Kernels for structured data

Learning from structured data is becoming increasingly important. However, most prior work on kernel methods has focused on learning from attribute-value data. Only recently have researchers started investigating kernels for structured data. This paper describes how kernel definitions can be simplified by identifying the structure of the data and how kernels can be defined on this structure. We propose a kernel for structured data, prove that it is positive definite, and show how it can be adapted in practical applications.

[1]  C. Watkins Dynamic Alignment Kernels , 1999 .

[2]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[3]  Rocco A. Servedio,et al.  Efficiency versus Convergence of Boolean Kernels for On-Line Learning Algorithms , 2001, NIPS.

[4]  Ken Sadohara,et al.  Learning of Boolean Functions Using Support Vector Machines , 2001, ALT.

[5]  Thomas G. Dietterich,et al.  Solving the Multiple Instance Problem with Axis-Parallel Rectangles , 1997, Artif. Intell..

[6]  David Haussler,et al.  Convolution kernels on discrete structures , 1999 .

[7]  Mark J. F. Gales,et al.  Speech Recognition using SVMs , 2001, NIPS.

[8]  Stefan Wrobel,et al.  Relational Instance-Based Learning with Lists and Terms , 2001, Machine Learning.

[9]  Bernhard E. Boser,et al.  A training algorithm for optimal margin classifiers , 1992, COLT '92.

[10]  John W. Lloyd,et al.  Knowledge Representation, Computation, and Learning in Higher-order Logic , 2002 .

[11]  Hava T. Siegelmann,et al.  Support Vector Clustering , 2002, J. Mach. Learn. Res..

[12]  N. Cristianini,et al.  On Kernel-Target Alignment , 2001, NIPS.

[13]  Alonzo Church,et al.  A formulation of the simple theory of types , 1940, Journal of Symbolic Logic.

[14]  Alexander J. Smola,et al.  Learning with kernels , 1998 .

[15]  Gunnar Rätsch,et al.  A New Discriminative Kernel from Probabilistic Models , 2001, Neural Computation.

[16]  David Haussler,et al.  Exploiting Generative Models in Discriminative Classifiers , 1998, NIPS.

[17]  Nello Cristianini,et al.  Classification using String Kernels , 2000 .

[18]  Ian H. Witten,et al.  Data mining: practical machine learning tools and techniques with Java implementations , 2002, SGMD.

[19]  Thomas Gärtner,et al.  WBCsvm: Weighted Bayesian Classification based on Support Vector Machines , 2001, ICML.

[20]  Alexander J. Smola,et al.  Kernel Machines and Boolean Functions , 2001, NIPS.

[21]  Bernhard Schölkopf,et al.  Dynamic Alignment Kernels , 2000 .

[22]  Ryszard S. Michalski,et al.  Matching Methods with Problems: A Comparative Analysis of Constructive Induction Approaches , 1994 .

[23]  Stephen Muggleton,et al.  To the international computing community: A new East-West challenge , 1994 .

[24]  Ralf Hinze,et al.  Haskell 98 — A Non−strict‚ Purely Functional Language , 1999 .

[25]  Maurice Bruynooghe,et al.  A polynomial time computable metric between point sets , 2001, Acta Informatica.

[26]  Thomas Gärtner,et al.  Multi-Instance Kernels , 2002, ICML.