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Multiview Partitioning via Tensor Methods
May 2013 (vol. 25 no. 5)
pp. 1056-1069
Xinhai Liu, Credit Reference Center & Financial Res. Inst., People's Bank of China, Beijing, China
Shuiwang Ji, Dept. of Comput. Sci., Old Dominion Univ., Norfolk, VA, USA
Wolfgang Glänzel, Dept. of MSI, Katholieke Univ. Leuven, Leuven, Belgium
B. De Moor, Dept. of Electr. Eng., Katholieke Univ. Leuven, Leuven, Belgium
Clustering by integrating multiview representations has become a crucial issue for knowledge discovery in heterogeneous environments. However, most prior approaches assume that the multiple representations share the same dimension, limiting their applicability to homogeneous environments. In this paper, we present a novel tensor-based framework for integrating heterogeneous multiview data in the context of spectral clustering. Our framework includes two novel formulations; that is multiview clustering based on the integration of the Frobenius-norm objective function (MC-FR-OI) and that based on matrix integration in the Frobenius-norm objective function (MC-FR-MI). We show that the solutions for both formulations can be computed by tensor decompositions. We evaluated our methods on synthetic data and two real-world data sets in comparison with baseline methods. Experimental results demonstrate that the proposed formulations are effective in integrating multiview data in heterogeneous environments.
Index Terms:
Tensile stress,Tin,Vectors,Clustering algorithms,Optimization,Kernel,Matrix decomposition,higher order orthogonal iteration,Multiview clustering,tensor decomposition,spectral clustering,multilinear singular value decomposition
Xinhai Liu, Shuiwang Ji, Wolfgang Glänzel, B. De Moor, "Multiview Partitioning via Tensor Methods," IEEE Transactions on Knowledge and Data Engineering, vol. 25, no. 5, pp. 1056-1069, May 2013, doi:10.1109/TKDE.2012.95
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