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Abstract:
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Matrix valued data has become increasingly prevalent in many applications. Most of the existing clustering methods for this type of data are tailored to the mean model and do not account for the dependence structure of the features, which can be very informative, especially in high-dimensional settings. To extract the information from the dependence structure, we propose a new latent variable model for the features arranged in matrix form. Under this model, we further propose a class of hierarchical clustering algorithms using the difference of a weighted covariance matrix as the dissimilarity measure. Theoretically, we show that under mild conditions, our algorithm attains clustering consistency in the high-dimensional setting. To investigate how the weight affects the theoretical performance of our algorithm, we establish the minimax lower bound for clustering under our latent variable model and identify the minimax rate-optimal weight with respect to the magnitude of some cluster separation metric. The practical implementation of our algorithm with the optimal weight along with simulation results and applications to a real genomic dataset are also discussed.
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