Sparse robust subspace learning via boolean weight

Unsupervised feature selection is a hot topic in the field of machine learning, which is more convenient and important because it does not require labeled data. Currently, unsupervised feature selection algorithms based on ℓ_2,1-norm are very mature and have certain robustness to outliers, but they still have some problems that cannot be ignored. For example, the sparsity of ℓ_2,1-norm is not ideal, they cannot achieve row sparsity but only element sparsity. Second, fine-tuning meaningless regularization parameters increases cost and makes it easy to fall into suboptimal solutions. To release the above problems, we propose an unsupervised feature selection algorithm via Sparse Robust Subspace Learning (SRSL), which combines reconstruction term and variance term so that the model simultaneously preserves reconstruction information and enhances separability. What is more, using the ℓ_2,0-norm constraint on transformation matrix makes our model have a row-sparse property. In addition, we design the boolean weight so that the model not only eliminates outliers fundamentally to enhance robustness, but also achieves the effect of anomaly detection. To solve this NP-hard problem, we carefully design an optimization algorithm, which has strict convergence guarantees and obtains a closed-form solution. Experimental results on several real-world datasets demonstrate that our algorithm outperforms other comparison algorithms in both clustering and anomaly detection applications.