Abstract book (pdf) - ICPR 2010

13:50-14:10, Paper TuBT4.2
Localized Multiple Kernel Regression
Gönen, Mehmet, Bogazici Univ.
Alpaydin, Ethem, Bogazici Univ.
Multiple kernel learning (MKL) uses a weighted combination of kernels where the weight of each kernel is optimized
during training. However, MKL assigns the same weight to a kernel over the whole input space. Our main objective is the
formulation of the localized multiple kernel learning (LMKL) framework that allows kernels to be combined with different
weights in different regions of the input space by using a gating model. In this paper, we apply the LMKL framework to
regression estimation and derive a learning algorithm for this extension. Canonical support vector regression may over fit
unless the kernel parameters are selected appropriately; we see that even if provide more kernels than necessary, LMKL
uses only as many as needed and does not overfit due to its inherent regularization.
14:10-14:30, Paper TuBT4.3
Probabilistic Clustering using the Baum-Eagon Inequality
Rota Bulo’, Samuel, Univ. Ca’ Foscari di Venezia
Pelillo, Marcello, Ca’ Foscari Univ.
The paper introduces a framework for clustering data objects in a similarity-based context. The aim is to cluster objects
into a given number of classes without imposing a hard partition, but allowing for a soft assignment of objects to clusters.
Our approach uses the assumption that similarities reflect the likelihood of the objects to be in a same class in order to
derive a probabilistic model for estimating the unknown cluster assignments. This leads to a polynomial optimization in
probability domain, which is tackled by means of a result due to Baum and Eagon. Experiments on both synthetic and real
standard datasets show the effectiveness of our approach.
14:30-14:50, Paper TuBT4.4
Ensemble Clustering via Random Walker Consensus Strategy
Abdala, Daniel Duarte, Univ. of Münster
Wattuya, Pakaket, Univ. of Münster
Jiang, Xiaoyi, Univ. of Münster
In this paper we present the adaptation of a random walker algorithm for combination of image segmentations to work
with clustering problems. In order to achieve it, we pre-process the ensemble of clusterings to generate its graph representation.
We show experimentally that a very small neighborhood will produce similar results if compared with larger choices.
This fact alone improves the computational time needed to produce the final consensual clustering. We also present an experimental
comparison between our results against other graph based and well known combination clustering methods in
order to assess the quality of this approach.
14:50-15:10, Paper TuBT4.5
Bhattacharyya Clustering with Applications to Mixture Simplifications
Nielsen, Frank, Ecole Polytechnique/SONY CLS
Boltz, Sylvain, Ecole Polytechnique/SONY CLS
Schwander, Olivier, Ecole Polytechnique/SONY CLS
Bhattacharrya distance (BD) is a widely used distance in statistics to compare probability density functions (PDFs). It has
shown strong statistical properties (in terms of Bayes error) and it relates to Fisher information. It has also practical advantages,
since it strongly relates on measuring the overlap of the supports of the PDFs. Unfortunately, even with common
parametric models on PDFs, few closed-form formulas are known. Moreover, the BD centroid estimation was limited to
univariate gaussian PDFs in the literature and no convergence guarantees were provided. In this paper, we propose a
closed-form formula for BD on a general class of parametric distributions named exponential families. We show that the
BD is a Burbea-Rao divergence for the log normalizer of the exponential family. We propose an efficient iterative scheme
to compute a BD centroid on exponential families. Finally, these results allow us to define a Bhattacharrya hierarchical
clustering algorithms (BHC). It can be viewed as a generalization of k-means on BD. Results on image segmentation
shows the stability of the method.
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