Exponential Fuzzy C-Means for Collaborative Filtering

Collaborative filtering(CF) is one of the most popular techniques behind the success of recommendation system.It predicts the interest of users by collecting information from past users who have the same opinions.The most popular approaches used in CF research area are Matrix factorization methods such as SVD.However,many wellknown recommendation systems do not use this method but still stick with Neighborhood models because of simplicity and explainability.There are some concerns that limit neighborhood models to achieve higher prediction accuracy.To address these concerns,we propose a new exponential fuzzy clustering(XFCM) algorithm by reformulating the clustering’s objective function with an exponential equation in order to improve the method for membership assignment.The proposed method assigns data to the clusters by aggressively excluding irrelevant data,which is better than other fuzzy C-means(FCM) variants.The experiments show that XFCM-based CF improved 6.9% over item-based method and 3.0% over SVD in terms of mean absolute error for 100 K and 1 M MovieLens dataset.     

Possibilistic Exponential Fuzzy Clustering

Generally, abnormal points (noise and outliers) cause cluster analysis to produce low accuracy especially in fuzzy clustering. These data not only stay in clusters but also deviate the centroids from their true positions. Traditional fuzzy clustering like Fuzzy C-Means (FCM) always assigns data to all clusters which is not reasonable in some circumstances. By reformulating objective function in exponential equation, the algorithm aggressively selects data into the clusters. However noisy data and outliers cannot be properly handled by clustering process therefore they are forced to be included in a cluster because of a general probabilistic constraint that the sum of the membership degrees across all clusters is one. In order to improve this weakness, possibilistic approach relaxes this condition to improve membership assignment. Nevertheless, possibilistic clustering algorithms generally suffer from coincident clusters because their membership equations ignore the distance to other clusters. Although there are some possibilistic clustering approaches that do not generate coincident clusters, most of them require the right combination of multiple parameters for the algorithms to work. In this paper, we theoretically study Possibilistic Exponential Fuzzy Clustering (PXFCM) that integrates possibilistic approach with exponential fuzzy clustering. PXFCM has only one parameter and not only partitions the data but also filters noisy data or detects them as outliers. The comprehensive experiments show that PXFCM produces high accuracy in both clustering results and outlier detection without generating coincident problems.