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. |
Kirjan sisältä
Tulokset 1 - 5 kokonaismäärästä 39
Sivu xiii
... n dimension of input space R radius of the ball containing the data e-insensitive loss function insensitive to errors less than e w weight vector b bias - dual variables or Lagrange multipliers L primal Lagrangian W dual Lagrangian ...
... n dimension of input space R radius of the ball containing the data e-insensitive loss function insensitive to errors less than e w weight vector b bias - dual variables or Lagrange multipliers L primal Lagrangian W dual Lagrangian ...
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
Note that if AT is a vector space, the input vectors are column vectors as are the weight vectors. If we wish to form a row vector from x, we can take the transpose xj. Several simple iterative algorithms optimising different cost ...
Note that if AT is a vector space, the input vectors are column vectors as are the weight vectors. If we wish to form a row vector from x, we can take the transpose xj. Several simple iterative algorithms optimising different cost ...
Sivu 12
... for a linearly separable training set. Figure 2.2 shows the geometric margin at two points with respect to a hyperplane in two dimensions. The geometric margin will equal the functional margin if the weight vector is a unit vector.
... for a linearly separable training set. Figure 2.2 shows the geometric margin at two points with respect to a hyperplane in two dimensions. The geometric margin will equal the functional margin if the weight vector is a unit vector.
Sivu 14
Proof For the analysis we augment the input vectors by an extra coordinate with value R. We denote the new vector by x, = (x|, R)', where x' denotes the transpose of x. Similarly we add an extra coordinate to the weight vector w by ...
Proof For the analysis we augment the input vectors by an extra coordinate with value R. We denote the new vector by x, = (x|, R)', where x' denotes the transpose of x. Similarly we add an extra coordinate to the weight vector w by ...
Mitä ihmiset sanovat - Kirjoita arvostelu
Yhtään arvostelua ei löytynyt.
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
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 |