Asymmetric clustering using the alpha–beta divergence

Olszewski, Dominik; Šter, Branko

doi:10.1016/j.patcog.2013.11.019

Cited by 23 publications

(12 citation statements)

References 26 publications

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“…Thus, it yields a fast hard/soft data partitioning technique with respect to mixed or symmetrized α-divergences. Recently, the advantage of clustering using α-divergences by tuning α in applications has been demonstrated in [18]. We thus expect the computationally fast mixed α-seeding with guaranteed performance to be useful in a growing number of applications.…”

Section: Discussionmentioning

confidence: 99%

“…We also consider clustering histograms by explicitly building the symmetrized α-centroids and end up with a variational k-means when the centroids are not available in closed-form, Finally, we investigate soft mixed α-clustering and discuss topics related to α-clustering. Note that clustering with respect to non-symmetrized α-divergences has been recently investigated independently in [18] and proven useful in several applications.…”

Section: Contributionsmentioning

confidence: 99%

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On Clustering Histograms with k-Means by Using Mixed α-Divergences

Nielsen

Nock

Амари

2014

Entropy

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Clustering sets of histograms has become popular thanks to the success of the generic method of bag-of-X used in text categorization and in visual categorization applications. In this paper, we investigate the use of a parametric family of distortion measures, called the α-divergences, for clustering histograms. Since it usually makes sense to deal with symmetric divergences in information retrieval systems, we symmetrize the α-divergences using the concept of mixed divergences. First, we present a novel extension of k-means clustering to mixed divergences. Second, we extend the k-means++ seeding to mixed α-divergences and report a guaranteed probabilistic bound. Finally, we describe a soft clustering technique for mixed α-divergences.

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Section: Discussionmentioning

confidence: 99%

Section: Contributionsmentioning

confidence: 99%

On Clustering Histograms with k-Means by Using Mixed α-Divergences

Nielsen

Nock

Амари

2014

Entropy

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“…In the paper [33], the usage of an asymmetric dissimilarity measure in centroid-based clustering is proposed. The dissimilarity employed is the Alpha-Beta divergence, which is asymmetrized using its parameters, and the degree of asymmetry of the Alpha-Betadivergence is computed on the basis of the within-cluster variances.…”

Section: Related Workmentioning

confidence: 99%

Asymmetric $$k$$ k -Means Clustering of the Asymmetric Self-Organizing Map

Olszewski

2015

Neural Process Lett

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An asymmetric approach to clustering of the asymmetric self-organizing map is proposed. The clustering is performed using an improved asymmetric version of the well-known k-means algorithm. The improved asymmetric k-means algorithm is the second proposal of this paper. As a result, we obtain a two-stage fully asymmetric data analysis technique. In this way, we maintain the methodological consistency of the both utilized methods, because they are both formulated in asymmetric versions, and consequently, they both properly adjust to asymmetric relationships in analyzed data. The results of our experiments on real data confirm the effectiveness of the proposed approach.

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“…They respectively belong to the three aforementioned categories. There are also many recent works focused on improving the performance of the classic clustering schemes [ 16 , 17 , 18 , 19 ], or exploiting novel clustering methods using different closeness measures [ 20 , 21 , 22 , 23 ].…”

Section: Introductionmentioning

confidence: 99%

A Clustering-Oriented Closeness Measure Based on Neighborhood Chain and Its Application in the Clustering Ensemble Framework Based on the Fusion of Different Closeness Measures

Liang

Han

2017

Sensors

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Closeness measures are crucial to clustering methods. In most traditional clustering methods, the closeness between data points or clusters is measured by the geometric distance alone. These metrics quantify the closeness only based on the concerned data points’ positions in the feature space, and they might cause problems when dealing with clustering tasks having arbitrary clusters shapes and different clusters densities. In this paper, we first propose a novel Closeness Measure between data points based on the Neighborhood Chain (CMNC). Instead of using geometric distances alone, CMNC measures the closeness between data points by quantifying the difficulty for one data point to reach another through a chain of neighbors. Furthermore, based on CMNC, we also propose a clustering ensemble framework that combines CMNC and geometric-distance-based closeness measures together in order to utilize both of their advantages. In this framework, the “bad data points” that are hard to cluster correctly are identified; then different closeness measures are applied to different types of data points to get the unified clustering results. With the fusion of different closeness measures, the framework can get not only better clustering results in complicated clustering tasks, but also higher efficiency.

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Asymmetric clustering using the alpha–beta divergence

Cited by 23 publications

References 26 publications

On Clustering Histograms with k-Means by Using Mixed α-Divergences

On Clustering Histograms with k-Means by Using Mixed α-Divergences

Asymmetric $$k$$ k -Means Clustering of the Asymmetric Self-Organizing Map

A Clustering-Oriented Closeness Measure Based on Neighborhood Chain and Its Application in the Clustering Ensemble Framework Based on the Fusion of Different Closeness Measures

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