Degree Name

Doctor of Philosophy


School of Computing and Information Technology


Symmetric positive definite (SPD) visual representations are effective due to their ability to capture high-order statistics to describe images. Reliable and efficient calculation of SPD matrix representation from small sized feature maps with a high number of channels in CNN is a challenging issue. This thesis presents three novel methods to address the above challenge. The first method, called Relation Dropout (ReDro), is inspired by the fact that eigen-decomposition of a block diagonal matrix can be efficiently obtained by eigendecomposition of each block separately. Thus, instead of using a full covariance matrix as in the literature, this thesis randomly group the channels and form a covariance matrix per group. ReDro is inserted as an additional layer preceding the matrix normalisation step and the random grouping is made transparent to all subsequent layers. ReDro can be seen as a dropout-related regularisation which discards some pair-wise channel relationships across each group. The second method, called FastCOV, exploits the intrinsic connection between eigensytems of XXT and XTX. Specifically, it computes position-wise covariance matrix upon convolutional feature maps instead of the typical channel-wise covariance matrix. As the spatial size of feature maps is usually much smaller than the channel number, conducting eigen-decomposition of the position-wise covariance matrix avoids rank-deficiency and it is faster than the decomposition of the channel-wise covariance matrix. The eigenvalues and eigenvectors of the normalised channel-wise covariance matrix can be retrieved by the connection of the XXT and XTX eigen-systems. The third method, iSICE, deals with the reliable covariance estimation from small sized and highdimensional CNN feature maps. It exploits the prior structure of the covariance matrix to estimate sparse inverse covariance which is developed in the literature to deal with the covariance matrix’s small sample issue. Given a covariance matrix, this thesis iteratively minimises its log-likelihood penalised by a sparsity with gradient descend. The resultant representation characterises partial correlation instead of indirect correlation characterised in covariance representation. As experimentally demonstrated, all three proposed methods improve the image classification performance, whereas the first two proposed methods reduce the computational cost of learning large SPD visual representations.

FoR codes (2020)

460304 Computer vision, 460308 Pattern recognition, 461103 Deep learning



Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.