Multi-Manifold Concept Factorization for Data Clustering
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Ping Li,Jiajun Bu,Deng Cai. Multi-Manifold Concept Factorization for Data Clustering. International Journal of Software and Informatics, 2013,7(3):407~418
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Fund:This work is sponsored by National Basic Research Program of China (2011CB302206) and the Fundamental Research Funds for the Central Universities (2013FZA5012).
Abstract:Clustering plays an important role in many fields, such as pattern recognition and data mining. Its goal is to group the collected data points into their respective clusters. To this end, a number of matrix factorization based methods have been developed to obtain satisfying clustering results by extracting the latent concepts in the data, e.g., concept factorization (CF) and locally consistent concept factorization (LCCF). LCCF takes into account the local manifold structure of the data, but it is nontrivial to estimate the intrinsic manifold, reflecting the true data structure. To address this issue, we in this paper present a novel method called Multi-Manifold Concept Factorization (MMCF) to derive more promising clustering performance. Specifically, we assume the intrinsic manifold lies in a convex hull of some predefined candidate manifolds. The basic idea is to learn a convex combination of a group of candidate manifolds, which is utilized to approximate the intrinsic manifold of the data. In this way, the low-dimensional data representation derived from MMCF is able to better preserve the locally geometrical structure of the data. To optimize the objective function, we develop an alternating algorithm and learn the manifold coefficients using the entropic mirror descent algorithm. The effectiveness of the proposed approach has been demonstrated through a set of evaluations on several real-world data sets.
keywords:concept factorization  multi-manifold learning  locally geometrical structure  data clustering
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