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 50
Sivu 10
A hyperplane is an affine subspace of dimension n — 1 which divides the space into two half spaces which correspond to the inputs of the two distinct classes. For example in Figure 2.1 the hyperplane is the dark line, with the positive ...
A hyperplane is an affine subspace of dimension n — 1 which divides the space into two half spaces which correspond to the inputs of the two distinct classes. For example in Figure 2.1 the hyperplane is the dark line, with the positive ...
Sivu 17
Let x, denote this extended vector and S the corresponding training set. We now extend w with the value y,^,/A in the ith additional entry to give the vector w. Observe that y, «w - X,-} + b) = y, ({w - x,-} + b) + £, > y, showing that ...
Let x, denote this extended vector and S the corresponding training set. We now extend w with the value y,^,/A in the ith additional entry to give the vector w. Observe that y, «w - X,-} + b) = y, ({w - x,-} + b) + £, > y, showing that ...
Sivu 18
Once a sample S has been fixed, one can think of the vector a as alternative representation of the hypothesis in different or dual coordinates. This expansion is however not unique: different a can correspond to the same hypothesis w.
Once a sample S has been fixed, one can think of the vector a as alternative representation of the hypothesis in different or dual coordinates. This expansion is however not unique: different a can correspond to the same hypothesis w.
Sivu 20
The problem of linear regression consists in finding a linear function /(x) = (w - x) + b that best interpolates a given set 5 of training points labelled from Y £ R. Geometrically this corresponds to a hyperplane fitting the given ...
The problem of linear regression consists in finding a linear function /(x) = (w - x) + b that best interpolates a given set 5 of training points labelled from Y £ R. Geometrically this corresponds to a hyperplane fitting the given ...
Sivu 26
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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 |