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Understanding the Tucker decomposition, and compressing tensor-valued data (with R code) | 0-fold Cross-Validation

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In many applications, data naturally form an n-way tensor with n > 2, rather than a “tidy” table. As mentioned in the beginning of my last blog post, a tensor is essentially a multi-dimensional array: a tensor of order one is a vector, which simply is a column of numbers, a tensor of order two is a matrix, which is basically numbers arranged in a rectangle, a tensor of order three looks like numbers arranged in rectangular box (or a cube, if all modes have the same dimension), an nth order (or n-way) tensor looks like numbers arranged in an n-hyperrectangle… you get the idea…

In many applications, data naturally form an n-way tensor with n > 2, rather than a “tidy” table. As mentioned in the beginning of my last blog post, a tensor is essentially a multi-dimensional array: a tensor of order one is a vector, which simply is a column of numbers, a tensor of order two is a matrix, which is basically numbers arranged in a rectangle, a tensor of order three looks like numbers arranged in rectangular box (or a cube, if all modes have the same dimension), an nth order (or n-way) tensor looks like numbers arranged in an n-hyperrectangle… you get the idea… In this…

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