Supervised Multiview Feature Selection Exploring Homogeneity and Heterogeneity With $\ell_{1,2}$ -Norm and Automatic View Generation

It is useful and challenging to analyze and select object features of very high resolution (VHR) remote sensing imagery. The overwhelming majority of existing feature selection methods always concatenate all of the features into a long feature vector and then select features from the vector, ignoring the homogeneity and heterogeneity of underlying feature subspaces. In this paper, we propose a supervised multiview feature selection (SMFS) method. Unlike the existing multiview methods, SMFS requires no prior knowledge of the number of views, and is independent of a prefixed classifier. By utilizing homogeneity and heterogeneity of the data, SMFS employs affinity propagation to automatically decompose features into multiple disjoint and meaningful feature groups or views without any prior knowledge. A group or view consists of homogeneous features, describing a unique data characteristic. Different views represent heterogeneous data characteristics. Then, features are evaluated and selected based on joint ℓ
_1,2
-norm minimization of a loss function and a regularization term. Different from the popular ℓ
₂
,
₁
-norm, joint ℓ
_1,2
-norm enforces the intraview sparsity, instead of interview sparsity. Consequently, a view can be represented by a few representative features in each view, and the information of heterogeneous views can be well kept by the remaining representative features. The experimental results on four VHR satellite images attest to the effectiveness and practicability of SMFS in comparison with single-view algorithms. Furthermore, some discussions are conducted to give insights into homogeneity and heterogeneity of features.