3,856 research outputs found
A survey of kernel and spectral methods for clustering
Clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines. The focus of this paper is the partitioning clustering problem with a special interest in two recent approaches: kernel and spectral methods. The aim of this paper is to present a survey of kernel and spectral clustering methods, two approaches able to produce nonlinear separating hypersurfaces between clusters. The presented kernel clustering methods are the kernel version of many classical clustering algorithms, e.g., K-means, SOM and neural gas. Spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized. An explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation. Besides, fuzzy kernel clustering methods are presented as extensions of kernel K-means clustering algorithm. (C) 2007 Pattem Recognition Society. Published by Elsevier Ltd. All rights reserved
Hierarchically Clustered Adaptive Quantization CMAC and Its Learning Convergence
No abstract availabl
Fast Color Quantization Using Weighted Sort-Means Clustering
Color quantization is an important operation with numerous applications in
graphics and image processing. Most quantization methods are essentially based
on data clustering algorithms. However, despite its popularity as a general
purpose clustering algorithm, k-means has not received much respect in the
color quantization literature because of its high computational requirements
and sensitivity to initialization. In this paper, a fast color quantization
method based on k-means is presented. The method involves several modifications
to the conventional (batch) k-means algorithm including data reduction, sample
weighting, and the use of triangle inequality to speed up the nearest neighbor
search. Experiments on a diverse set of images demonstrate that, with the
proposed modifications, k-means becomes very competitive with state-of-the-art
color quantization methods in terms of both effectiveness and efficiency.Comment: 30 pages, 2 figures, 4 table
Local feature weighting in nearest prototype classification
The distance metric is the corner stone of nearest neighbor (NN)-based methods, and therefore, of nearest prototype (NP) algorithms. That is because they classify depending on the similarity of the data. When the data is characterized by a set of features which may contribute to the classification task in different levels, feature weighting or selection is required, sometimes in a local sense. However, local weighting is typically restricted to NN approaches. In this paper, we introduce local feature weighting (LFW) in NP classification. LFW provides each prototype its own weight vector, opposite to typical global weighting methods found in the NP literature, where all the prototypes share the same one. Providing each prototype its own weight vector has a novel effect in the borders of the Voronoi regions generated: They become nonlinear. We have integrated LFW with a previously developed evolutionary nearest prototype classifier (ENPC). The experiments performed both in artificial and real data sets demonstrate that the resulting algorithm that we call LFW in nearest prototype classification (LFW-NPC) avoids overfitting on training data in domains where the features may have different contribution to the classification task in different areas of the feature space. This generalization capability is also reflected in automatically obtaining an accurate and reduced set of prototypes.Publicad
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