The robustness of subnetworks for the interconnection network of a computer system is an important consideration for the system performance. It can be measured by the extent to which subnetworks can stay fault-free when faults are present in the system. In this paper, we evaluate the subnetwork robustness for then-dimensional split-star network$S_{n}^{2}$. Let$S_{n-m}^{2}, 1 \leq m \leq n-3$, be a subnetwork of$S_{n}^{2}$, and letpbe the node reliability, the probability that a single node remains fault-free. We determine two values that reflect how robust$S_{n-m}^{2}$subnetworks are, from two perspectives. We first establish the upper/lower bounds for$\mathcal{F}_{m} (S_{n}^{2})$, the minimum number of faulty nodes to make all$S_{n-m}^{2}$subnetworks faulty. Then, we determine the subnetwork reliability, denoted by$\mathcal{R}_{m} (S_{n}^{2}, p)$, which is the probability that at least one fault-free$S_{n-m}^{2}$subnetwork exists in$S_{n}^{2}$, given the node reliabilityp. The upper/lower bounds and an approximation expression for$\mathcal{R}_{m} (S_{n}^{2}, p)$are obtained. We also propose a simulation method to estimate$\mathcal{R}_{m} (S_{n}^{2}, p)$. The experimental results show that a) whenpis relatively low,$\mathcal{R}_{m} (S_{n}^{2}, p)$can be approximated by the mean value of its upper and lower bounds, or the estimation value by the approximation expression; b) whenpis high,$\mathcal{R}_{m} (S_{n}^{2}, p)$can be more accurately estimated by our simulation method.

The in-air handwriting is a natural and promising human-computer interaction way. Compared with handwritten Chinese characters on touch screen, the in-air handwritten Chinese characters have their unique characteristics, e.g., each character is always written in a single stroke. In this paper, we propose a high-order directional feature for recognizing in-air handwritten Chinese characters. The proposed highorder features characterize the rate of direction change and the change rate of the rate of direction change, and can be easily be combined with the 8-directional features to get an enhanced version. Additionally, we exploit the locality-sensitive dictionary learning and sparse representation based classifier (LSRC) to recognize in-air handwritten Chinese characters. Since few work has applied the SRC in on-line handwritten Chinese character recognition (OHCCR), we evaluate the proposed system on both an in-air handwritten Chinese character dataset, the IAHCC-UCAS2015 dataset, and a handwritten Chinese character dataset, the SCUT-COUCH2009 database. The experimental results show that the proposed high-order directional features, when combined with the firstorder directional features (8-directional features), can improve the recognition accuracy, and they are more suitable for IAHCCR than traditional OHCCR. Additionally, the results also demonstrate the LSRC is a good choice for IAHCCR.

Recently, sparse representation has been successfully applied by some generative tracking methods. However, few methods consider the correlation between the representations of each particle in time domain and space domain. Additionally, most methods use the raw pixels as templates which can not well adapt to the sophisticated object changes. To solve these problems, we consider the sparse representation in kernel space and propose a multi-task kernel dynamic sparse tracking algorithm (MTKDST). As compared to previous methods, our method exploits the dependencies between particles in the space domain and the correlation of particle representation in the time domain to improve the tracking performance. Furthermore, we also adopt the multikernel fusion mechanism to utilize multiple complementary visual features (e.g., spatial color histogram and spatial gradient-orientation histogram) to enhance the robustness of the proposed method. The comprehensive experiments on several challenging image sequences demonstrate that the proposed method outperforms the state-of-the-art approaches in tracking accuracy.

Recently, sparse representation has been widely applied to some generative tracking methods, which learn the representation of each particle independently and do not consider the correlation between the representation of each particle in the time domain. In this paper, we formulate the object tracking in a particle filter framework as a multi-task dynamic sparse learning problem, which we denote as Multi-Task Dynamic Sparse Tracking(MTDST). By exploring the popular sparsity-inducing ℓ1, 2mixed norms, we regularize the representation problem to enforce joint sparsity and learn the particle representations together. Meanwhile, we also introduce the innovation sparse term in the tracking model. As compared to previous methods, our method mines the independencies between particles and the correlation of particle representation in the time domain, which improves the tracking performance. In addition, because the loft least square is robust to the outliers, we adopt the loft least square to replace the least square to calculate the likelihood probability. In the updating scheme, we eliminate the influences of occlusion pixels when updating the templates. The comprehensive experiments on the several challenging image sequences demonstrate that the proposed method consistently outperforms the existing state-of-the-art methods.

Sparse representation has been widely applied to some generative tracking methods. However, these methods do not consider the correlation between sparse representation coefficients in the time domain. In this paper, we propose a novel incremental subspace dynamic sparse tracking (ISDST) model with the error term of Gaussian-Laplacian distribution, which fully considers the correlation of object representations between consecutive frames by compressive sensing, and can effectively handle the occlusion in scenes. Next, the outlier entries, especially caused by the occlusion, have some group effect, so we adopt the spatial structured sparse via l1, 2mixed norms instead of the original l1sparse items. In addition, since the occlusion changes is very little between consecutive frames, we maintain an occlusion mask and eliminate the influence of occlusion pixels in the process of calculating the likelihood probability. Extensive experiments on challenging sequences demonstrate that our method consistently outperforms existing state-of-the-art methods.

In this paper, we present a novel foreground object detection method based on the sparse model of the spectrum of spatiotemporal DCT domain, which is robust for high dynamic scenes. First, we adopt the three-dimensional Discrete Cosine Transform (DCT) to calculate the spatiotemporal spectrum representation of the current frame. Then, identification of foreground pixels is formulated as the analysis of the sparse solution of an optimization problem, where foreground pixels correspond to an outlier of the sparse model. Finally, the background updating method is presented to adaptively update the dictionary of sparse model corresponding to background representation. The experimental results on four challenging video sequences show that the proposed method is more robust to high dynamic changes of scenes compared with four representative methods.

Foreground object detection is a crucial technique of intelligent surveillance systems, and it is still a challenging problem in complex scenes with illumination variations and dynamic backgrounds. Intuitively, the foreground object pixels are often not sparsely distributed but tend to be clustered. Motivated by this hypothesis, we present a new structured sparse model to extract foreground objects, which introduces the spatial neighborhood information into a unified optimization framework by l1,2 mixed norms. Simultaneously, we also give the solving method of the proposed model in details. Moreover, we apply the model to the sparse signal recovery and background subtraction in videos. In the experiments, better performance is obtained over previous methods. The experimental results validate the hypothesis and the effectiveness of the proposed method.