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In this paper, a general optimization formulation is proposed for the subspace segmentation by low rank representation via the sparse-prompting quasi-rank function. We prove that, with the clean data from independent linear subspaces, the optimal solution to our optimization formulation not only is the lowest rank but also forms a block-diagonal matrix, which implies that it is reasonable to use any sparse-prompting quasi-rank function as the measure of the low rank in subspace clustering. With the data contaminated by Gaussian noise and/or gross errors, the alternating direction method of multipliers is applied to solving it and every sub-optimization problem has a closed-form optimal solution when the band restricted thresholding operator induced by its corresponding sparse-prompting function has an analytic expression, in which the gross errors part is replaced with the sparse-prompting matrix function. Finally, taking a specific sparse-prompting function, the fraction function, we conduct a series of simulations on different databases to get the performance of our algorithm tested, and experimental results show that our algorithm can obtain lower clustering error rate and higher value of evaluation indicators ACC, NMI and ARI than other state-of-the-art subspace clustering algorithms on different databases.

Recently there have been renewed interests in high order neural networks (HONNs) for its powerful mapping capability. Ridge polynomial neural network (RPNN) is an important kind of HONNs, which always occupies a key position as an efficient instrument in the tasks of classification or regression. In order to make the convergence speed faster and the network generalization ability stronger, we introduce a regularization model for RPNN with Group Lasso penalty, which deals with the structural sparse problem at the group level in this paper. Nevertheless, there are two main obstacles for introducing the Group Lasso penalty, one is numerical oscillation and the other is convergence analysis challenge. In doing so, we adopt smoothing function to approximate the Group Lasso penalty to overcome these drawbacks. Meanwhile, strong and weak convergence theorems, and monotonicity theorems are provided for this novel algorithm. We also demonstrate the efficiency of our proposed algorithm by numerical experiments, and compare it to the no regularizer, $L_{2}$ regularizer, $L_{1/2}$ regularizer, smoothing $L_{1/2}$ regularizer, and the Group Lasso regularizer, and also the relevant theoretical analysis has been verified.

Accurate and timely perception of collision in highly variable environments is still a challenging problem for artificial visual systems. As a source of inspiration, the lobula giant movement detectors (LGMDs) in locust's visual pathways have been studied intensively, and modelled as quick collision detectors against challenges from various scenarios including vehicles and robots. However, the state-of-the-art LGMD models have not achieved acceptable robustness to deal with more challenging scenarios like the various vehicle driving scenes, due to the lack of adaptive signal processing mechanisms. To address this problem, we propose an improved neuronal system model, called LGMD+, that is featured by novel modelling of spatiotemporal inhibition dynamics with biological plausibilities including 1) lateral inhibitions with global biases defined by a variant of Gaussian distribution, spatially, and 2) an adaptive feed-forward inhibition mediation pathway, temporally. Accordingly, the LGMD+ performs more effectively to detect merely approaching objects threatening head-on collision risks by appropriately suppressing motion distractors caused by vibrations, near-miss or approaching stimuli with deviations from the centre view. Through evolutionary learning with a systematic dataset of various crash and non-collision driving scenarios, the LGMD+ shows improved robustness outperforming the previous related methods. After evolution, its computational simplicity, flexibility and robustness have also been well demonstrated by real-time experiments of autonomous micro-mobile robots.

The perception of different visual motion cues is crucial for autonomous mobile robots to react to or interact with the dynamic visual world. It is still a great challenge for a micro mobile robot to cope with dynamic environments due to the restricted computational resources and the limited functionalities of its visual systems. In this study, we propose a compound visual neural system to automatically extract and fuse different visual motion cues in real-time using the extremely constrained computation power of micro mobile robots. The proposed visual system contains multiple bio-inspired visual motion perceptive neurons each with a unique role, for example to extract collision visual cues, darker collision cue and directional motion cues. In the embedded system, these multiple visual neurons share a similar presynaptic network to minimise the consumption of computation resources. In the postsynaptic part of the system, visual cues pass results to corresponding action neurons using lateral inhibition mechanism. The translational motion cues, which are identified by comparing pairs of directional cues, are given the highest priority, followed by the darker colliding cues and approaching cues. Systematic experiments with both virtual visual stimuli and real-world scenarios have been carried out to validate the system's functionality and reliability. The proposed methods have demonstrated that (1) with extremely limited computation power, it is still possible for a micro mobile robot to extract multiple visual motion cues robustly in a complex dynamic environment; (2) the cues extracted can be fused with a lateral inhibited postsynaptic network, thus enabling the micro robots to respond effectively with different actions, accordingly to different states, in real-time. The proposed embedded visual system has been modularised and can be easily implemented in other autonomous mobile platforms for real-time applications. The system could also be used by neurophysiologists to test new hypotheses pertaining to biological visual neural systems.

In this paper, we introduce a two-step inertial primal-dual algorithm (TSIPD) for solving the minimizations of the sum a smooth function with Lipschitzian gradient and two non-smooth convex functions with linear operators. This is a complete splitting approach, in the sense that non-smooth functions are treated separately by their proximity operators. In order to prove the convergence of the TSIPD, we transform the problem into a fixed point equation with good performance, and prove the convergence of the algorithm base on the fixed point theory. This work brings together and significantly extends several classical splitting schemes, like the primal-dual method (PD3O) proposed by Yan, and the recent three-operator splitting scheme proposed by Davis and Yin. The validity of the proposed method is demonstrated on an image denoising problem. Numerical results show that our iterative algorithm (TSIPD) has better performance than the original one (PD3O).