Similarity Measures and Weighted Fuzzy C-Mean Clustering Algorithm

In this paper we study the fuzzy c-mean clustering algorithm combined with principal components method. Demonstratively analysis indicate that the new clustering method is well rather than some clustering algorithms. We also consider the validity of clustering method. Keywords—FCM algorithm, Principal Components Analysis, ClusI. FUZZY SET THEORETIC SIMILARITY MEASURES ONE of the most important issues in recommender systems research is computing similarity between users, and between items (products, events, services, etc.). This in turns highly depends on the appropriateness and reliability of the methods of representation. The set-theoretic, proximity-based and logic-based are the three classes of measures of similarity. In fuzzy set and possibility framework, similarity of users or items is computed based on the membership functions of the fuzzy sets associated with the users or item features. Based on the work of Cross and Sudkamp [1], those similarity measures [2] that are relevant to item recommendation application are adapted. For items Ij and Ik that are defined as {xi, μxi(Ij)), i = 1, 2, . . . , N} and {xi, μxi(Ik)), i = 1, 2, . . . , N}, a similarity measure between Ij and Ik is denoted by S(Ik, Ij), and the different similarity measures are defined as S1(Ik, Ij) = ∑ i min(μxi(Ik), μxi(Ij)) ∑ i max(μxi(Ik), μxi(Ij)) , (1) S2(Ik, Ij) = ∑ i μxi(Ik)μxi(Ij) √ ∑ i (μxi(Ik)) 2√∑ i (μxi(Ij))) 2 , (2) S3(Ik, Ij) = 1− d2(Ik, Ij) max i {μxi(Ik), μxi(Ij)} , (3) S4(Ik, Ij) = 1− 2 ZIk + ZIj d2(Ik, Ij) 2 , (4) where d2(Ik, Ij) = √