Abstract:
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In this paper, we conduct multivariate functional data clustering in an unsupervised manner. Dimensions of high volume data are significantly reduced by using only partial multivariate functional principal components. The multivariate functional principal component analysis (MFPCA) enables us to transform multi-dimensional and continuously measured data into an orthonormal matrix, where each dimension in the original data can be expressed by corresponding columns in the transformed matrix. In this way, clustering techniques can be applied to the transformed matrix. In our study, we assume this transformed data follow a Gaussian mixture model with K distinct centers, and the covariance matrix is the same across all clusters. We use penalty based maximum likelihood to conduct clustering with automatic variable selection. In addition, grouped variable selection is considered in this study. Because principal scores belonging to the same original function should have the same tendency to be in or out for the variable selection procedure. An application of engineer system sensory data is studied. Model performances are evaluated in the simulation study.
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