This is a note on tensor decomposition.

Motivation: The Rotation Problem

Tensor Decomposition

\[T=\sum_{i=1}^r u^{(i)}\otimes v^{(i)}\otimes w^{(i)}\]

Jennrich’s Algorithm

Guarantees for Jennrich’s Algorithm can be easily founded by the perburbation bounds Chap 3.4.

Applications

Where can we apply the tensor decomposition?

Phylogenetic Trees and HMMs

Community Detection

Independent Component Analysis