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 1 - 5 kokonaismäärästä 32
Sivu 6
... minimising the number of training errors of a thresholded linear function is also NP-hard. In view of these difficulties it is immediately apparent that there are severe restrictions on the applicability of the approach, and any ...
... minimising the number of training errors of a thresholded linear function is also NP-hard. In view of these difficulties it is immediately apparent that there are severe restrictions on the applicability of the approach, and any ...
Sivu 15
... minimising the norm of the weight vector. 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 ...
... minimising the norm of the weight vector. 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 ...
Sivu 20
... minimises the sum of the squares of the distances from the training points. This technique is known as least squares, and is known to be optimal in the case of linear targets corrupted by Gaussian noise. Figure 2.5 : A one dimensional ...
... minimises the sum of the squares of the distances from the training points. This technique is known as least squares, and is known to be optimal in the case of linear targets corrupted by Gaussian noise. Figure 2.5 : A one dimensional ...
Sivu 21
... minimises a combination of square loss and norm of the w vector. This solution, proposed by Hoerl and Kennard, is ... minimise the sum of the squared deviations of the data, t The function L is known as the square loss function as it ...
... minimises a combination of square loss and norm of the w vector. This solution, proposed by Hoerl and Kennard, is ... minimise the sum of the squared deviations of the data, t The function L is known as the square loss function as it ...
Sivu 22
... minimise L by differentiating with respect to the parameters (w,/>), and setting the resulting n + I linear expressions to zero. This is best expressed in matrix notation by setting w = (w'.fc) , and X = x;. \. \ , where x,- = (xj, 1) ...
... minimise L by differentiating with respect to the parameters (w,/>), and setting the resulting n + I linear expressions to zero. This is best expressed in matrix notation by setting w = (w'.fc) , and X = x;. \. \ , where x,- = (xj, 1) ...
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 |
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