A New Composite Dissimilarity Measure for Planar Curves Based on Higher-Order Derivatives

With the rapid development of information technology, the problem of curve matching has appeared in many application domains, including sequence analysis, signals processing, speech recognition, etc. Many similarity measures have been studied for matching curves based on Euclidean distance, which shows fragility in portraying the morphological information of curve data. In this paper, we propose a novel weighted composite curve dissimilarity metric (WCDM). First, the WCDM measures the dissimilarity based on the higher-order semantic difference between curve shapes and location difference. These two differences are calculated using the curvature difference and Euclidean distance between the curves, respectively. Second, a new dynamic weighting function is defined by employing the relationship between the trends of the curves. This function aims at adjusting the contributions of the curvature difference and the Euclidean distance to compose the dissimilarity measure WCDM. Finally, to ascertain the rationality of the WCDM, its metric properties are studied and proved theoretically. Comparison experiments on clustering and classification tasks are carried out on curve sets transformed from UCR time series datasets, and an application analysis of the WCDM is conducted on spectral data. The experimental results indicate the effectiveness of the WCDM. Specifically, clustering and classification based on the WCDM are superior to those based on ED, DTW, Hausdorff, Fréchet, and LCSS on at least 8 out of 14 datasets across all evaluation indices. In particular, the Purity and ARI on the Beetlefly dataset are improved by more than 7.5%, while accuracy on the Beef, Chinatown, and OliveOil datasets increases by 13.32%, 10.08%, and 12.83%, respectively.