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info.json
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{
"abstract": "Cluster analysis by nonnegative low-rank approximations has experienced a remarkable progress in the past decade. However, the majority of such approximation approaches are still restricted to nonnegative matrix factorization (NMF) and suffer from the following two drawbacks: 1) they are unable to produce balanced partitions for large-scale manifold data which are common in real-world clustering tasks; 2) most existing NMF-type clustering methods cannot automatically determine the number of clusters. We propose a new low-rank learning method to address these two problems, which is beyond matrix factorization. Our method approximately decomposes a sparse input similarity in a normalized way and its objective can be used to learn both cluster assignments and the number of clusters. For efficient optimization, we use a relaxed formulation based on Data- Cluster-Data random walk, which is also shown to be equivalent to low-rank factorization of the doubly-stochastically normalized cluster incidence matrix. The probabilistic cluster assignments can thus be learned with a multiplicative majorization-minimization algorithm. Experimental results show that the new method is more accurate both in terms of clustering large-scale manifold data sets and of selecting the number of clusters.",
"authors": [
"Zhirong Yang",
"Jukka Cor",
"er",
"Erkki Oja"
],
"id": "15-549",
"issue": 187,
"pages": [
1,
25
],
"title": "Low-Rank Doubly Stochastic Matrix Decomposition for Cluster Analysis",
"volume": 17,
"year": 2016
}