Improving projected fuzzy K-means clustering via robust learning

Fuzzy K-Means clustering has been an attractive research area for many multimedia tasks. Due to the interference of the noise and outliers, the performance of fuzzy K-Means clustering has been limited. In this paper, a projected fuzzy K-Means clustering method, referred to as Robust Projected Fuzzy K-Means (RPFKM) is proposed as a response to such a challenge. RPFKM improves fuzzy K-Means clustering in three perspectives. First, unlike existing fuzzy K-Means algorithms where the clustering process is conducted in the original space, RPFKM learns the fuzzy membership relationship between samples and prototypes in the low-dimensional space to eliminate the influence of the noise and irrelevant features. Second, it employs the ℓ₂₁ norm to reduce the contribution of outliers to the learning of prototypes. Third, it also considers the sensitivity of fuzzy clustering to the number of reduced dimensions, and the reconstruction term is introduced to hold the main energy of the original data. Furthermore, an iterative re-weighted algorithm is developed to solve the proposed method. The evaluation results of our proposed method and the state-of-the-art methods on real-world and synthetic data sets show the effectiveness and efficiency of our approach.