Tensor network decomposition, originated from quantum physics to model entangled many-particle quantum systems, turns out to be a promising mathematical technique to efficiently represent and process big data in parsimonious manner. In this study, we show that tensor networks can systematically partition structured data, e.g. color images, for distributed storage and communication in privacy-preserving manner. Leveraging the sea of big data and metadata privacy, empirical results show that neighbouring subtensors with implicit information stored in tensor network formats cannot be identified for data reconstruction. This technique complements the existing encryption and randomization techniques which store explicit data representation at one place and highly susceptible to adversarial attacks such as side-channel attacks and de-anonymization. Furthermore, we propose a theory for adversarial examples that mislead convolutional neural networks to misclassification using subspace analysis based on singular value decomposition (SVD). The theory is extended to analyze higher-order tensors using tensor-train SVD (TT-SVD); it helps to explain the level of susceptibility of different datasets to adversarial attacks, the structural similarity of different adversarial attacks including global and localized attacks, and the efficacy of different adversarial defenses based on input transformation. An efficient and adaptive algorithm based on robust TT-SVD is then developed to detect strong and static adversarial attacks.
In the field of computer vision, SVD has been used for image denoising, compression, and forensic such as steganography and watermarking. Higher-order SVD can help to disentangle the constituents factors or modes of image ensembles, e.g., TensorFaces @cite_2 for facial images with different lighting conditions, viewpoint and poses. Closely related to our work is the use of SVD to extract features for visual quality assessment. Reference images are usually provided for comparison between images before and after processing @cite_66 , whereas no reference measure requires assumptions on the patches to be analyzed such as anisotropy @cite_20 ; all of the SVD-based image quality metrics work on grayscale images. Adversary does not provide the reference images for comparison; our work extends the SVD properties to higher-order tensors and analyze the robustness of correlation structure extracted from input data for image classification by CNNs.
@cite_66 @cite_20 @cite_2
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We study the use of machine learning for visual quality evaluation with comprehensive singular value decomposition (SVD)-based visual features. In this paper, the two-stage process and the relevant work in the existing visual quality metrics are first introduced followed by an in-depth analysis of SVD for visual quality assessment. Singular values and vectors form the selected features for visual quality assessment. Machine learning is then used for the feature pooling process and demonstrated to be effective. This is to address the limitations of the existing pooling techniques, like simple summation, averaging, Minkowski summation, etc., which tend to be ad hoc. We advocate machine learning for feature pooling because it is more systematic and data driven. The experiments show that the proposed method outperforms the eight existing relevant schemes. Extensive analysis and cross validation are performed with ten publicly available databases (eight for images with a total of 4042 test images and two for video with a total of 228 videos). We use all publicly accessible software and databases in this study, as well as making our own software public, to facilitate comparison in future research. Across the field of inverse problems in image and video processing, nearly all algorithms have various parameters which need to be set in order to yield good results. In practice, usually the choice of such parameters is made empirically with trial and error if no “ground-truth” reference is available. Some analytical methods such as cross-validation and Stein's unbiased risk estimate (SURE) have been successfully used to set such parameters. However, these methods tend to be strongly reliant on restrictive assumptions on the noise, and also computationally heavy. In this paper, we propose a no-reference metric Q which is based upon singular value decomposition of local image gradient matrix, and provides a quantitative measure of true image content (i.e., sharpness and contrast as manifested in visually salient geometric features such as edges,) in the presence of noise and other disturbances. This measure 1) is easy to compute, 2) reacts reasonably to both blur and random noise, and 3) works well even when the noise is not Gaussian. The proposed measure is used to automatically and effectively set the parameters of two leading image denoising algorithms. Ample simulated and real data experiments support our claims. Furthermore, tests using the TID2008 database show that this measure correlates well with subjective quality evaluations for both blur and noise distortions. Natural images are the composite consequence of multiple factors related to scene structure, illumination, and imaging. Multilinear algebra, the algebra of higher-order tensors, offers a potent mathematical framework for analyzing the multifactor structure of image ensembles and for addressing the difficult problem of disentangling the constituent factors or modes. Our multilinear modeling technique employs a tensor extension of the conventional matrix singular value decomposition (SVD), known as the N-mode SVD. As a concrete example, we consider the multilinear analysis of ensembles of facial images that combine several modes, including different facial geometries (people), expressions, head poses, and lighting conditions. Our resulting "TensorFaces" representation has several advantages over conventional eigenfaces. More generally, multilinear analysis shows promise as a unifying framework for a variety of computer vision problems.