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Support Vector Machines: Classification Algorithms and Applications. Olvi L. Mangasarian Department of Mathematics -UCSD with G. M. Fung, Y.-J. Lee, J.W. Shavlik, W. H. Wolberg University of Wisconsin – Madison and Collaborators at ExonHit – Paris. What is a Support Vector Machine?.
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Olvi L. Mangasarian
Department of Mathematics -UCSD
G. M. Fung, Y.-J. Lee, J.W. Shavlik, W. H. Wolberg
University of Wisconsin – Madison
Collaborators at ExonHit – Paris
where e is a vector of ones.Standard Support Vector MachineAlgebra of 2-Category Linearly Separable Case
function [w, gamma] = psvm(A,d,nu)% PSVM: linear and nonlinear classification
% INPUT: A, d=diag(D), nu. OUTPUT: w, gamma% [w, gamma] = psvm(A,d,nu);
r=(speye(n+1)/nu+H’*H)\v % solve (I/nu+H’*H)r=v
w=r(1:n);gamma=r(n+1); % getting w,gamma from r
Suppose that the knowledge set: belongs to the class A+. Hence it must lie in the halfspace :
Adding one set of constraints for each knowledge set to the 1-norm SVM LP, we have:Knowledge-Based SVM Classification
57 categorical values
57 x 4 =228
Note: Only KSVM and SVM1 utilize a simple linear classifier
Standard quadratic programming (QP) formulation of SVM:
Once, but not twice differentiable. However Generlized Hessian exists!
is a representative sample
of the entire dataset
is1% to 10%of the rows of
in nonlinear SSVM
the rectangular kernel
gives lousy results!
UsingOvercoming Computational & Storage DifficultiesUse a Rectangular Kernel
(i) Choose a random subset matrix
entire data matrix
(ii) Solvethe following problem by the Newton
method with corresponding
(iii) The separating surface is defined by the optimal
solutionReduced Support Vector Machine AlgorithmNonlinear Separating Surface:
may generate a classifier using
random rows from the entire dataset
such that the distance between its rows
exceeds a certain tolerance
Breast Cancer Prognosis & ChemotherapyGood, Intermediate & Poor Patient Groupings(6 Input Features : 5 Cytological, 1 Histological)(Grouping: Utilizes 2 Histological Features &Chemotherapy)
2.7915 T11 + 0.13436 S24 -1.0269 U23 -2.8108 Z23 -1.8668 A19 -1.5177 X05 +2899.1 = 0.
Alternative RNA splicing
DATAS: Differential Analysis of Transcripts with Alternative Splicing
Detection of Alternative RNA Isoforms via DATAS
(Levels of mRNA that Correlate with Senitivity to Chemotherapy)