Component-wise robust linear fuzzy clustering for collaborative filtering Original Research Article

Automated collaborative filtering is a popular technique for reducing information overload and the task is to predict missing values in a data matrix. Extraction of local linear models is a useful technique for predicting the missing values. Linear models featuring local structures of the high-dimensional incomplete data set are estimated by a modified linear fuzzy clustering algorithm. Fuzzy c-varieties (FCV) is a linear fuzzy clustering algorithm that estimates local principal component vectors as the vectors spanning prototypes of clusters. Least squares techniques, however, often fail to account for “outliers”, which are common in real applications. In this paper, a technique for making the FCV algorithm robust to intra-sample outliers is proposed. 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. In numerical experiments, the diagnostic power of the filtering system is shown to be improved by predicting missing values using robust local linear models.