Joint sparse matrix regression and nonnegative spectral analysis for two-dimensional unsupervised feature selection

Highlights：

• We propose a novel two-dimensional unsupervised feature selection model to directly conduct the feature selection on the matrix data. For sparse matrix regression under unsupervised case, the key point is to connect the matrix and its cluster label. In this work, we utilize a nonnegative spectral clustering to compute a cluster label matrix. To integrate the merits of both sparse matrix regression and nonnegative spectral clustering, we joint these two techniques as a whole optimization model for feature selection.

• Our JSMRNS extends the SMR model to its unsupervised case. Although JSMRNS is the combination of sparse matrix regression and nonnegative spectral clustering, our JSMRNS can be viewed as the two-dimensional extension of the NDFS model through theoretical analysis, which ensures that our JSMRNS works. Moreover, in certain situation, JSMRNS can approximate the vector-based regression model, i.e., NDFS.

• We devise an efficient optimization strategy to solve this joint sparse matrix regression and nonnegative spectral analysis optimization problem. Some theoretical discussions are presented to show the convergence behavior and computational complexity of the optimization strategy. Moreover, we give the detailed discussions to compare with the subspace learning and some relevant models. Extensive experimental results also confirm the effectiveness of our proposed method.