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Mastering Support Vector Machines: Large-Margin Classifiers and the Kernel Trick

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This lecture explores Support Vector Machines (SVM) as a powerful tool for classification tasks, focusing on large-margin linear classifiers in non-separable cases. Discover how SVMs handle complex data using the kernel trick to transform input space, enabling efficient classification of non-linearly separable datasets. Gain insights into the theoretical underpinnings and practical applications of SVMs, including key concepts, mathematical foundations, and examples that illustrate the strengths of this approach in machine learning.

Mastering Support Vector Machines: Large-Margin Classifiers and the Kernel Trick

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Presentation Transcript

1. 1 Lecture 5Support Vector Machines Large-margin linear classifier Non-separable case The Kernel trick

2. 2

Support Vector Machines

Support Vector Machines. Chapter 12. Separating Hyperplanes – Separable Case Extension to Non-separable case – SVM Nonlinear SVM SVM as a Penalization method SVM regression. Outline. Separating Hyperplanes.

1.03k views • 49 slides

Support Vector Machines

Support Vector Machines . Adapted from Lectures by Raymond Mooney (UT Austin) and Andrew Moore (CMU). Text classification. Earlier: Algorithms for text classification K Nearest Neighbor classification Simple, expensive at test time, low bias, high variance, non-linear

1.11k views • 64 slides

Support Vector Machines

Support Vector Machines. Hongning Wang CS@UVa. Today’s lecture. Support vector machines Max margin classifier Derivation of linear SVM Binary and multi-class cases Different types of losses in discriminative models Kernel method Non-linear SVM Popular implementations.

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Lecture 10: Support Vector Machines

Lecture 10: Support Vector Machines. Machine Learning Queens College. Today. Support Vector Machines Note : we ’ ll rely on some math from Optimality Theory that we won ’ t derive. Maximum Margin. Are these really “ equally valid ” ?.

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LECTURE 15: SUPPORT VECTOR MACHINES

LECTURE 15: SUPPORT VECTOR MACHINES. Objectives: Empirical Risk Minimization Large-Margin Classifiers Soft Margin Classifiers SVM Training Relevance Vector Machines Resources: DML: Introduction to SVMs AM: SVM Tutorial JP: SVM Resources OC: Taxonomy NC: SVM Tutorial. Class 2. Class 1.

747 views • 12 slides

LECTURE 16: SUPPORT VECTOR MACHINES

LECTURE 16: SUPPORT VECTOR MACHINES. Objectives: Empirical Risk Minimization Large-Margin Classifiers Soft Margin Classifiers SVM Training Relevance Vector Machines Resources: DML: Introduction to SVMs AM: SVM Tutorial JP: SVM Resources OC: Taxonomy NC: SVM Tutorial. Class 2. Class 1.

264 views • 12 slides

Support Vector Machines

Support Vector Machines. Perceptron Revisited:. y( x ) = sign( w . x + b ). Linear Classifier:. w . x + b &gt; 0. w . x + b = 0. w . x + b &lt; 0. Which one is the best?. d. Notion of Margin. Distance from a data point to the boundary:

447 views • 25 slides

Support Vector Machines

Support Vector Machines. Lecturer : Yishay Mansour Itay Kirshenbaum. Lecture Overview. In this lecture we present in detail one of the most theoretically well motivated and practically most eﬀective classiﬁcation algorithms in modern machine learning: Support Vector Machines (SVMs). .

714 views • 41 slides

Support Vector Machines

Support Vector Machines. Reading: Ben- Hur and Weston, “A User’s Guide to Support Vector Machines” (linked from class web page). Notation. Assume a binary classification problem: h ( x )  {−1, 1} Instances are represented by vector x   n .

845 views • 53 slides

Support Vector Machines

Support Vector Machines. Pattern Recognition Sergios Theodoridis Konstantinos Koutroumbas Second Edition A Tutorial on Support Vector Machines for Pattern Recognition Data Mining and Knowledge Discovery, 1998 C. J. C. Burges. Separable Case. Maximum Margin Formulation. Separable Case.

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Support Vector Machines

Support Vector Machines . More information can be found in http://www.cs.cmu.edu/~awm/tutorials. a. Linear Classifiers. x. f . y est. f ( x , w ,b ) = sign( w . x - b ). denotes +1 denotes -1. How would you classify this data?. a. Linear Classifiers. x. f . y est.

645 views • 33 slides

Support Vector Machines

Support Vector Machines. Modified from Prof. Andrew W. Moore’s Lecture Notes www.cs.cmu.edu/~awm. History. SVM is a classifier derived from statistical learning theory by Vapnik and Chervonenkis SVMs introduced by Boser, Guyon, Vapnik in COLT-92

719 views • 52 slides

Support Vector Machines

Support Vector Machines. Presented By Sherwin Shaidaee. Papers. Vladimir N. Vapnik, “The Statistical Learning Theory”. Springer, 1998 Yunqiang Chen, Xiang Zhou, and Thomas S. Huang, University of Illinois, “ONE-CLASS SVM FOR LEARNING IN IMAGE RETRIEVAL”, 2001

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Support Vector Machines

Support Vector Machines. Presented by: Yasmin Anwar. Outlines. Introduction Support Vector Machines SVM Tools SVM Applications Text Classification Conclusion. Introduction. Proposed by Boser, Guyon and Vapnik in 1992. SVMs are one of the best classification methods.

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Lecture 5 Support Vector Machines

Lecture 5 Support Vector Machines. Large-margin linear classifier Non-separable case The Kernel trick. Large-margin linear classifier. Let ’ s assume the linearly separable case. The optimal separating hyperplane separates the two classes and maximizes the distance to the closest point.

422 views • 27 slides

Support Vector Machines

Support Vector Machines. SVMs. Feature Space. Separable?. Kernels and Support Vectors. Calculation. Higgs Parameters. Higgs Parameters. Higgs Output. Higgs Purity / Efficiency. Kernel Width. L2 b Tagger Parameters. L2 b Tagger Parameters. L2 b Tagger Output. SVR. NN.

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Support Vector Machines

Summer Course: Data Mining. Support Vector Machines. Support Vector Machines and other penalization classifiers. Presenter: Georgi Nalbantov. Presenter: Georgi Nalbantov. August 2009. Contents. Purpose Linear Support Vector Machines Nonlinear Support Vector Machines

760 views • 52 slides

Support Vector Machines

Support Vector Machines. 1. Introduction to SVMs 2. Linear SVMs 3. Non-linear SVMs. References: 1. S.Y. Kung, M.W. Mak, and S.H. Lin. Biometric Authentication: A Machine Learning Approach, Prentice Hall, to appear.

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Support Vector Machines

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