Robust Linear Clustering with Least Squares Criterion and Its Application to Collaborative Filtering

Abstract

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.