紀要論文

行列補完のためのニューラルネットワークによる局所低ランク近似

Neural Network based on Locally Low Rank Approximation for Matrix Completion

jpn

24321192

https://doi.org/10.15002/00025258

法政大学大学院情報科学研究科

法政大学大学院紀要. 情報科学研究科編

17

1

6

2022-03-24

Version of Record

This paper deals with matrix completion when each column vector belongs to a low-dimensional manifold. One of the most common matrix completion methods is the matrix rank minimization method. The completion is achieved by solving an optimization problem with the matrix rank as the objective function, but the optimization with the objective function is NP-hard. Many relaxation problems using alternative functions have been proposed, but the estimation accuracy deteriorates when the data belong to a low-dimensional manifold. Recently, GAIN (Generative Adversarial Imputation Net), a matrix completion method based on machine learning, has been proposed as a solution to the matrix problem when the data belong to a low-dimensional manifold, but it is a simple three-layer neural network method, and high completion accuracy cannot be expected when the target manifold is complex or has a high dimensionality. This paper proposes an architecture for matrix completion based on clustering and projection, taking advantage of the fact that any manifold can be locally approximated in a low-dimensional linear space. Furthermore, an activation function is applied to the architecture to improve the accuracy. Numerical simulations demonstrate the effectiveness of the proposed method.

Article

AA12746425