A general adaptive unsupervised feature selection with auto-weighting

Feature selection (FS) is essential in machine learning and data mining as it makes handling high-dimensional data more efficient and reliable. More attention has been paid to unsupervised feature selection (UFS) due to the extra resources required to obtain labels for data in the real world. Most of the existing embedded UFS utilize a sparse projection matrix for FS. However, this may introduce additional regularization terms, and it is difficult to control the sparsity of the projection matrix well. Moreover, such methods may seriously destroy the original feature structure in the embedding space. Instead, avoiding projecting the original data into the low-dimensional embedding space and identifying features directly from the raw features that perform well in the process of making the data show a distinct cluster structure is a feasible solution. Inspired by this, this paper proposes a model called A General Adaptive Unsupervised Feature Selection with Auto-weighting (GAWFS), which utilizes two techniques, non-negative matrix factorization, and adaptive graph learning, to simulate the process of dividing data into clusters, and identifies the features that are most discriminative in the clustering process by a feature weighting matrix $\Theta$. Since the weighting matrix is sparse, it also plays the role of FS or a filter. Finally, experiments comparing GAWFS with several state-of-the-art UFS methods on synthetic datasets and real-world datasets are conducted, and the results demonstrate the superiority of the GAWFS.