An Introduction to Support Vector Machines and Other Kernel-based Learning MethodsThis 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 33
Sivu 5
These bounds will typically depend on certain quantities such as the margin of the classifier, and hence motivate algorithms which optimise the particular measure. The drawback of such an approach is that the algorithm is only as good ...
These bounds will typically depend on certain quantities such as the margin of the classifier, and hence motivate algorithms which optimise the particular measure. The drawback of such an approach is that the algorithm is only as good ...
Sivu 10
We will refer to the quantities w and b as the weight vector and bias, terms borrowed from the neural networks literature. Sometimes — b is replaced by 9, a quantity known as the threshold. As we are studying supervised learning from ...
We will refer to the quantities w and b as the weight vector and bias, terms borrowed from the neural networks literature. Sometimes — b is replaced by 9, a quantity known as the threshold. As we are studying supervised learning from ...
Sivu 11
This quantity will play a central role throughout the book and so we will introduce a more formal definition here. Definition 2.2 We define the (functional) margin of an example (x,, y,) with respect to a hyperplane (w, ...
This quantity will play a central role throughout the book and so we will introduce a more formal definition here. Definition 2.2 We define the (functional) margin of an example (x,, y,) with respect to a hyperplane (w, ...
Sivu 12
... 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 boundary in the input space.
... 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 boundary in the input space.
Sivu 15
Remark 2.5 The critical quantity in the bound is the square of the ratio of the radius of the ball containing the data and the margin of the separating hyperplane. This ratio is invariant under a positive rescaling of the data, ...
Remark 2.5 The critical quantity in the bound is the square of the ratio of the radius of the ball containing the data and the margin of the separating hyperplane. This ratio is invariant under a positive rescaling of the data, ...
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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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Yleiset termit ja lausekkeet
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
Kirjaluettelon tiedot
| Otsikko | An Introduction to Support Vector Machines and Other Kernel-based Learning Methods |
| Kirjailijat | Nello Cristianini, John Shawe-Taylor |
| Kustantaja | Cambridge University Press, 2000 |
| ISBN | 1139643630, 9781139643634 |
| Vie sitaatti | BiBTeX EndNote RefMan |