Low-Rank Outlier-Robust Fuzzy Clustering With Adaptive Intrinsic Structure Preservation

Fuzzy clustering is an efficient tool for unsupervised data analysis, but its performance is often degraded by redundant information and outliers. To solve this issue for boosting clustering results, we propose a novel low-rank outlier-robust fuzzy clustering approach with adaptive instrinsic structure preservation (LORFC). In this method, a new low-rank feature space that contains the global components of raw data is dynamically learned for simultaneous fuzzy clustering joint feature selection, to reduce the influence of redundant information. In addition, the outliers are sufficiently extracted and removed from the low-rank features, to ensure robust clustering performance. Moreover, the local information is also embeded into this low-rank feature space by an adaptive graph, to thoroughly capture the intrinsic struture contained in data. Based on these strategies, LORFC is capable of achieving superior and reliable clustering performance, as it is not only immune to redundant information and outliers but also aware of the global joint local structure of data. LORFC is optimized by the alternative direction multiplier method (ADMM), and its temporal complexity and theoretical convergence are analyzed. In the comprehensive experiments conducted on twelve datasets, LORFC achieves better clustering results than several state-of-the-art fuzzy clustering methods in terms of clustering accuracy (CA) and normalized mutual information (NMI). Moreover, it also performs well in the test of handling extra outliers and feature selection.