Recently, adversarial attack methods have been developed to challenge the robustness of machine learning models. However, mainstream evaluation criteria experience limitations, even yielding discrepancies among results under different settings. By ex
amining various attack algorithms, including gradient-based and query-based attacks, we notice the lack of a consensus on a uniform standard for unbiased performance evaluation. Accordingly, we propose a Piece-wise Sampling Curving (PSC) toolkit to effectively address the aforementioned discrepancy, by generating a comprehensive comparison among adversaries in a given range. In addition, the PSC toolkit offers options for balancing the computational cost and evaluation effectiveness. Experimental results demonstrate our PSC toolkit presents comprehensive comparisons of attack algorithms, significantly reducing discrepancies in practice.
Low rank tensor ring model is powerful for image completion which recovers missing entries in data acquisition and transformation. The recently proposed tensor ring (TR) based completion algorithms generally solve the low rank optimization problem by
alternating least squares method with predefined ranks, which may easily lead to overfitting when the unknown ranks are set too large and only a few measurements are available. In this paper, we present a Bayesian low rank tensor ring model for image completion by automatically learning the low rank structure of data. A multiplicative interaction model is developed for the low-rank tensor ring decomposition, where core factors are enforced to be sparse by assuming their entries obey Student-T distribution. Compared with most of the existing methods, the proposed one is free of parameter-tuning, and the TR ranks can be obtained by Bayesian inference. Numerical Experiments, including synthetic data, color images with different sizes and YaleFace dataset B with respect to one pose, show that the proposed approach outperforms state-of-the-art ones, especially in terms of recovery accuracy.
Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However, existing
algorithms need predefined tensor ring rank which may be hard to determine in practice. To address the issue, we propose a hierarchical tensor ring decomposition for more compact representation. We use the standard tensor ring to decompose a tensor into several 3-order sub-tensors in the first layer, and each sub-tensor is further factorized by tensor singular value decomposition (t-SVD) in the second layer. In the low rank tensor completion based on the proposed decomposition, the zero elements in the 3-order core tensor are pruned in the second layer, which helps to automatically determinate the tensor ring rank. To further enhance the recovery performance, we use total variation to exploit the locally piece-wise smoothness data structure. The alternating direction method of multiplier can divide the optimization model into several subproblems, and each one can be solved efficiently. Numerical experiments on color images and hyperspectral images demonstrate that the proposed algorithm outperforms state-of-the-arts ones in terms of recovery accuracy.
Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The tensor ring (TR) decomposition is invariant under the permutation of tensors with different mode properties
, which ensures the uniformity of decomposed factors and mode attributes. The TR has powerful expression ability and achieves success in some multi-dimensional data processing applications. To let coupled tensors help each other for missing component estimation, in this paper we utilize TR for coupled completion by sharing parts of the latent factors. The optimization model for coupled TR completion is developed with a novel Frobenius norm. It is solved by the block coordinate descent algorithm which efficiently solves a series of quadratic problems resulted from sampling pattern. The excess risk bound for this optimization model shows the theoretical performance enhancement in comparison with other coupled nuclear norm based methods. The proposed method is validated on numerical experiments on synthetic data, and experimental results on real-world data demonstrate its superiority over the state-of-the-art methods in terms of recovery accuracy.
Low-rank tensor completion recovers missing entries based on different tensor decompositions. Due to its outstanding performance in exploiting some higher-order data structure, low rank tensor ring has been applied in tensor completion. To further de
al with its sensitivity to sparse component as it does in tensor principle component analysis, we propose robust tensor ring completion (RTRC), which separates latent low-rank tensor component from sparse component with limited number of measurements. The low rank tensor component is constrained by the weighted sum of nuclear norms of its balanced unfoldings, while the sparse component is regularized by its l1 norm. We analyze the RTRC model and gives the exact recovery guarantee. The alternating direction method of multipliers is used to divide the problem into several sub-problems with fast solutions. In numerical experiments, we verify the recovery condition of the proposed method on synthetic data, and show the proposed method outperforms the state-of-the-art ones in terms of both accuracy and computational complexity in a number of real-world data based tasks, i.e., light-field image recovery, shadow removal in face images, and background extraction in color video.
Tensor completion estimates missing components by exploiting the low-rank structure of multi-way data. The recently proposed methods based on tensor train (TT) and tensor ring (TR) show better performance in image recovery than classical ones. Compar
ed with TT and TR, the projected entangled pair state (PEPS), which is also called tensor grid (TG), allows more interactions between different dimensions, and may lead to more compact representation. In this paper, we propose to perform image completion based on low-rank tensor grid. A two-stage density matrix renormalization group algorithm is used for initialization of TG decomposition, which consists of multiple TT decompositions. The latent TG factors can be alternatively obtained by solving alternating least squares problems. To further improve the computational efficiency, a multi-linear matrix factorization for low rank TG completion is developed by using parallel matrix factorization. Experimental results on synthetic data and real-world images show the proposed methods outperform the existing ones in terms of recovery accuracy.
