TY - JOUR
T1 - Tensor Dictionary Learning for Positive Definite Matrices
AU - Sivalingam, Ravishankar
AU - Boley, Daniel
AU - Morellas, Vassilios
AU - Papanikolopoulos, Nikolaos
N1 - Publisher Copyright:
© 1992-2012 IEEE.
PY - 2015/11/1
Y1 - 2015/11/1
N2 - Sparse models have proven to be extremely successful in image processing and computer vision. However, a majority of the effort has been focused on sparse representation of vectors and low-rank models for general matrices. The success of sparse modeling, along with popularity of region covariances, has inspired the development of sparse coding approaches for these positive definite descriptors. While in earlier work, the dictionary was formed from all, or a random subset of, the training signals, it is clearly advantageous to learn a concise dictionary from the entire training set. In this paper, we propose a novel approach for dictionary learning over positive definite matrices. The dictionary is learned by alternating minimization between sparse coding and dictionary update stages, and different atom update methods are described. A discriminative version of the dictionary learning approach is also proposed, which simultaneously learns dictionaries for different classes in classification or clustering. Experimental results demonstrate the advantage of learning dictionaries from data both from reconstruction and classification viewpoints. Finally, a software library is presented comprising C++ binaries for all the positive definite sparse coding and dictionary learning approaches presented here.
AB - Sparse models have proven to be extremely successful in image processing and computer vision. However, a majority of the effort has been focused on sparse representation of vectors and low-rank models for general matrices. The success of sparse modeling, along with popularity of region covariances, has inspired the development of sparse coding approaches for these positive definite descriptors. While in earlier work, the dictionary was formed from all, or a random subset of, the training signals, it is clearly advantageous to learn a concise dictionary from the entire training set. In this paper, we propose a novel approach for dictionary learning over positive definite matrices. The dictionary is learned by alternating minimization between sparse coding and dictionary update stages, and different atom update methods are described. A discriminative version of the dictionary learning approach is also proposed, which simultaneously learns dictionaries for different classes in classification or clustering. Experimental results demonstrate the advantage of learning dictionaries from data both from reconstruction and classification viewpoints. Finally, a software library is presented comprising C++ binaries for all the positive definite sparse coding and dictionary learning approaches presented here.
KW - Sparse coding
KW - dictionary learning
KW - optimization
KW - positive definite matrices
KW - region covariance descriptors
UR - http://www.scopus.com/inward/record.url?scp=84941013693&partnerID=8YFLogxK
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U2 - 10.1109/TIP.2015.2440766
DO - 10.1109/TIP.2015.2440766
M3 - Article
C2 - 26054070
AN - SCOPUS:84941013693
SN - 1057-7149
VL - 24
SP - 4592
EP - 4601
JO - IEEE Transactions on Image Processing
JF - IEEE Transactions on Image Processing
IS - 11
M1 - 7117399
ER -