Dynamic time alignment kernel-based fuzzy clustering of non-equal length vector time series

Time series clustering is an effective vehicle to explore and visualize the structure of a suite of time series. In this study, we generalize the kernel-based fuzzy c-means clustering algorithm by involving the dynamic time alignment kernel (DTAK) to cluster vector time series. In this method, the nonlinear time alignment embedded in DTAK makes the kernel-based fuzzy c-means available for sequences with variable lengths. However, it is noted that DTAK is not a strictly positive definite kernel, especially when the sample size is large. To overcome this, some strategies are presented to make the proposed algorithm available for large data sets. In addition, it is a challenge task to calculate the average sequence for a series of time series with different lengths. In kernel-based fuzzy c-means algorithm, it is not necessary to calculate the average sequence, which will increase the effectiveness of clustering techniques for time series. In the experiments, the kernel-based fuzzy c-means with DTAK is evaluated by both the data sets from the UCI KDD Archive and real-world data sets. Experimental results delivered by the proposed method demonstrate its effectiveness and robustness.