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Robust Kernel Methods in Clustering and Dimensionality Reduction Problems

In this report we propose robust methods for kernel K-means clustering and kernel Principal component analysis (PCA). Often these methods tend to get sensitive towards outliers because of the use of ML estimators. Here we replace these estimators with robust M-estimators (Huber’s), and thus make the methods more robust towards outliers. These robust versions can also be applied to non-convex clustering and non-linear PCA by using inner product kernels. The usual setup for K-means clustering and PCA are given below: