New Knowledge-Transmission Mechanisms Based Horizontal Collaborative Fuzzy Clustering Algorithms for Unequal-Length Time Series

In clustering of unequal-length time series, how to deal with the unequal lengths is a crucial step. In this paper, the given unequal-length clustering problem is first changed into several equal-length clustering sub-problems by dividing the given group of unequal-length time series into some groups of equal-length subsequences. For each sub-problem, the standard fuzzy c-means algorithm can give the clustering result represented by a partition matrix and cluster centers. In order to obtain the final clustering result, horizontal collaborative fuzzy clustering algorithm is employed to fuse the clustering results of the sub-problems. In horizontal collaborative fuzzy clustering algorithm, the collaborative knowledge is transmitted by partition matrixes whose sizes should be the same to the final partition matrix. But in the scenario here, the obtained partition matrixes most often have different sizes, thus we cannot directly use the horizontal collaborative fuzzy clustering algorithm. This paper here presents two new manners for extending the partition matrixes to have same size to the final partition matrix. In the first new manner, each added element in the extended partition matrix is the element in the same position of the extending matrix. In the second new manner, each added column is same to the corresponding column of the extending matrix; while each added element in the pre-existing column is set to be 0. The main difference between the two manners is that the normalization condition does not hold for some columns in the first new manner. Thus, normalization should be made for those columns. Meanwhile, this paper investigates the selection of the extending matrix which is crucial in the two new extending manners. Both the two new extending manners can make the partition knowledge be effectively transmitted and thus assume the proposed clustering algorithms good clustering results. Experiments showed the effectiveness of the proposed manners.