Seeing All From a Few: $\ell_{1}$ -Norm-Induced Discriminative Prototype Selection

Prototype selection aims to remove redundancy and irrelevance from large-scale data by selecting an informative subset, which makes it possible to see all data from a few prototypes. However, due to the outliers and uncertain distribution of the data, the selected prototypes are generally less representative and diversified. To alleviate this issue, we develop, in this paper, a ℓ
₁
-norm-induced discriminative prototype selection model (ℓ
₁
-ProSe). Inspired by the good performance of sparse representation, the sparsity property of data is rationally exploited in the formulated model. Meanwhile, to characterize the pairwise similarity in the learned sparse representation space, a more promising ℓ
₁
-norm metric is applied for robust selection instead of the popularly used Euclidean metric in previous works. Considering the convexity of the model to be solved, a composite block coordinate descent solver is presented with rigorous theoretical analysis on its convergence. Furthermore, we extend our model to support online prototype selection by using already obtained prototypes and newly arrived data. Experimental results on synthetic data sets and some applications such as video summarization, motion segmentation, and scene categorization demonstrate that the proposed method is considerably superior to the state-of-the-art methods in the prototype selection.