Journal
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
Volume 32, Issue 11, Pages 2006-2021Publisher
IEEE COMPUTER SOC
DOI: 10.1109/TPAMI.2010.15
Keywords
Multiway clustering; probabilistic clustering; hypergraph; parallel factor analysis (PARAFAC); model order selection; multiway array; higher order tensor; supersymmetric tensors; affinity arrays; enumeration of clusters; estimation of PARAFAC components; principal components enumeration
Funding
- National Natural Science Foundation of China [U0635001, 60874061]
- National Basic Research Program of China (973 Program) [2010CB731800]
- Fundamental Research Funds for Central Univresity, SCUT [x2xD2102070]
- CPSF [20070410237, 200801248]
- National Institute of Information and Communications Technology
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Recently, there has been a growing interest in multiway probabilistic clustering. Some efficient algorithms have been developed for this problem. However, not much attention has been paid on how to detect the number of clusters for the general n-way clustering (n >= 2). To fill this gap, this problem is investigated based on n-way algebraic theory in this paper. A simple, yet efficient, detection method is proposed by eigenvalue decomposition (EVD), which is easy to implement. We justify this method. In addition, its effectiveness is demonstrated by the experiments on both simulated and real-world data sets.
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