Noise adaptive tensor train decomposition for low-rank embedding of noisy data

Abstract

Tensor decomposition is a multi-modal dimensionality reduction technique to support similarity search and retrieval. Yet, the decomposition process itself is expensive and subject to dimensionality curse. Tensor train decomposition is designed to avoid the explosion of intermediary data, which plagues other tensor decomposition techniques. However, many tensor decomposition schemes, including tensor train decomposition is sensitive to noise in the input data streams. While recent research has shown that it is possible to improve the resilience of the tensor decomposition process to noise and other forms of imperfections in the data by relying on probabilistic techniques, these techniques have a major deficiency: they treat the entire tensor uniformly, ignoring potential non-uniformities in the noise distribution. In this paper, we note that noise is rarely uniformly distributed in the data and propose a Noise-Profile Adaptive Tensor Train Decompositionmethod, which aims to tackle this challenge. $$\mathtt{NTTD}$$ leverages a model-based noise adaptive tensor train decomposition strategy: any rough priori knowledge about the noise profiles of the tensor enable us to develop a sample assignment strategy that best suits the noise distribution of the given tensor.