Managing Data From Knowledge Bases: Querying and Extraction by Wei Emma Zhang & Quan Z. Sheng

Author:Wei Emma Zhang & Quan Z. Sheng
Language: eng
Format: epub
ISBN: 9783319949352
Publisher: Springer International Publishing

4.1 Overview of Clustering with Non-negative Matrix Factorization

Given a matrix, Non-negative Matrix Factorization (NMF) aims to find two non-negative factor matrices whose product approximates that matrix. This enhances the interpretability initiated by Paatero and Tapper [134] as Positive Matrix Factorization and popularized by Lee and Seung [130]. NMF has enjoyed much success in text mining [135], image processing [136], recommendation systems [137] and many other areas, and has attracted much theoretical and practical attention.

Orthogonal NMF (ONMF), first introduced by Ding et al. [138], is a variant of NMF with an additional orthogonal constraint on one of the factor matrices. Without loss of generality, the problem can be written as follows:

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