Fast and compact Kronecker-structured dictionary learning for classification and representation

Ishan Jindal, Matthew S. Nokleby

Abstract: In this paper, we present a computationally fast, storage-efficient approach, termed Kronecker-Structured Learning of Discriminative Dictionaries (K-SLD <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), for learning a Kronecker-structured, overcomplete dictionary for the classification and representation of multidimensional signals like images, medical tomographic data, and videos. We evaluate the performance of K-SLD <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> on several datasets, including Extended YaleB and the UCI EEG database. The use of Kronecker-structured dictionaries improves the classification performance over state-of-the-art dictionary-based methods when the number of training samples is small, at it is competitive with methods employing SIFT features even without feature extraction. Furthermore, Kronecker-structured dictionaries offer a more compact representation of signal classes, packing in more atoms with no more than 5% of the storage requirements of existing subspace models.