Selective Multiple Power Iteration: from Tensor PCA to gradient-based exploration of landscapes

no code implementations • 23 Dec 2021 • Mohamed Ouerfelli, Mohamed Tamaazousti, Vincent Rivasseau

Various numerical simulations for $k=3$ in the conventionally considered range $n \leq 1000$ show that the experimental performances of SMPI improve drastically upon existent algorithms and becomes comparable to the theoretical optimal recovery.

Tensor Decomposition

A new framework for tensor PCA based on trace invariants

no code implementations • 1 Jan 2021 • Mohamed Ouerfelli, Mohamed Tamaazousti, Vincent Rivasseau

We consider the Principal Component Analysis (PCA) problem for tensors $T \in (\mathbb{R}^n)^{\otimes k}$ of large dimension $n$ and of arbitrary order $k\geq 3$.