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 52
Sivu xiii
... 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 <> confidence ...
... 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 <> confidence ...
Sivu 15
... 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 iterating several ...
... 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 iterating several ...
Sivu 16
... norm. All of the other points in the figure have their slack variable equal to zero since they have a (positive) margin of more than y. Theorem 2.7 ( Freund and Schapire) Let S be a non-trivial training set with no duplicate examples ...
... norm. All of the other points in the figure have their slack variable equal to zero since they have a (positive) margin of more than y. Theorem 2.7 ( Freund and Schapire) Let S be a non-trivial training set with no duplicate examples ...
Sivu 19
... norm of the vector a satisfies the bound on the number of mistakes given in Theorem 2.3. 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 ...
... norm of the vector a satisfies the bound on the number of mistakes given in Theorem 2.3. 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 ...
Sivu 21
... norm of the w vector. This solution, proposed by Hoerl and Kennard, is known as ridge regression. Both these algorithms require the inversion of a matrix, though a simple iterative procedure also exists (the Adaline algorithm developed ...
... norm of the w vector. This solution, proposed by Hoerl and Kennard, is known as ridge regression. Both these algorithms require the inversion of a matrix, though a simple iterative procedure also exists (the Adaline algorithm developed ...
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