We present an alternative approach to decompose non-negative tensors, called many-body
approximation. Traditional decomposition methods assume low-rankness in the …

We propose a fast non-gradient-based method of rank-1 non-negative matrix factorization
(NMF) for missing data, called A1GM, that minimizes the KL divergence from an input matrix …

This paper presents a method to build explicit tensor-train (TT) representations. We show
that a wide class of tensors can be explicitly represented with sparse TT-cores, obtaining, in …

Although low-rank approximation of multi-dimensional arrays has been widely discussed in
linear algebra, its statistical properties remain unclear. In this paper, we use information …

We present an expectation-maximization (EM) based unified framework for non-negative
tensor decomposition that optimizes the Kullback-Leibler divergence. To avoid iterations in …

We propose a nonnegative tensor decomposition with focusing on the relationship between
the modes of tensors. Traditional decomposition methods assume low-rankness in the …

This study formulates dimensionality reduction of non-negative multi-dimensional arrays as
a convex problem. The key idea is to describe model manifolds containing dimensionality …

抄録 テンソルを低ランクテンソルで近似する低ランク分解は, 目的関数の非凸性の為に,
多くの場合で大域解を求めることが困難である. 本研究ではテンソル分解で用いられてきたランクの …

We propose an algorithm, called A1GM, for rank-1 non-negative matrix factorization with
missing values with respect to the KL divergence. A1GM is based on a closed formula …