Prototypes help to explain the predictions of deep classification models for time series. However, most models learn prototypes by randomly initializing an uncertain number of low-discriminative prototypes, which may lead to unstable models and unreliable results. To address these issues, we propose a new class D iscriminative P rototype L earning Net work (DPL-Net), which learns an appropriate number of class-discriminative prototypes, thus improving classification performance. Specifically, the proposed P rototype I nitialization M echanism (PIM) introduces a new proximity metric based on the silhouette coefficient and statistical metrics. It facilitates the automatic determination of the class-discriminative prototypes for each class. Then, the encoder layer encodes the prototypes derived from PIM and the input series using one-dimensional convolutional neural networks (1D-CNN). Finally, the prototype classification layer optimizes the prototypes according to the regularization terms, while simultaneously classifying the input sequence based on its similarity to the updated prototypes. The comparison experiments are conducted on 26 UCR datasets compared with 10 baselines. The results show that our proposed approach achieves the best accuracy on 11 datasets. Specifically, our method outperforms PIP, CSSL, and LSS by an average of 16.33%, 9.77% and 5.96% on 22, 14 and 16 datasets, respectively. The interpretability experimental results and the application analysis on spectral data indicate that the learned prototypes can provide reasonable explanations for the classification results of the model.

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.

Semi-supervised density-based clustering (SDC) is a density-based clustering technique that integrates both labeled and unlabeled data to improve the accuracy and robustness of cluster assignments. However, many SDC algorithms rely on global parameters to distinguish core from non-core points, which may not be effective for clusters with varying densities or complex shapes. To address this limitation, we propose the S emi-supervised D ensity-based C lustering algorithm with G ranular balls (SDCG), which operates in three phases. First, we construct a set of granular balls to perform an initial segmentation of the data, leveraging the available labeled data, with points within the same granular ball being considered similar. Next, we introduce a strategy that combines coverage and specificity to adjust the granularity of each granule, ensuring that points within the same granule belong to the same cluster. Finally, we employ an adaptive label propagation mechanism based on mutual nearest-neighbor voting, where non-core points are assigned labels according to the highest-voting labels from their mutual nearest neighbors. Overall, SDCG is parameter-free and is able to adaptively perform clustering, improving the performance of the algorithm. Experimental comparisons on both synthetic and real datasets show that our method outperforms existing approaches in terms of efficiency and accuracy, particularly for datasets with varying densities and complex shapes.