Symmetric Nonnegative Matrix Factorization: Algorithms and Applications to Probabilistic Clustering
Symmetric Nonnegative Matrix Factorization: Algorithms and Applications to Probabilistic Clustering
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对称非负矩阵分解：概率聚类的算法和应用
DOI：
10.1109/tnn.2011.2172457
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发表时间：
2011-12-01
影响因子：
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通讯作者：
Cichocki, Andrzej
中科院分区：
文献类型：
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作者：
He, Zhaoshui;Xie, Shengli;Cichocki, Andrzej
非负矩阵分解（NMF）是一种无监督学习方法，广泛应用于图像处理和文档语义分析等领域。本文主要研究对称NMF (SNMF)，它是NMF分解的一种特例。针对这一问题，提出了3种直接使用3级基本线性代数子程序的并行乘法更新算法。首先，通过最小化欧氏距离，提出了一种乘法更新算法，并证明了该算法在温和条件下的收敛性。在此基础上，我们进一步提出了另外两种快速并行算法：α-SNMF和β -SNMF算法。所有这些都很容易实现。这些算法被应用于概率聚类。我们证明了它们在面部图像聚类、文档分类和基因表达模式聚类方面的有效性。
Nonnegative matrix factorization (NMF) is an unsupervised learning method useful in various applications including image processing and semantic analysis of documents. This paper focuses on symmetric NMF (SNMF), which is a special case of NMF decomposition. Three parallel multiplicative update algorithms using level 3 basic linear algebra subprograms directly are developed for this problem. First, by minimizing the Euclidean distance, a multiplicative update algorithm is proposed, and its convergence under mild conditions is proved. Based on it, we further propose another two fast parallel methods: α-SNMF and β -SNMF algorithms. All of them are easy to implement. These algorithms are applied to probabilistic clustering. We demonstrate their effectiveness for facial image clustering, document categorization, and pattern clustering in gene expression.