Semiring Rank Matrix Factorization

Abstract

Abstract-Rank data, in which each row is a complete or partial ranking of available items (columns), is ubiquitous. Among others, it can be used to represent preferences of users, levels of gene expression, and outcomes of sports events. It can have many types of patterns, among which consistent rankings of a subset of the items in multiple rows, and multiple rows that rank the same subset of the items highly. In this article, we show that the problems of finding such patterns can be formulated within a single generic framework that is based on the concept of semiring matrix factorisation. In this framework, we employ the max-product semiring rather than the plus-product semiring common in traditional linear algebra. We apply this semiring matrix factorisation framework on two tasks: sparse rank matrix factorisation and rank matrix tiling. Experiments on both synthetic and real world datasets show that the framework is capable of discovering different types of structure as well as obtaining high quality solutions.

Aplikasi Dekomposisi Rank Pada Pembentukan Invers Moore-Penrose Matriks Atas Aljabar Max-Plus Tersimetri

“…Penelitian dekomposisi rank juga dikembangkan pada objek kajian semiring. Beberapa penelitian terkait dekomposisi rank pada matriks atas semiring antara lain pada (Le Van et al, 2015).…”