A0945
Title: Sparse Kronecker product decomposition: A general framework of signal region detection in image regression
Authors: Long Feng - University of Hong Kong (Hong Kong) [presenting]
Abstract: The aim is to present the first Frequentist framework on signal region detection in high-resolution and high-order image regression problems. Image data and scalar-on-image regression have been intensively studied in recent years. However, most existing studies on such topics focused on outcome prediction, while the research on image region detection is rather limited, even though the latter is often more important. A general framework named Sparse Kronecker Product Decomposition (SKPD) is developed to tackle this issue. The SKPD framework is general in the sense that it works for both matrices and (high-order) tensors represented image data. This framework includes 1) the one-term SKPD, 2) the multiterm SKPD, and 3) the nonlinear SKPD. Nonconvex optimization problems are proposed to estimate the one-term and multiterm SKPDs, and path-following algorithms for nonconvex optimization are developed. The computed solutions of the path-following algorithm are guaranteed to converge to the truth with a particularly chosen initialization, even though the optimization is nonconvex. Moreover, the one-term and multiterm SKPD could also guarantee region detection consistency. The nonlinear SKPD is highly connected to shallow convolutional neural networks (CNN), particularly to CNN with one convolutional layer and one fully connected layer. Real brain imaging data in the UK Biobank database validate the effectiveness of SKPDs.
