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Abstract:
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The third-order Tucker decomposition decomposes a three-dimensional tensor into a product of two orthogonal matrices and one smaller core tensor. This decomposition accounts for the dependency structure between and within matrix observations concatenated into a tensor. This model can be used to analyze dependent images, such as medical images taken from the same patient over multiple time periods or ripped frames from video data. The problem of inference in this framework has yet to be solved. In order to develop our inferential procedures, we assume our data to follow a tensor normal distribution. We introduce likelihood-ratio tests, score tests, and regression-based test for the one-, two-, and k-population problems and derive the distributions of the resulting test statistics. Practical implementation of the method will be illustrated.
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