Abstract
Most existing clustering algorithms are slow for dividing a large dataset into a large number of clusters. In this paper, we propose a truncated FCM algorithm to address this problem. The main idea behind our proposed algorithm is to keep only a small number of cluster centers during the iterative process of the FCM algorithm. Our numerical experiments on both synthetic and real datasets show that the proposed algorithm is much faster than the original FCM algorithm and the accuracy is comparable to that of the original FCM algorithm.
Highlights
Data clustering refers to a process of dividing a set of items into homogeneous groups or clusters such that items in the same cluster are similar to each other and items from different clusters are distinct [10, 1]
Since we know the labels of the data points of the two synthetic datasets, we use the corrected Rand index [8, 14, 15, 16] to measure the accuracy of the clustering algorithms
As we mentioned in the introduction section of this article, data clustering was used to divide a large portfolio of variable annuity contracts into hundreds of clusters in order to find representative contracts for metamodeling [11, 13]
Summary
Data clustering refers to a process of dividing a set of items into homogeneous groups or clusters such that items in the same cluster are similar to each other and items from different clusters are distinct [10, 1]. In the TFCM algorithm, a subset of the full fuzzy partition matrix is stored and the number of distance calculations at each iteration is reduced. The standard FCM algorithm with the initial cluster centers obtained from the first phase is applied to partition the whole dataset. The FCM algorithm with the cluster centers obtained from the first phase is applied to partition the original dataset. [23] proposed a modified version of the FCM algorithm by eliminating the need to store the fuzzy partition matrix U. We propose the truncated fuzzy c-means algorithm to approximate the FCM algorithm when the desired number of clusters is large. The fuzzy partition matrix U ∈ UT that minimizes the objective function (4) is given by uil =. We can obtain the optimal weights given in Equation (6) by solving the equations obtained by taking derivatives of Pi(ui, λ, Ii) with respect to λ and uil for l ∈ Ii and equating the derivatives to zero
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