非负矩阵分解
聚类分析
正交性
约束(计算机辅助设计)
因子(编程语言)
因式分解
矩阵分解
计算机科学
人工智能
光学(聚焦)
模式识别(心理学)
口译(哲学)
基质(化学分析)
数学
算法
特征向量
几何学
程序设计语言
材料科学
复合材料
物理
光学
量子力学
作者
Chris Ding,Tao Li,Wei Peng,Haesun Park
标识
DOI:10.1145/1150402.1150420
摘要
Currently, most research on nonnegative matrix factorization (NMF)focus on 2-factor $X=FG^T$ factorization. We provide a systematicanalysis of 3-factor $X=FSG^T$ NMF. While it unconstrained 3-factor NMF is equivalent to it unconstrained 2-factor NMF, itconstrained 3-factor NMF brings new features to it constrained 2-factor NMF. We study the orthogonality constraint because it leadsto rigorous clustering interpretation. We provide new rules for updating $F,S, G$ and prove the convergenceof these algorithms. Experiments on 5 datasets and a real world casestudy are performed to show the capability of bi-orthogonal 3-factorNMF on simultaneously clustering rows and columns of the input datamatrix. We provide a new approach of evaluating the quality ofclustering on words using class aggregate distribution andmulti-peak distribution. We also provide an overview of various NMF extensions andexamine their relationships.
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