Abstract book (pdf) - ICPR 2010

09:20-09:40, Paper WeAT4.2
Von Mises-Fisher Mean Shift for Clustering on a Hypersphere
Kobayashi, Takumi, Nat. Inst. of Advanced Industrial Science
Otsu, Nobuyuki, Nat. Inst. of Advanced Industrial Science
We propose a method of clustering sample vectors on a hypersphere. Sample vectors are normalized in many cases, especially
when applying kernel functions, and thus lie on a (unit) hypersphere. Considering the constraint of the hypersphere,
the proposed method utilizes the von Mises-Fisher distribution in the framework of mean shift. It is also extended to the
kernel-based clustering method via kernel tricks to cope with complex distributions. The algorithms of the proposed methods
are based on simple matrix calculations. In the experiments, including a practical motion clustering task, the proposed
methods produce favorable clustering results.
09:40-10:00, Paper WeAT4.3
Nonlinear Mappings for Generative Kernels on Latent Variable Models
Carli, Anna, Univ. of Verona
Bicego, Manuele, Univ. of Verona
Baldo, Sisto, Univ. of Verona
Murino, Vittorio, Univ. of Verona
Generative kernels have emerged in the last years as an effective method for mixing discriminative and generative approaches.
In particular, in this paper, we focus on kernels defined on generative models with latent variables (e.g. the states
in a Hidden Markov Model). The basic idea underlying these kernels is to compare objects, via a inner product, in a feature
space where the dimensions are related to the latent variables of the model. Here we propose to enhance these kernels via
a nonlinear normalization of the space, namely a nonlinear mapping of space dimensions able to exploit their discriminative
characteristics. In this paper we investigate three possible nonlinear mappings, for two HMM-based generative kernels,
testing them in different sequence classification problems, with really promising results.
10:00-10:20, Paper WeAT4.4
Multiple Kernel Learning with High Order Kernels
Wang, Shuhui, Chinese Acad. of Sciences
Jiang, Shuqiang, Chinese Acad. of Sciences
Huang, Qingming, Chinese Acad. of Sciences
Tian, Qi, Univ. of Texas at San Antonio
Previous Multiple Kernel Learning approaches (MKL) employ different kernels by their linear combination. Though some
improvements have been achieved over methods using single kernel, the advantages of employing multiple kernels for
machine learning are far from being fully developed. In this paper, we propose to use high order kernels to enhance the
learning of MKL when a set of original kernels are given. High order kernels are generated by the products of real power
of the original kernels. We incorporate the original kernels and high order kernels into a unified localized kernel logistic
regression model. To avoid over-fitting, we apply group LASSO regularization to the kernel coefficients of each training
sample. Experiments on image classification prove that our approach outperforms many of the existing MKL approaches.
10:20-10:40, Paper WeAT4.5
Kernel-Based Implicit Regularization of Structured Objects
Dupé, François-Xavier, GREYC
Bougleux, Sébastien, Univ. de Caen
Brun, Luc, ENSICAEN
Lezoray, Olivier, Univ. de Caen
Elmoataz, Abderrahim, Univ. de Caen
Weighted Graph regularization provides a rich framework that allows to regularize functions defined over the vertices of a weighted
graph. Until now, such a framework has been only defined for real or multivalued functions hereby restricting the regularization framework
to numerical data. On the other hand, several kernels have been defined on structured objects such as strings or graphs. Using definite
positive kernels, each original object is associated by the ``kernel trick’’ to one element of an Hilbert space. As a consequence, this
paper proposes to extend the weighted graph regularization framework to objects implicitly defined by their kernel hereby performing
the regularization within the Hilbert space associated to the kernel. This work opens the door to the regularization of structured objects.
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