Abstract
Curve clustering is an important fundamental problem in biomedical applications involving clustering protein sequences or cell shapes in microscopy images. Existing model-based clustering techniques rely on simple probability models that are not generally valid for analyzing shapes of curves. In this chapter, we talk about an efficient Bayesian method to cluster curve data using a carefully chosen metric on the shape space. Rather than modeling the infinite-dimensional curves, we focus on modeling a summary statistic which is the inner product matrix obtained from the data. The inner-product matrix is modeled using a Wishart with parameters with carefully chosen hyperparameters which induce clustering and allow for automatic inference on the number of clusters. Posterior is sampled through an efficient Markov chain Monte Carlo procedure based on the Chinese restaurant process. This method is demonstrated on a variety of synthetic data and real data examples on protein structure analysis.
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Zhang, Z., Pati, D., Srivastava, A. (2015). Bayesian Shape Clustering. In: Mitra, R., Müller, P. (eds) Nonparametric Bayesian Inference in Biostatistics. Frontiers in Probability and the Statistical Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-19518-6_3
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DOI: https://doi.org/10.1007/978-3-319-19518-6_3
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