This paper proposes using the neural networks to efficiently solve the second-order cone programs (SOCP). To establish the neural networks, the SOCP is first reformulated as a second-order cone complementarity problem (SOCCP) with the KarushKuhnTucker conditions of the SOCP. The SOCCP functions, which transform the SOCCP into a set of nonlinear equations, are then utilized to design the neural networks. We propose two kinds of neural networks with the different SOCCP functions. The first neural network uses the FischerBurmeister function to achieve an unconstrained minimization with a merit function. We show that the merit function is a Lyapunov function and this neural network is asymptotically stable. The second neural network utilizes the natural residual function with the cone projection function to achieve low computation complexity. It is shown to be Lyapunov stable and converges globally

Image retargeting techniques adjust images into different sizes and have attracted much attention recently. Objective quality assessment (OQA) of image retargeting results is often desired to automatically select the best results. Existing OQA methods train a model using some benchmarks (e.g., RetargetMe), in which subjective scores evaluated by users are provided. Observing that it is challenging even for human subjects to give consistent scores for retargeting results of different source images (diff-source-results), in this paper we propose a learning-based OQA method that trains a General Regression Neural Network (GRNN) model based on relative scores --- which preserve the ranking --- of retargeting results of the same source image (same-source-results). In particular, we develop a novel training scheme with provable convergence that learns a common base scalar for same-source-results. With this source specific offset, our computed scores not only preserve the ranking of subjective scores for same-source-results, but also provide a reference to compare the diff-source-results. We train and evaluate our GRNN model using human preference data collected in RetargetMe. We further introduce a subjective benchmark to evaluate the generalizability of different OQA methods. Experimental results demonstrate that our method outperforms ten representative OQA methods in ranking prediction and has better generalizability to different datasets.

Personal videos often contain visual distractors, which are objects that are accidentally captured that can distract viewers from focusing on the main subjects. We propose a method to automatically detect and localize these distractors through learning from a manually labeled dataset. To achieve spatially and temporally coherent detection, we propose extracting features at the Temporal-Superpixel (TSP) level using a traditional SVM-based learning framework. We also experiment with end-to-end learning using Convolutional Neural Networks (CNNs), which achieves slightly higher performance than other methods. The classification result is further refined in a post-processing step based on graph-cut optimization. Experimental results show that our method achieves an accuracy of 81% and a recall of 86%. We demonstrate several ways of removing the detected distractors to improve the video quality, including video hole filling; video frame replacement; and camera path re-planning. The user study results show that our method can significantly improve the aesthetic quality of videos.

Learning rate is arguably the most important hyper-parameter to tune when training a neural network. As manually setting right learning rate remains a cumbersome process, adaptive learning rate algorithms aim at automating such a process. Motivated by the success of the Barzilai–Borwein (BB) step-size method in many gradient descent methods for solving convex problems, this paper aims at investigating the potential of the BB method for training neural networks. With strong motivation from related convergence analysis, the BB method is generalized to adaptive learning rate of mini-batch gradient descent. The experiments showed that, in contrast to many existing methods, the proposed BB method is highly insensitive to initial learning rate, especially in terms of generalization performance. Also, the BB method showed its advantages on both learning speed and generalization performance over other available methods.

This paper proposes a neural network approach for efficiently solving general nonlinear convex programs with second-order cone constraints. The proposed neural network model was developed based on a smoothed natural residual merit function involving an unconstrained minimization reformulation of the complementarity problem. We study the existence and convergence of the trajectory of the neural network. Moreover, we show some stability properties for the considered neural network, such as the Lyapunov stability, asymptotic stability, and exponential stability. The examples in this paper provide a further demonstration of the effectiveness of the proposed neural network. This paper can be viewed as a follow-up version of [20], [26] because more stability results are obtained.