynomial SVM(degree2,C=∞) (26)
4.4Separating Viginica with a polynomial SVM(degree10,C=∞) (26)
4.5Separating Viginica with a Radial Basis Function SVM(σ=1.0,C=∞)27
4.6Separating Viginica with a polynomial SVM(degree2,C=10) (27)
4.7The effect of C on the paration of Versilcolor with a linear spline SVM.28
5.1Loss Functions (29)
5.2Linear regression (33)
5.3Polynomial Regression (35)
5.4Radial Basis Function Regression (35)
5.5Spline Regression (36)2012高考英语作文
5.6B-spline Regression (36)
5.7Exponential RBF Regression (36)
6.1Titanium Linear Spline Regression( =0.05,C=∞) (39)
6.2Titanium B-Spline Regression( =0.05,C=∞) (40)
6.3Titanium Gaussian RBF Regression( =0.05,σ=1.0,C=∞) (40)
6.4Titanium Gaussian RBF Regression( =0.05,σ=0.3,C=∞) (40)
6.5Titanium Exponential RBF Regression( =0.05,σ=1.0,C=∞) (41)
6.6Titanium Fourier Regression( =0.05,degree3,C=∞) (41)
6.7Titanium Linear Spline Regression( =0.05,C=10) (42)
v
vi LIST OF FIGURES
6.8Titanium B-Spline Regression( =0.05,C=10) (42)
