Applications of Tensor Decompositions

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This report explores how data structures known as tensors can be used to perform multidimensional data analysis. If a matrix can be thought of as a two-dimensional array, then a tensor can be thought of as a multi-dimensional array (with more than two dimensions). Tensor decompositions are algorithms and tools that can allow the user to directly perform analysis on this type of data. After explaining the basics of tensors, we work with two di erent three-dimensional data sets and decompose the tensors in order to provide analysis and interpretations of various aspects of the data.