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Model-based hierarchical clustering with Bregman divergences and Fishers mixture model: application to depth image analysis

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Abstract

Model-based clustering is a method that clusters data with an assumption of a statistical model structure. In this paper, we propose a novel model-based hierarchical clustering method for a finite statistical mixture model based on the Fisher distribution. The main foci of the proposed method are: (a) provide efficient solution to estimate the parameters of a Fisher mixture model (FMM); (b) generate a hierarchy of FMMs and (c) select the optimal model. To this aim, we develop a Bregman soft clustering method for FMM. Our model estimation strategy exploits Bregman divergence and hierarchical agglomerative clustering. Whereas, our model selection strategy comprises a parsimony-based approach and an evaluation graph-based approach. We empirically validate our proposed method by applying it on simulated data. Next, we apply the method on real data to perform depth image analysis. We demonstrate that the proposed clustering method can be used as a potential tool for unsupervised depth image analysis.

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Notes

  1. The bijection is expressed as: \(f(x|\theta )=\text {exp}(-D_{G}(t(x),\eta ))J_{G}(x)\) where \(J_{G}\) is a uniquely determined function. For more details, please see Theorem 3 of Banerjee et al. (2005b).

  2. In order to compare different methods, we used MATLAB implementation provided either by the authors (SPKM and soft-MoVMF) or by standard toolbox (GMM). For the KMDR, we used the available R package skmeans (Buchta et al. 2012).

  3. available at: http://cs.nyu.edu/~silberman/datasets/nyu_depth_v2.html

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Acknowledgments

This work has been supported by the research Grants from the ARC6 of région Rhône-Alpes, France.

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  1. Laboratoire Hubert Curien UMR CNRS 5516 - Université Jean Monnet, Saint Etienne, France

    Md. Abul Hasnat, Olivier Alata & Alain Trémeau

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  1. Md. Abul Hasnat
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  2. Olivier Alata
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  3. Alain Trémeau
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Correspondence to Md. Abul Hasnat.

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Hasnat, M.A., Alata, O. & Trémeau, A. Model-based hierarchical clustering with Bregman divergences and Fishers mixture model: application to depth image analysis. Stat Comput 26, 861–880 (2016). https://doi.org/10.1007/s11222-015-9576-3

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