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Subspace clustering methods have been widely studied recently. When the inputs are 2-dimensional (2D) data, existing subspace clustering methods usually convert them into vectors, which severely damages inherent structures and relationships from original data. In this paper, we propose a novel subspace clustering method for 2D data. It directly uses 2D data as inputs such that the learning of representations benefits from inherent structures and relationships of the data. It simultaneously seeks image projection and representation coefficients such that they mutually enhance each other and lead to powerful data representations. An efficient algorithm is developed to solve the proposed objective function with provable decreasing and convergence property. Extensive experimental results verify the effectiveness of the new method., Comment: accepted to Pattern Recognition

Graphs have become increasingly popular in modeling structures and interactions in a wide variety of problems during the last decade. Graph-based clustering and semi-supervised classification techniques have shown impressive performance. This paper proposes a graph learning framework to preserve both the local and global structure of data. Specifically, our method uses the self-expressiveness of samples to capture the global structure and adaptive neighbor approach to respect the local structure. Furthermore, most existing graph-based methods conduct clustering and semi-supervised classification on the graph learned from the original data matrix, which doesn't have explicit cluster structure, thus they might not achieve the optimal performance. By considering rank constraint, the achieved graph will have exactly $c$ connected components if there are $c$ clusters or classes. As a byproduct of this, graph learning and label inference are jointly and iteratively implemented in a principled way. Theoretically, we show that our model is equivalent to a combination of kernel k-means and k-means methods under certain condition. Extensive experiments on clustering and semi-supervised classification demonstrate that the proposed method outperforms other state-of-the-art methods., Comment: Appear in Pattern Recognition

The screen content images (SCIs) usually comprise various content types with sharp edges, in which the artifacts or distortions can be well sensed by the vanilla structure similarity measurement in a full reference manner. Nonetheless, almost all of the current SOTA structure similarity metrics are "locally" formulated in a single-level manner, while the true human visual system (HVS) follows the multi-level manner, and such mismatch could eventually prevent these metrics from achieving trustworthy quality assessment. To ameliorate, this paper advocates a novel solution to measure structure similarity "globally" from the perspective of sparse representation. To perform multi-level quality assessment in accordance with the real HVS, the above-mentioned global metric will be integrated with the conventional local ones by resorting to the newly devised selective deep fusion network. To validate its efficacy and effectiveness, we have compared our method with 12 SOTA methods over two widely-used large-scale public SCI datasets, and the quantitative results indicate that our method yields significantly higher consistency with subjective quality score than the currently leading works. Both the source code and data are also publicly available to gain widespread acceptance and facilitate new advancement and its validation.

The existing fusion based RGB-D salient object detection methods usually adopt the bi-stream structure to strike the fusion trade-off between RGB and depth (D). The D quality usually varies from scene to scene, while the SOTA bi-stream approaches are depth quality unaware, which easily result in substantial difficulties in achieving complementary fusion status between RGB and D, leading to poor fusion results in facing of low-quality D. Thus, this paper attempts to integrate a novel depth quality aware subnet into the classic bi-stream structure, aiming to assess the depth quality before conducting the selective RGB-D fusion. Compared with the SOTA bi-stream methods, the major highlight of our method is its ability to lessen the importance of those low-quality, no-contribution, or even negative-contribution D regions during the RGB-D fusion, achieving a much improved complementary status between RGB and D.

Previous video salient object detection (VSOD) approaches have mainly focused on designing fancy networks to achieve their performance improvements. However, with the slow-down in development of deep learning techniques recently, it may become more and more difficult to anticipate another breakthrough via fancy networks solely. To this end, this paper proposes a universal learning scheme to get a further 3\% performance improvement for all state-of-the-art (SOTA) methods. The major highlight of our method is that we resort the "motion quality"---a brand new concept, to select a sub-group of video frames from the original testing set to construct a new training set. The selected frames in this new training set should all contain high-quality motions, in which the salient objects will have large probability to be successfully detected by the "target SOTA method"---the one we want to improve. Consequently, we can achieve a significant performance improvement by using this new training set to start a new round of network training. During this new round training, the VSOD results of the target SOTA method will be applied as the pseudo training objectives. Our novel learning scheme is simple yet effective, and its semi-supervised methodology may have large potential to inspire the VSOD community in the future.

