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As one of the most widely used clustering techniques, the fuzzy $k$ -means (FKM) assigns every data point to each cluster with a certain degree of membership. However, conventional FKM approach relies on the square data fitting term, which is sensitive to the outliers with ignoring the prior information. In this paper, we develop a novel and robust fuzzy $k$ -means clustering algorithm, namely, joint learning of fuzzy $k$ -means and nonnegative spectral clustering with side information. The proposed method combines fuzzy $k$ -means and nonnegative spectral clustering into a unified model, which can further exploit the prior knowledge of data pairs such that both the quality of affinity graph and the clustering performance can be improved. In addition, for the purpose of enhancing the robustness, the adaptive loss function is adopted in the objective function, since it smoothly interpolates between $\ell _{1}$ -norm and $\ell _{2}$ -norm. Finally, experimental results on benchmark datasets verify the effectiveness and the superiority of our clustering method. [ABSTRACT FROM AUTHOR]

Prior to pattern recognition, feature selection is often used to identify relevant features and discard irrelevant ones for obtaining improved analysis results. In this paper, we aim to develop an unsupervised feature ranking algorithm that evaluates features using discovered local coherent patterns, which are known as biclusters. The biclusters (viewed as submatrices) are discovered from a data matrix. These submatrices are used for scoring relevant features from two aspects, i.e., the interdependence of features and the separability of instances. The features are thereby ranked with respect to their accumulated scores from the total discovered biclusters before the pattern classification. Experimental results show that this proposed method can yield comparable or even better performance in comparison with the well-known Fisher score, Laplacian score, and variance score using three UCI data sets, well improve the results of gene expression data analysis using gene ontology annotation, and finally demonstrate its advantage of unsupervised feature ranking for high-dimensional data. [ABSTRACT FROM AUTHOR]