Joint Active Learning with Feature Selection via CUR Matrix Decomposition
This addresses the challenge of noisy, high-dimensional data in scenarios with few or no labeled samples, offering a practical solution for unsupervised learning tasks.
The paper tackles the problem of joint sample and feature selection in unsupervised learning by proposing a framework based on CUR matrix decomposition, which achieves efficient one-shot selection without iterative labeling and demonstrates efficacy on public datasets compared to state-of-the-art methods.
This paper presents an unsupervised learning approach for simultaneous sample and feature selection, which is in contrast to existing works which mainly tackle these two problems separately. In fact the two tasks are often interleaved with each other: noisy and high-dimensional features will bring adverse effect on sample selection, while informative or representative samples will be beneficial to feature selection. Specifically, we propose a framework to jointly conduct active learning and feature selection based on the CUR matrix decomposition. From the data reconstruction perspective, both the selected samples and features can best approximate the original dataset respectively, such that the selected samples characterized by the features are highly representative. In particular, our method runs in one-shot without the procedure of iterative sample selection for progressive labeling. Thus, our model is especially suitable when there are few labeled samples or even in the absence of supervision, which is a particular challenge for existing methods. As the joint learning problem is NP-hard, the proposed formulation involves a convex but non-smooth optimization problem. We solve it efficiently by an iterative algorithm, and prove its global convergence. Experimental results on publicly available datasets corroborate the efficacy of our method compared with the state-of-the-art.