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 52
Sivu xiii
p-norm In natural logarithm e base of the natural logarithm log logarithm to the base 2 x', X' transpose of vector, matrix N, R natural, real numbers S training sample / training set size '/ learning rate E error probability ...
p-norm In natural logarithm e base of the natural logarithm log logarithm to the base 2 x', X' transpose of vector, matrix N, R natural, real numbers S training sample / training set size '/ learning rate E error probability ...
Sivu 15
The resulting value of the norm is inversely proportional to the margin. The 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 ...
The resulting value of the norm is inversely proportional to the margin. The 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 ...
Sivu 16
Figure 2.4 shows the size of the margin slack variables for two misclassified points for a hyperplane with unit norm. All of the other points in the figure have their slack variable equal to zero since they have a (positive) margin of ...
Figure 2.4 shows the size of the margin slack variables for two misclassified points for a hyperplane with unit norm. All of the other points in the figure have their slack variable equal to zero since they have a (positive) margin of ...
Sivu 19
We can therefore view the 1-norm of a as a measure of the complexity of the target concept in the dual representation. Remark 2.11 The training data only enter the algorithm through the entries of the matrix G = ((x, - x;}).
We can therefore view the 1-norm of a as a measure of the complexity of the target concept in the dual representation. Remark 2.11 The training data only enter the algorithm through the entries of the matrix G = ((x, - x;}).
Sivu 21
... motivated the introduction of a variation of this technique, which is analogous to the maximal margin hyperplane in the classification case: choosing a function that minimises a combination of square loss and norm of the w vector.
... motivated the introduction of a variation of this technique, which is analogous to the maximal margin hyperplane in the classification case: choosing a function that minimises a combination of square loss and norm of the w vector.
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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 |