Robust Low-rank subspace segmentation with finite mixture noise. (September 2019) - Guo, Xianglin; Xie, Xingyu; Liu, Guangcan; Wei, Mingqiang; Wang, Jun
Highlights: The model first resorts to powerful and intrinsically flexible mixture of exponent power (MoEP) distribution to model complex noise in multiple subspace clustering context. The matrix variate elliptically contoured distribution is leveraged as a low-rank component prior. A practical algorithm termed MoEP-RSS infers the parameters of MoEP as well as the final clustering results. Abstract: Subspace segmentation or clustering remains a challenge of interest in computer vision when handling complex noise existing in high-dimensional data. Most of the current sparse representation or minimum-rank based techniques are constructed on ℓ1 -norm or ℓ2 -norm losses, which is sensitive to outliers. Finite mixture model, as a class of powerful and flexible tools for modeling complex noise, becomes a must. Among all the choices, exponential family mixture is extremely useful in practice due to its universal approximation ability for any continuous distribution and hence covers a broader scope of characteristics of noise distribution. Equipped with such a modeling idea, this paper focuses on the complex noise contaminated subspace clustering problem by using finite mixture of exponential power (MoEP) distributions. We then harness a penalized likelihood function to perform automatic model selection and hence avoid over-fitting. Moreover, we introduce a novel prior on the singular values of representation matrix, which leads to a novel penalty in our nonconvex and nonsmooth optimization. The parameters of the MoEP model can be estimated with a Maximum A Posteriori (MAP) method. Meanwhile, the subspace is computed with joint weighted ℓ p -norm and Schatten- q quasi-norm minimization. Both theoretical and experimental results show the effectiveness of our method.