Unsupervised feature selection method based on dual manifold learning and dual spatial latent representation

In unsupervised feature selection, the intrinsic structural information of data is often ignored, and the interconnection relationships between data are often not fully utilized. This paper proposes an unsupervised feature selection method based on dual manifold learning and dual spatial latent representation to fully explore and utilize the inherent information in data. Firstly, the dual manifold learning utilizes the geometric structure of the data space to guide the learning of mapping relationships between high-dimensional data and low-dimensional representations and the final pseudo-label learning. The dual manifold learning makes the utilization of local structural information in the data space more complete. Secondly, the non-negative matrix factorization is performed on the dual graphs of the original data space graph and the data adjacency graph. And the decomposed matrix is used as the latent representation matrix of the data and final pseudo-label matrix. This can achieve a balance between semantic loss and noise interference. Finally, this article applies the ℓ_2,p-norm on the feature transformation matrix. The ℓ_2,p-norm is easier to optimize and can more flexibly obtain sparser solutions by adjusting p. The comprehensive experiment is conducted on 8 real datasets to test the effectiveness of our method and exhibits the capability of our method in identifying more discriminative features.