The current main stream methods formulate their video saliency mainly from two independent venues, i.e., the spatial and temporal branches. As a complementary component, the main task for the temporal branch is to intermittently focus the spatial branch on those regions with salient movements. In this way, even though the overall video saliency quality is heavily dependent on its spatial branch, however, the performance of the temporal branch still matter. Thus, the key factor to improve the overall video saliency is how to further boost the performance of these branches efficiently. In this paper, we propose a novel spatiotemporal network to achieve such improvement in a full interactive fashion. We integrate a lightweight temporal model into the spatial branch to coarsely locate those spatially salient regions which are correlated with trustworthy salient movements. Meanwhile, the spatial branch itself is able to recurrently refine the temporal model in a multi-scale manner. In this way, both the spatial and temporal branches are able to interact with each other, achieving the mutual performance improvement. Our method is easy to implement yet effective, achieving high quality video saliency detection in real-time speed with 50 FPS.

In this paper, we propose a new Semi-Nonnegative Matrix Factorization method for 2-dimensional (2D) data, named TS-NMF. It overcomes the drawback of existing methods that seriously damage the spatial information of the data by converting 2D data to vectors in a preprocessing step. In particular, projection matrices are sought under the guidance of building new data representations, such that the spatial information is retained and projections are enhanced by the goal of clustering, which helps construct optimal projection directions. Moreover, to exploit nonlinear structures of the data, manifold is constructed in the projected subspace, which is adaptively updated according to the projections and less afflicted with noise and outliers of the data and thus more representative in the projected space. Hence, seeking projections, building new data representations, and learning manifold are seamlessly integrated in a single model, which mutually enhance other and lead to a powerful data representation. Comprehensive experimental results verify the effectiveness of TS-NMF in comparison with several state-of-the-art algorithms, which suggests high potential of the proposed method for real world applications.

Leveraging on the underlying low-dimensional structure of data, low-rank and sparse modeling approaches have achieved great success in a wide range of applications. However, in many applications the data can display structures beyond simply being low-rank or sparse. Fully extracting and exploiting hidden structure information in the data is always desirable and favorable. To reveal more underlying effective manifold structure, in this paper, we explicitly model the data relation. Specifically, we propose a structure learning framework that retains the pairwise similarities between the data points. Rather than just trying to reconstruct the original data based on self-expression, we also manage to reconstruct the kernel matrix, which functions as similarity preserving. Consequently, this technique is particularly suitable for the class of learning problems that are sensitive to sample similarity, e.g., clustering and semisupervised classification. To take advantage of representation power of deep neural network, a deep auto-encoder architecture is further designed to implement our model. Extensive experiments on benchmark data sets demonstrate that our proposed framework can consistently and significantly improve performance on both evaluation tasks. We conclude that the quality of structure learning can be enhanced if similarity information is incorporated.

Conventional smoothed particle hydrodynamics based on Eulerian kernels (CESPH) is widely-used in large deformation analysis in geomaterials. Despite being popular, it suffers from tensile instability and rank-deficiency; thus, it needs several numerical treatments to be stable. In this work, we present a stabilized total-Lagrangian SPH method (TLSPH), which is inherently free of tensile instability. A stiffness-based hourglass control algorithm is employed to cure the hourglass mode caused by rank-deficiency. Periodic update of reference configuration is used in simulations to allow TLSPH to model large deformation and post-failure flow in geomaterials. Several numerical examples are presented to show the performance of the stabilized TLSPH method. The comparison between TLSPH and CESPH are discussed. The influences of hourglass control and configuration update are also discussed and shown in the numerical examples. It is found that the presented stabilized TLSPH is robust and can model large deformation and plastic flows in geomaterials. Particularly, the stabilized TLSPH delivers accurate and smooth stress results., Comment: 18 pages, 15 figures

Existing nonnegative matrix factorization methods focus on learning global structure of the data to construct basis and coefficient matrices, which ignores the local structure that commonly exists among data. In this paper, we propose a new type of nonnegative matrix factorization method, which learns local similarity and clustering in a mutually enhancing way. The learned new representation is more representative in that it better reveals inherent geometric property of the data. Nonlinear expansion is given and efficient multiplicative updates are developed with theoretical convergence guarantees. Extensive experimental results have confirmed the effectiveness of the proposed model.

