@inproceedings{f714ed84c1874c3987911eb3dc0f7c0a,
title = "Geometrical formulation of the nonnegative matrix factorization",
abstract = "Nonnegative matrix factorization (NMF) has many applications as a tool for dimension reduction. In this paper, we reformulate the NMF from an information geometrical viewpoint. We show that a conventional optimization criterion is not geometrically natural, thus we propose to use more natural criterion. By this formulation, we can apply a geometrical algorithm based on the Pythagorean theorem. We also show the algorithm can improve the existing algorithm through numerical experiments.",
keywords = "Dimension reduction, Information geometry, Topic model",
author = "Shotaro Akaho and Hideitsu Hino and Neneka Nara and Noboru Murata",
year = "2018",
month = jan,
day = "1",
doi = "10.1007/978-3-030-04182-3_46",
language = "English",
isbn = "9783030041816",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer-Verlag",
pages = "525--534",
editor = "Long Cheng and Seiichi Ozawa and Leung, {Andrew Chi Sing}",
booktitle = "Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings",
note = "25th International Conference on Neural Information Processing, ICONIP 2018 ; Conference date: 13-12-2018 Through 16-12-2018",
}