Yuying Li

Yuying Li, Mehdi Faraji

This work concentrates on Extremal Regions of Extremum Level (EREL) selection. EREL is a recently proposed feature detector aiming at detecting regions from a set of extremal regions. This is a branching problem derived from segmentation of arterial wall boundaries from Intravascular Ultrasound (IVUS) images. For each IVUS frame, a set of EREL regions is generated to describe the luminal area of human coronary. Each EREL is then fitted by an ellipse to represent the luminal border. The goal is to assign the most appropriate EREL as the lumen. In this work, EREL selection carries out in two rounds. In the first round, the pattern in a set of EREL regions is analyzed and used to generate an approximate luminal region. Then, the two-dimensional (2D) correlation coefficients are computed between this approximate region and each EREL to keep the ones with tightest relevance. In the second round, a compactness measure is calculated for each EREL and its fitted ellipse to guarantee that the resulting EREL has not affected by the common artifacts such as bifurcations, shadows, and side branches. We evaluated the selected ERELs in terms of Hausdorff Distance (HD) and Jaccard Measure (JM) on the train and test set of a publicly available dataset. The results show that our selection strategy outperforms the current state-of-the-art.

Edward Cheung, Yuying Li

Frank-Wolfe methods (FW) have gained significant interest in the machine learning community due to its ability to efficiently solve large problems that admit a sparse structure (e.g. sparse vectors and low-rank matrices). However the performance of the existing FW method hinges on the quality of the linear approximation. This typically restricts FW to smooth functions for which the approximation quality, indicated by a global curvature measure, is reasonably good. In this paper, we propose a modified FW algorithm amenable to nonsmooth functions by optimizing for approximation quality over all affine approximations given a neighborhood of interest. We analyze theoretical properties of the proposed algorithm and demonstrate that it overcomes many issues associated with existing methods in the context of nonsmooth low-rank matrix estimation.

Edward Cheung, Yuying Li

The Frank-Wolfe (FW) algorithm has been widely used in solving nuclear norm constrained problems, since it does not require projections. However, FW often yields high rank intermediate iterates, which can be very expensive in time and space costs for large problems. To address this issue, we propose a rank-drop method for nuclear norm constrained problems. The goal is to generate descent steps that lead to rank decreases, maintaining low-rank solutions throughout the algorithm. Moreover, the optimization problems are constrained to ensure that the rank-drop step is also feasible and can be readily incorporated into a projection-free minimization method, e.g., Frank-Wolfe. We demonstrate that by incorporating rank-drop steps into the Frank-Wolfe algorithm, the rank of the solution is greatly reduced compared to the original Frank-Wolfe or its common variants.