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12
Estimating the Support of a HighDimensional Distribution
, 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propo ..."
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Cited by 766 (29 self)
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Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propose a method to approach this problem by trying to estimate a function f which is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space. The expansion coefficients are found by solving a quadratic programming problem, which we do by carrying out sequential optimization over pairs of input patterns. We also provide a preliminary theoretical analysis of the statistical performance of our algorithm. The algorithm is a natural extension of the support vector algorithm to the case of unlabelled d...
An Investigation of Feature Models for Music Genre Classification Using the Support Vector Classifier
 In International Conference on Music Information Retrieval
, 2005
"... In music genre classification the decision time is typically of the order of several seconds, however, most automatic music genre classification systems focus on short time features derived from 10 −50ms. This work investigates two models, the multivariate Gaussian model and the multivariate autoreg ..."
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Cited by 24 (3 self)
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In music genre classification the decision time is typically of the order of several seconds, however, most automatic music genre classification systems focus on short time features derived from 10 −50ms. This work investigates two models, the multivariate Gaussian model and the multivariate autoregressive model for modelling short time features. Furthermore, it was investigated how these models can be integrated over a segment of short time features into a kernel such that a support vector machine can be applied. Two kernels with this property were considered, the convolution kernel and product probability kernel. In order to examine the different methods an 11 genre music setup was utilized. In this setup the Mel Frequency Cepstral Coefficients were used as short time features. The accuracy of the best performing model on this data set was ∼ 44 % compared to a human performance of ∼ 52 % on the same data set.
Feature Selection and Classification on Matrix Data: From Large Margins . . .
 ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 16
, 2003
"... We investigate the problem of learning a classification task for datasets which are described by matrices. Rows and columns of these matrices correspond to objects, where row and column objects may belong to different sets, and the entries in the matrix express the relationships between them. We ..."
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Cited by 2 (0 self)
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We investigate the problem of learning a classification task for datasets which are described by matrices. Rows and columns of these matrices correspond to objects, where row and column objects may belong to different sets, and the entries in the matrix express the relationships between them. We interpret the matrix elements as being produced by an unknown kernel which operates on object pairs and we show that  under mild assumptions  these kernels correspond to dot products in some (unknown) feature space. Minimizing a
Feature Selection and Classification on Matrix Data: From Large Margins to Small Covering Numbers
 Advances in Neural Information Processing Systems 16
, 2003
"... We investigate the problem of learning a classification task for datasets which are described by matrices. Rows and columns of these matrices correspond to objects, where row and column objects may belong to different sets, and the entries in the matrix express the relationships between them. We int ..."
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Cited by 1 (0 self)
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We investigate the problem of learning a classification task for datasets which are described by matrices. Rows and columns of these matrices correspond to objects, where row and column objects may belong to different sets, and the entries in the matrix express the relationships between them. We interpret the matrix elements as being produced by an unknown kernel which operates on object pairs and we show that under mild assumptions these kernels correspond to dot products in some (unknown) feature space. Minimizing a bound for the generalization error of a linear classifier which has been obtained using covering numbers we derive an objective function for model selection according to the principle of structural risk minimization. The new objective function has the advantage that it allows the analysis of matrices which are not positive definite, and not even symmetric or square. We then consider the case that row objects are interpreted as features. We suggest an additional constraint, which imposes sparseness on the row objects and show, that the method can then be used for feature selection. Finally, we apply this method to data obtained from DNA microarrays, where “column ” objects correspond to samples, “row ” objects correspond to genes and matrix elements correspond to expression levels. Benchmarks are conducted using standard onegene classification and support vector machines and Knearest neighbors after standard feature selection. Our new method extracts a sparse set of genes and provides superior classification results. 1
Classification and Feature Selection on Matrix Data with Application to GeneExpression Analysis
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Sparse Representation in Szeg}o Kernels through Reproducing Kernel Hilbert Space Theory with Applications
"... Abstract. This paper discusses generalization bounds for complex data learning which serve as a theoretical foundation for complex support vector machine (SVM). Drawn on the generalization bounds, a complex SVM approach based on the Szego ̋ kernel of the Hardy space H2(D) is formulated. It is appli ..."
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Abstract. This paper discusses generalization bounds for complex data learning which serve as a theoretical foundation for complex support vector machine (SVM). Drawn on the generalization bounds, a complex SVM approach based on the Szego ̋ kernel of the Hardy space H2(D) is formulated. It is applied to the frequencydomain identification problem of discrete linear timeinvariant system (LTIS). Experiments show that the proposed algorithm is effective in applications.
Kernel Methods and Support Vector Machines
, 2009
"... The tutorial is intended to give a broad introduction to the kernel approach to pattern analysis. This will cover: • Why linear pattern functions? • Why kernel approach? • How to plug and play with the different components of a kernelbased pattern analysis system? Chicago/TTI Summer School, June 20 ..."
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The tutorial is intended to give a broad introduction to the kernel approach to pattern analysis. This will cover: • Why linear pattern functions? • Why kernel approach? • How to plug and play with the different components of a kernelbased pattern analysis system? Chicago/TTI Summer School, June 2009 1 What won’t be included: • Other approaches to Pattern Analysis • Complete History • Bayesian view of kernel methods • More recent developments