We introduce a discriminative regression approach to supervised classification in this paper. It estimates a representation model while accounting for discriminativeness between classes, thereby enabling accurate derivation of categorical information. This new type of regression models extends existing models such as ridge, lasso, and group lasso through explicitly incorporating discriminative information. As a special case we focus on a quadratic model that admits a closed-form analytical solution. The corresponding classifier is called discriminative regression machine (DRM). Three iterative algorithms are further established for the DRM to enhance the efficiency and scalability for real applications. Our approach and the algorithms are applicable to general types of data including images, high-dimensional data, and imbalanced data. We compare the DRM with currently state-of-the-art classifiers. Our extensive experimental results show superior performance of the DRM and confirm the effectiveness of the proposed approach.

Robust principal component analysis (RPCA) has drawn significant attentions due to its powerful capability in recovering low-rank matrices as well as successful appplications in various real world problems. The current state-of-the-art algorithms usually need to solve singular value decomposition of large matrices, which generally has at least a quadratic or even cubic complexity. This drawback has limited the application of RPCA in solving real world problems. To combat this drawback, in this paper we propose a new type of RPCA method, RES-PCA, which is linearly efficient and scalable in both data size and dimension. For comparison purpose, AltProj, an existing scalable approach to RPCA requires the precise knowlwdge of the true rank; otherwise, it may fail to recover low-rank matrices. By contrast, our method works with or without knowing the true rank; even when both methods work, our method is faster. Extensive experiments have been performed and testified to the effectiveness of proposed method quantitatively and in visual quality, which suggests that our method is suitable to be employed as a light-weight, scalable component for RPCA in any application pipelines.

This paper presents numerical simulations of metal machining processes with Eulerian and Total Lagrangian Smoothed Particle Hydrodynamics (SPH). Being a mesh-free method, SPH can conveniently handle large deformation and material separation. However, the Eulerian SPH (ESPH) in which the kernel functions are computed based on the current particle positions suffers from the tensile instability. The Total Lagrangian SPH (TLSPH) is free of this instability as the kernel functions are calculated in the reference configurations. In this work, the metals are modelled using the Johnson-Cook constitutive model, which can capture strain hardening and thermal softening in metals. The processing/cutting tools are modelled as rigid bodies, while the metal-tool contact forces are considered using the standard SPH interaction and the particle-particle pinball contact in ESPH and TLSPH, respectively. The two methods are employed to model several cases with impact, pressing, and cutting; the results are compared with reference experimental and numerical results. It is found that both the two SPH methods can capture the salient phenomena in metal processing, e.g. strain localisation, large deformation, and material separation. However, the TLSPH approach provides a better simulation of strain localisation and chip morphology. This work shows that the TLSPH method has the potential to model the metal machining processes efficiently without any numerical instabilities., Comment: 21 pages, 19 figures

An algorithm is proposed to model crack initiation and propagation within the total Lagrangian Smoothed Particle Hydrodynamics (TLSPH) framework. TLSPH avoids the two main deficiencies of conventional SPH, i.e., tensile instability and inconsistency, by making use of the Lagrangian kernel and gradient correction, respectively. In the present approach, the support domain of a particle is modified, where it only interacts with its immediately neighbouring particles. A virtual link defines the level of interaction between each particle pair. The state of the virtual link is determined by damage law or cracking criterion. The virtual link approach allows easy and natural modelling of cracking surfaces without explicit cracking treatments such as particle splitting, field enrichment or visibility criterion. The performance of the proposed approach is demonstrated via a few numerical examples of both brittle and ductile failure under impact loading., Comment: 28 pages, 20 figures