In this paper, we address the subspace clustering problem. Given a set of data samples (vectors) approximately drawn from a union of multiple subspaces, our goal is to cluster the samples into their respective subspaces and remove possible outliers as well. To this end, we propose a novel objective function named Low-Rank Representation (LRR), which seeks the lowest rank representation among all the candidates that can represent the data samples as linear combinations of the bases in a given dictionary. It is shown that the convex program associated with LRR solves the subspace clustering problem in the following sense: When the data is clean, we prove that LRR exactly recovers the true subspace structures; when the data are contaminated by outliers, we prove that under certain conditions LRR can exactly recover the row space of the original data and detect the outlier as well; for data corrupted by arbitrary sparse errors, LRR can also approximately recover the row space with theoretical guarantees. Since the subspace membership is provably determined by the row space, these further imply that LRR can perform robust subspace clustering and error correction in an efficient and effective way.

Rain streaks can severely degrade the visibility, which causes many current computer vision algorithms fail to work. So it is necessary to remove the rain from images. We propose a novel deep network architecture based on deep convolutional and recurrent neural networks for single image deraining. As contextual information is very important for rain removal, we first adopt the dilated convolutional neural network to acquire large receptive field. To better fit the rain removal task, we also modify the network. In heavy rain, rain streaks have various directions and shapes, which can be regarded as the accumulation of multiple rain streak layers. We assign different alpha-values to various rain streak layers according to the intensity and transparency by incorporating the squeeze-and-excitation block. Since rain streak layers overlap with each other, it is not easy to remove the rain in one stage. So we further decompose the rain removal into multiple stages. Recurrent neural network is incorporated to preserve the useful information in previous stages and benefit the rain removal in later stages. We conduct extensive experiments on both synthetic and real-world datasets. Our proposed method outperforms the state-of-the-art approaches under all evaluation metrics. Codes and supplementary material are available at our project webpage: https://xialipku.github.io/RESCAN.

In this paper, we consider the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is based on the recently proposed tensor-tensor product (or t-product) [15]. Induced by the t-product, we first rigorously deduce the tensor spectral norm, tensor nuclear norm, and tensor average rank, and show that the tensor nuclear norm is the convex envelope of the tensor average rank within the unit ball of the tensor spectral norm. These definitions, their relationships and properties are consistent with matrix cases. Equipped with the new tensor nuclear norm, we then solve the TRPCA problem by solving a convex program and provide the theoretical guarantee for the exact recovery. Our TRPCA model and recovery guarantee include matrix RPCA as a special case. Numerical experiments verify our results, and the applications to image recovery and background modeling problems demonstrate the effectiveness of our method.

Because of its excellent dielectric properties, silicon oxide (SiO(x)) has long been used and considered as a passive, insulating component in the construction of electronic devices. In contrast, here we demonstrate resistive switches and memories that use SiO(x) as the sole active material and can be implemented in entirely metal-free embodiments. Through cross-sectional transmission electron microscopy, we determine that the switching takes place through the voltage-driven formation and modification of silicon (Si) nanocrystals (NCs) embedded in the SiO(x) matrix, with SiO(x) itself also serving as the source of the formation of this Si pathway. The small sizes of the Si NCs (d ∼ 5 nm) suggest that scaling to ultrasmall domains could be feasible. Meanwhile, the switch also shows robust nonvolatile properties, high ON/OFF ratios (>10(5)), fast switching (sub-100-ns), and good endurance (10(4) write-erase cycles). These properties in a SiO(x)-based material composition showcase its potentials in constructing memory or logic devices that are fully CMOS compatible.

This paper studies the Tensor Robust Principal Component (TRPCA) problem which extends the known Robust P-CA [4] to the tensor case. Our model is based on a new tensor Singular Value Decomposition (t-SVD) [14] and its induced tensor tubal rank and tensor nuclear norm. Consider that we have a 3-way tensor X ∈ R n1×n2×n3 such that X = L 0 + S 0 , where L 0 has low tubal rank and S 0 is sparse. Is that possible to recover both components? In this work, we prove that under certain suitable assumptions, we can recover both the low-rank and the sparse components exactly by simply solving a convex program whose objective is a weighted combination of the tensor nuclear norm and the 1 -norm, i.e., min L,E L * + λ E 1 , s.t. X = L + E, where λ = 1/ max(n 1 , n 2 )n 3 . Interestingly, TRPCA involves RPCA as a special case when n 3 = 1 and thus it is a simple and elegant tensor extension of RPCA. Also numerical experiments verify our theory and the application for the image denoising demonstrates the effectiveness of our method.

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Self-attention mechanism has been widely used for various tasks. It is designed to compute the representation of each position by a weighted sum of the features at all positions. Thus, it can capture long-range relations for computer vision tasks. However, it is computationally consuming. Since the attention maps are computed w.r.t all other positions. In this paper, we formulate the attention mechanism into an expectation-maximization manner and iteratively estimate a much more compact set of bases upon which the attention maps are computed. By a weighted summation upon these bases, the resulting representation is low-rank and deprecates noisy information from the input. The proposed Expectation-Maximization Attention (EMA) module is robust to the variance of input and is also friendly in memory and computation. Moreover, we set up the bases maintenance and normalization methods to stabilize its training procedure. We conduct extensive experiments on popular semantic segmentation benchmarks including PAS-CAL VOC, PASCAL Context and COCO Stuff, on which we set new records 1 .

Learning deeper convolutional neural networks becomes a tendency in recent years. However, many empirical evidences suggest that performance improvement cannot be gained by simply stacking more layers. In this paper, we consider the issue from an information theoretical perspective, and propose a novel method Relay Backpropagation, that encourages the propagation of effective information through the network in training stage. By virtue of the method, we achieved the first place in ILSVRC 2015 Scene Classification Challenge. Extensive experiments on two challenging large scale datasets demonstrate the effectiveness of our method is not restricted to a specific dataset or network architecture. Our models will be available to the research community later.