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Various tensor decompositions use different arrangements of factors to explain multi-way data. Components from different decompositions can vary in the number of parameters. Allowing a model to contain components from different decompositions results in a combinatoric number of possible models. Model selection balances approximation error and the number of parameters, but due to the number of possible...
Analysis of high dimensional data in modern applications, such as neuroscience, text mining, spectral analysis, chemometrices naturally requires tensor decomposition methods. The Tucker decompositions allow us to extract hidden factors (component matrices) with different dimension in each mode, and investigate interactions among various modalities. The alternating least squares (ALS) algorithms have...
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