Online Multilinear Dictionary Learning

A method for online tensor dictionary learning is proposed. With the assumption of separable dictionaries, tensor contraction is used to diminish a $N$-way model of $\mathcal{O}\left(L^N\right)$ into a simple matrix equation of $\mathcal{O}\left(NL^2\right)$ with a real-time capability. To avoid numerical instability due to inversion of sparse matrix, a class of stochastic gradient with memory is formulated via a least-square solution to guarantee convergence and robustness. Both gradient descent with exact line search and Newton's method are discussed and realized. Extensions onto how to deal with bad initialization and outliers are also explained in detail. Experiments on two synthetic signals confirms an impressive performance of our proposed method.

• Publication year

  2017

• Venue

  arXiv: Learning

• Publication date

  2017-03-07

• Fields of study

  Mathematics, Computer Science

• Identifiers
  arXiv 1703.02492
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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