Multivariate Time Series Data Clustering Method Based on Dynamic Time Warping and Affinity Propagation

Algorithm 2

Input: MTS data set , where each time series has -dimensional attribute.

Output: representative object set of MTS.

S1: obtain the corresponding similarity matrix and optimal bending path according to the formulas (2) and (4).

S2: based on the optimal bending path and formula (5), calculate the similarity between two MTSs and under the different component attribute.

S3: repeat steps S1 to S2, calculate the similarity between the corresponding component sequences of all MTSs under the different dimensional condition, and further achieve the corresponding similarity matrices . Herein, is the attribute dimension of MTS.

S4: use the AP algorithm to cluster each similarity matrix and then achieve the clustering results and under the different component attribute and the perspective of overall MTS, respectively.

S5: transform the clustering results and to the relation matrix, that is, and . Meanwhile, calculate the synthetic relation matrix from (6).

S6: employ the AP algorithm to cluster the comprehensive relation matrix and finally obtain the clustering result of MTS.