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. |
Kirjan sisältä
Tulokset 6 - 10 kokonaismäärästä 70
Sivu 11
Nello Cristianini, John Shawe-Taylor. Definition 2.1 We typically use X to denote the input space and Y to denote the ... Definition 2.2 We define the (functional) margin of an example (x,, y,) with respect to a hyperplane (w, b) to be ...
Nello Cristianini, John Shawe-Taylor. Definition 2.1 We typically use X to denote the input space and Y to denote the ... Definition 2.2 We define the (functional) margin of an example (x,, y,) with respect to a hyperplane (w, b) to be ...
Sivu 12
... definitions if we replace functional margin by geometric margin we obtain the equivalent quantity for the normalised linear function ( TOf w' ir^f ^ ) , which therefore measures the Euclidean distances of the points from the decision ...
... definitions if we replace functional margin by geometric margin we obtain the equivalent quantity for the normalised linear function ( TOf w' ir^f ^ ) , which therefore measures the Euclidean distances of the points from the decision ...
Sivu 15
... define the canonical maximal margin hyperplane with respect to a separable training set by fixing the margin equal to ... Definition 2.6 Fix a value y > 0, we can define the margin slack variable of an example (x,,y,) with respect to the ...
... define the canonical maximal margin hyperplane with respect to a separable training set by fixing the margin equal to ... Definition 2.6 Fix a value y > 0, we can define the margin slack variable of an example (x,,y,) with respect to the ...
Sivu 16
... define D = \ Then the number of mistakes in the first execution of the for loop of the perceptron algorithm of Table 2.1 on S is bounded by Proof The proof defines an extended input space parametrised by A in which there is a hyperplane ...
... define D = \ Then the number of mistakes in the first execution of the for loop of the perceptron algorithm of Table 2.1 on S is bounded by Proof The proof defines an extended input space parametrised by A in which there is a hyperplane ...
Sivu 17
... defined for any hyperplane, the bound of the theorem does not rely on the data being linearly separable. The problem of finding the linear separation of non-separable data with the smallest number of misclassifications is NP-complete. A ...
... defined for any hyperplane, the bound of the theorem does not rely on the data being linearly separable. The problem of finding the linear separation of non-separable data with the smallest number of misclassifications is NP-complete. A ...
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 |
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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