Robust Linear Clustering with Least Squares Criterion and Its Application to Collaborative Filtering
Katsuhiro Honda, Nobukazu Sugiura, Hidetomo Ichihashi · Transactions of the Institute of Systems Control and Information Engineers · 2003
Non-linear extensions of Principal Component Analysis (PCA) have been developed for detecting the lower-dimensional representations of real world data sets.Fuzzy c-Varieties (FCV) is the linear fuzzy clustering algorithm that can be regarded as a Local PCA technique.However least squares techniques often fail to account for "outliers".This paper proposes a technique for making the FCV algorithm robust to intra-sample outliers.The objective function based on the lower rank approximation of the data matrix is minimized by a robust M-estimation algorithm that is similar to FCM-type iterative procedures.The new method is also useful for estimating missing values and a numerical experiment of Collaborative Filtering reveals an improvement in recommendation performance.1.