Dictionary learning is an effective tool for pattern recognition and classification of time series data. Among various dictionary learning techniques, the dynamic time warping (DTW) is commonly used for dealing with temporal delays, scaling, transformation, and many other kinds of temporal misalignments issues. However, the DTW suffers overfitting or information loss due to its discrete nature in aligning time series data. To address this issue, we propose a generalized time warping invariant dictionary learning algorithm in this paper. Our approach features a generalized time warping operator, which consists of linear combinations of continuous basis functions for facilitating continuous temporal warping. The integration of the proposed operator and the dictionary learning is formulated as an optimization problem, where the block coordinate descent method is employed to jointly optimize warping paths, dictionaries, and sparseness coefficients. The optimized results are then used as hyperspace distance measures to feed classification and clustering algorithms. The superiority of the proposed method in terms of dictionary learning, classification, and clustering is validated through ten sets of public datasets in comparing with various benchmark methods.

翻译：字典学习是时间序列数据模式识别与分类的有效工具。在众多字典学习技术中，动态时间规整（DTW）常被用于处理时间延迟、缩放、变换及其他多种时间错位问题。然而，DTW因在时间序列对齐过程中的离散性质，容易引发过拟合或信息损失。针对这一问题，本文提出了一种广义时间扭曲不变性字典学习算法。该方法的核心在于一个广义时间扭曲算子，它由连续基函数的线性组合构成，便于实现连续时间扭曲。本文将所提出算子与字典学习的整合建模为优化问题，采用块坐标下降法联合优化扭曲路径、字典及稀疏系数。优化后的结果被用作超空间距离度量，以输入分类与聚类算法。通过与多种基准方法在十组公共数据集上的对比实验，验证了本方法在字典学习、分类及聚类性能上的优越性。