Saeed Varasteh Yazdi - Time warp invariant sparse coding and dictionary learning for time series classification and clustering

Learning dictionary for sparse representing time series is an important issue to extract latent temporal features, reveal salient primitives and sparsely represent complex temporal data. This thesis addresses the sparse coding and dictionary learning problem for time series classification and clustering under time warp. For that, we propose a time warp invariant sparse coding and dictionary learning framework where both input samples and atoms define time series of different lengths that involve varying delays. 
In the first part, we formalize an L0 sparse coding problem and propose a time warp invariant orthogonal matching pursuit based on a new cosine maximization time warp operator. For the dictionary learning stage, a non linear time warp invariant kSVD (TWI-kSVD) is proposed. Thanks to a rotation transformation between each atom and its sibling atoms, a singular value decomposition is used to jointly approximate the coefficients and update the dictionary, similar to the standard kSVD. In the second part, a time warp invariant dictionary learning for time series clustering is formalized and a gradient descent solution is proposed. 
The proposed methods are confronted to major shift invariant, convolved and kernel dictionary learning methods on several public and real temporal data. The conducted experiments show the potential of the proposed frameworks to efficiently sparse represent, classify and cluster time series under time warp.