Learning Partial Correlation based Deep Visual Representation for Image Classification

Visual representation based on covariance matrix has demonstrates its efficacy for image classification by characterising the pairwise correlation of different channels in convolutional feature maps. However, pairwise correlation will become misleading once there is another channel correlating with both channels of interest, resulting in the ``confounding'' effect. For this case, ``partial correlation'' which removes the confounding effect shall be estimated instead. Nevertheless, reliably estimating partial correlation requires to solve a symmetric positive definite matrix optimisation, known as sparse inverse covariance estimation (SICE). How to incorporate this process into CNN remains an open issue. In this work, we formulate SICE as a novel structured layer of CNN. To ensure end-to-end trainability, we develop an iterative method to solve the above matrix optimisation during forward and backward propagation steps. Our work obtains a partial correlation based deep visual representation and mitigates the small sample problem often encountered by covariance matrix estimation in CNN. Computationally, our model can be effectively trained with GPU and works well with a large number of channels of advanced CNNs. Experiments show the efficacy and superior classification performance of our deep visual representation compared to covariance matrix based counterparts.