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Max-margin non-negative matrix factorization with flexible spatial constraints based on factor analysis

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Abstract

Non-negative matrix factorization (NMF) is a popular feature encoding method for image understanding due to its non-negative properties in representation, but the learnt basis images are not always local due to the lack of explicit constraints in its objective. Various algebraic or geometric local constraints are hence proposed to shape the behaviour of the original NMF. Such constraints are usually rigid in the sense that they have to be specified beforehand instead of learning from the data. In this paper, we propose a flexible spatial constraint method for NMF learning based on factor analysis. Particularly, to learn the local spatial structure of the images, we apply a series of transformations such as orthogonal rotation and thresholding to the factor loading matrix obtained through factor analysis. Then we map the transformed loading matrix into a Laplacian matrix and incorporate this into a max-margin non-negative matrix factorization framework as a penalty term, aiming to learn a representation space which is non-negative, discriminative and localstructure- preserving. We verify the feasibility and effectiveness of the proposed method on several real world datasets with encouraging results.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Dakun Liu & Xiaoyang Tan

Authors
  1. Dakun Liu
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  2. Xiaoyang Tan
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Corresponding author

Correspondence to Xiaoyang Tan.

Additional information

Dakun Liu received his BS and MS in applied mathematics in 2006 and 2009, respectively. He is now a PhD candidate at Nanjing University of Aeronautics and Astronautics, China. His research interests include computer vision, machine learning, etc.

Xiaoyang Tan received his PhD in machine learning from Nanjing University, China in 2005. He is a professor and PhD supervisor at Nanjing University of Aeronautics and Astronautics, China. His research interests include computer vision, machine learning, etc.

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Liu, D., Tan, X. Max-margin non-negative matrix factorization with flexible spatial constraints based on factor analysis. Front. Comput. Sci. 10, 302–316 (2016). https://doi.org/10.1007/s11704-015-4590-3

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