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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In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data and as an application consider 3-D and 4- D (color) video data completion and de-noising. We exploit the recently proposed tensor-Singular Value Decomposition (t-SVD)[11]. Based on t-SVD, the notion of multilinear rank and a related tensor nuclear norm was proposed in [11] to characterize informational and structural complexity of multilinear data. We first show that videos with linear camera motion can be represented more efficiently using t-SVD compared to the approaches based on vectorizing or flattening of the tensors. Since efficiency in representation implies efficiency in recovery, we outline a tensor nuclear norm penalized algorithm for video completion from missing entries. Application of the proposed algorithm for video recovery from missing entries is shown to yield a superior performance over existing methods. We also consider the problem of tensor robust Principal Component Analysis (PCA) for de-noising 3-D video data from sparse random corruptions. We show superior performance of our method compared to the matrix robust PCA adapted to this setting as proposed in [4]. In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data and as an application consider 3-D and 4- D (color) video data completion and de-noising. We exploit the recently proposed tensor-Singular Value Decomposition (t-SVD)[11]. Based on t-SVD, the notion of multilinear rank and a related tensor nuclear norm was proposed in [11] to characterize informational and structural complexity of multilinear data. We first show that videos with linear camera motion can be represented more efficiently using t-SVD compared to the approaches based on vectorizing or flattening of the tensors. Since efficiency in representation implies efficiency in recovery, we outline a tensor nuclear norm penalized algorithm for video completion from missing entries. Application of the proposed algorithm for video recovery from missing entries is shown to yield a superior performance over existing methods. We also consider the problem of tensor robust Principal Component Analysis (PCA) for de-noising 3-D video data from sparse random corruptions. We show superior performance of our method compared to the matrix robust PCA adapted to this setting as proposed in [4]. In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensor- Singular Value Decomposition (t-SVD)[1], which is a group theoretic framework for tensor decomposition. In contrast to popular existing tensor decomposition techniques such as higher-order SVD (HOSVD), t-SVD has optimality properties similar to the truncated SVD for matrices. Based on t-SVD, we first construct novel tensor-rank like measures to characterize informational and structural complexity of multilinear data. Following that we outline a complexity penalized algorithm for tensor completion from missing entries. As an application, 3-D and 4-D (color) video data compression and recovery are considered. We show that videos with linear camera motion can be represented more efficiently using t-SVD compared to traditional approaches based on vectorizing or flattening of the tensors. Application of the proposed tensor completion algorithm for video recovery from missing entries is shown to yield a superior performance over existing methods. In conclusion we point out several research directions and implications to online prediction of multilinear data. With deep learning becoming the dominant approach in computer vision, the use of representations extracted from Convolutional Neural Nets (CNNs) is quickly gaining ground on Fisher Vectors (FVs) as favoured state-of-the-art global image descriptors for image instance retrieval. While the good performance of CNNs for image classification are unambiguously recognised, which of the two has the upper hand in the image retrieval context is not entirely clear yet. In this work, we propose a comprehensive study that systematically evaluates FVs and CNNs for image retrieval. The first part compares the performances of FVs and CNNs on multiple publicly available data sets. We investigate a number of details specific to each method. For FVs, we compare sparse descriptors based on interest point detectors with dense single-scale and multi-scale variants. For CNNs, we focus on understanding the impact of depth, architecture and training data on retrieval results. Our study shows that no descriptor is systematically better than the other and that performance gains can usually be obtained by using both types together. The second part of the study focuses on the impact of geometrical transformations such as rotations and scale changes. FVs based on interest point detectors are intrinsically resilient to such transformations while CNNs do not have a built-in mechanism to ensure such invariance. We show that performance of CNNs can quickly degrade in presence of rotations while they are far less affected by changes in scale. We then propose a number of ways to incorporate the required invariances in the CNN pipeline. Overall, our work is intended as a reference guide offering practically useful and simply implementable guidelines to anyone looking for state-of-the-art global descriptors best suited to their specific image instance retrieval problem.