Tensor Networks:

Tensors are generalizations of vectors and matrices; a vector is a first-order tensor and a matrix is a second-order tensor. Most of the data around us are better represented with multiple orders to capture the correlations across different attributes. For example, a color image can be considered as a third-order tensor, two of the dimensions (rows and columns) being spatial, and the third being spectral (color), while a color video sequence can be considered as an order four tensor, time being the fourth dimension besides spatial and spectral. Similarly, a colored 3-D MRI image across time can be considered as an order five tensor. Exploiting additional structure leads to better embedding algorithms for subspace analysis and the elements needed for data completion (as shown alongside).