Fuzzy clustering of short time-series and unevenly distributed sampling points

This paper proposes a new algorithm in the fuzzy-c-means family, which is designed to cluster time-series and is particularly suited for short time-series and those with unevenly spaced sampling points. Short time-series, which do not allow a conventional statistical model, and unevenly sampled time-series appear in many practical situations. The algorithm developed here is motivated by common experiments in molecular biology. Conventional clustering algorithms based on the Euclidean distance or the Pearson correlation coefficient are not able to include the temporal information in the distance metric. The temporal order of the data and the varying length of sampling intervals are important and should be considered in clustering time-series. The proposed short time-series (STS) distance is able to measure similarity of shapes which are formed by the relative change of amplitude and the corresponding temporal information. We develop a fuzzy time-series (FSTS) clustering algorithm by incorporating the STS distance into the standard fuzzy clustering scheme. An example is provided to demonstrate the performance of the proposed algorithm.