Adaptive robust principal component analysis.

Robust Principal Component Analysis (RPCA) is a powerful tool in machine learning and data mining problems. However, in many real-world applications, RPCA is unable to well encode the intrinsic geometric structure of data, thereby failing to obtain the lowest rank representation from the corrupted data. To cope with this problem, most existing methods impose the smooth manifold, which is artificially constructed by the original data. This reduces the flexibility of algorithms. Moreover, the graph, which is artificially constructed by the corrupted data, is inexact and does not characterize the true intrinsic structure of real data. To tackle this problem, we propose an adaptive RPCA (ARPCA) to recover the clean data from the high-dimensional corrupted data. Our proposed model is advantageous due to: (1) The graph is adaptively constructed upon the clean data such that the system is more flexible. (2) Our model simultaneously learns both clean data and similarity matrix that determines the construction of graph. (3) The clean data has the lowest-rank structure that enforces to correct the corruptions. Extensive experiments on several datasets illustrate the effectiveness of our model for clustering and low-rank recovery tasks.