Time series clustering is the process of grouping sequential correspondences in similar clusters. The key feature behind clustering time series data lies on the similarity/distance function used to identify the sequential matches. Dynamic Time Warping (DTW) is one of the common distance measures that have demonstrated competitive results compared to other functions. DTW aims to find the shortest path in the process of identifying sequential matches. DTW relies on dynamic programming to obtain the shortest path where the smaller distance is being computed. However, in the case of equivalent distances, DTW is selecting the path randomly. Hence, the selection could be misguided in such randomization process, which significantly affects the matching quality. This is due to randomization may lead to the longer path which drifts from obtaining the optimum path. This paper proposes a modified DTW that aims to enhance the dynamic selection of the shortest path when handling equivalent distances. Experiments were conducted using twenty UCR benchmark datasets. Also, the proposed modified DTW result has been compared with the state of the art competitive distance measures which is based on precision, recall and f-measure including the original DTW, Minkowski distance measure and Euclidean distance measure. The results showed that the proposed modified DTW reveal superior results in compared to the standard DTW, either using Minkowski or Euclidean. This can demonstrate the effectiveness of the proposed modification in which optimizing the shortest path has enhanced the performance of clustering. The proposed modified DTW can be used for having good clustering method for any time series data.
Clustering Spatio-temporal data is challenging because of the complexity of processing the spatial and temporal aspects. Various enhanced clustering approaches, such as partition-based and hierarchical-based algorithms have been proposed. However, the ST-DBSCAN density-based algorithm is commonly used to process irregularly shaped clusters. Moreover, ST-DBSCAN considers neighborhood parameters as spatial and non-spatial. The preliminary results from our experiments indicate that the ST-DBSCAN algorithm addresses temporal elements less effectively. Therefore, an improvement to the ST-DBSCAN algorithm was proposed by considering three neighborhood boundaries in neighborhood function. This experiment used the El Niño dataset from the UCI repository. The experimental results show that the proposed algorithm increased the performance indices by 27% compared to existing approaches. Further improvement using the hierarchical Ward's method (with thresholds of 0.3 and 0.1) reduced the number of clusters from 240 to 6 and increased performance indices by up to 73%. It can be concluded that ST-HDBSCAN is a suitable clustering algorithm for Spatio-temporal data.
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