An Introduction to Support Vector Machines and Other Kernel-based Learning MethodsCambridge University Press, 23.3.2000 This is the first comprehensive introduction to Support Vector Machines (SVMs), a generation learning system based on recent advances in statistical learning theory. SVMs deliver state-of-the-art performance in real-world applications such as text categorisation, hand-written character recognition, image classification, biosequences analysis, etc., and are now established as one of the standard tools for machine learning and data mining. Students will find the book both stimulating and accessible, while practitioners will be guided smoothly through the material required for a good grasp of the theory and its applications. The concepts are introduced gradually in accessible and self-contained stages, while the presentation is rigorous and thorough. Pointers to relevant literature and web sites containing software ensure that it forms an ideal starting point for further study. Equally, the book and its associated web site will guide practitioners to updated literature, new applications, and on-line software. |
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Tulokset 1 - 5 kokonaismäärästä 58
Sivu x
... theorems which are generally known by the name of the original author such as Mercer's theorem, and secondly in Chapter 8 which describes specific experiments reported in the research literature. The fundamental principle that guided ...
... theorems which are generally known by the name of the original author such as Mercer's theorem, and secondly in Chapter 8 which describes specific experiments reported in the research literature. The fundamental principle that guided ...
Sivu 12
... Theorem 2.3 (Novikoff) Let S be a non-trivial training set, and let R = max ||x,-|| . Suppose that there exists a vector wopt such that || wopt || = 1 and y,((w0pt - x,) +ftopt) > y for 1 < i < t. Then the number of mistakes made by the ...
... Theorem 2.3 (Novikoff) Let S be a non-trivial training set, and let R = max ||x,-|| . Suppose that there exists a vector wopt such that || wopt || = 1 and y,((w0pt - x,) +ftopt) > y for 1 < i < t. Then the number of mistakes made by the ...
Sivu 14
... w,|| > (w,,wopt} > trjy, which together imply the bound since bopt < R for a non-trivial separation of the data, and hence C I|wop,||2<||w0p.ll2 Remark 2.4 The theorem is usually given for zero bias 14 2 Linear Learning Machines.
... w,|| > (w,,wopt} > trjy, which together imply the bound since bopt < R for a non-trivial separation of the data, and hence C I|wop,||2<||w0p.ll2 Remark 2.4 The theorem is usually given for zero bias 14 2 Linear Learning Machines.
Sivu 15
... theorem proves that the algorithm converges in a finite number of iterations provided its margin is positive. Just iterating several times on the same sequence S, after a number of mistakes bounded by f^ the perceptron algorithm will ...
... theorem proves that the algorithm converges in a finite number of iterations provided its margin is positive. Just iterating several times on the same sequence S, after a number of mistakes bounded by f^ the perceptron algorithm will ...
Sivu 16
... Theorem 2.7 ( Freund and Schapire) Let S be a non-trivial training set with no duplicate examples, with ||xi|| < R. Let (w, b) be any hyperplane with ||w|| = 1. let y > 0 and define D = \ Then the number of mistakes in the first ...
... Theorem 2.7 ( Freund and Schapire) Let S be a non-trivial training set with no duplicate examples, with ||xi|| < R. Let (w, b) be any hyperplane with ||w|| = 1. let y > 0 and define D = \ Then the number of mistakes in the first ...
Sisältö
1 | |
9 | |
KernelInduced Feature Spaces | 26 |
Generalisation Theory | 52 |
Optimisation Theory | 79 |
Support Vector Machines | 93 |
Implementation Techniques | 125 |
Applications of Support Vector Machines | 149 |
A Pseudocode for the SMO Algorithm | 162 |
References | 173 |
Index | 187 |
Muita painoksia - Näytä kaikki
An Introduction to Support Vector Machines and Other Kernel-based Learning ... Nello Cristianini,John Shawe-Taylor Rajoitettu esikatselu - 2000 |
An Introduction to Support Vector Machines and Other Kernel-based Learning ... Nello Cristianini,John Shawe-Taylor Esikatselu ei käytettävissä - 2000 |
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1-norm soft margin algorithm analysis applied approach Bayesian bias bound Chapter choice classification computational consider constraints convergence convex corresponding datasets Definition described dual problem dual representation fat-shattering dimension feasibility gap feature mapping feature space finite Gaussian processes generalisation error geometric margin given Hence heuristics high dimensional Hilbert space hyperplane hypothesis inequality inner product space input space introduced iterative Karush-Kuhn-Tucker kernel function kernel matrix Lagrange multipliers Lagrangian learning algorithm linear functions linear learning machines loss function machine learning margin distribution margin slack vector maximal margin hyperplane maximise minimise norm objective function obtained on-line optimisation problem parameters perceptron perceptron algorithm performance positive semi-definite primal and dual quantity random examples real-valued function Remark result ridge regression Section sequence slack variables soft margin optimisation solution solve subset Support Vector Machines SVMs techniques Theorem training data training examples training points training set update Vapnik VC dimension weight vector zero