Tensor train (TT) decomposition represents an N-order tensor using O(N) matrices (i.e., factors) of small dimensions, achieved through products among these factors. Due to its compact representation, TT decomposition ...
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Tensor train (TT) decomposition represents an N-order tensor using O(N) matrices (i.e., factors) of small dimensions, achieved through products among these factors. Due to its compact representation, TT decomposition has found wide applications, including various tensor recovery problems in signal processing and quantum information. In this paper, we study the problem of reconstructing a TT format tensor from measurements that are contaminated by outliers with arbitrary values. Given the vulnerability of smooth formulations to corruptions, we use an l1 loss function to enhance robustness against outliers. We first establish the l1/l2-restricted isometry property (RIP) for Gaussian measurement operators, demonstrating that the information in the TT format tensor can be preserved using a number of measurements that grows linearly with N. We also prove the sharpness property for the l1 loss function optimized over TT format tensors. Building on the l1/l2-RIP and sharpness property, we then propose two complementary methods to recover the TT format tensor from the corrupted measurements: the projected subgradient method (PSubGM), which optimizes over the entire tensor, and the factorized Riemannian subgradient method (FRSubGM), which optimizes directly over the factors. Compared to PSubGM, the factorized approach FRSubGM significantly reduces the memory cost at the expense of a slightly slower convergence rate. Nevertheless, we show that both methods, with diminishing step sizes, converge linearly to the ground-truth tensor given an appropriate initialization, which can be obtained by a truncated spectral method. To the best of our knowledge, this is the first work to provide a theoretical analysis of the robust TT recovery problem and to demonstrate that TT-format tensors can be robustly recovered even when a certain fraction of measurements are arbitrarily corrupted. We conduct various numerical experiments to demonstrate the effectiveness of the two methods in robust
Perceptually-inspired objective functions such as the perceptual evaluation of speech quality (PESQ), signal-to-distortion ratio (SDR), and short-time objective intelligibility (STOI), have recently been used to optim...
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The hand localization problem has been a longstanding focus due to its many applications. The task involves modeling the hand as a singular point and determining its position within a defined coordinate system. Howeve...
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The fifth generation (5G) of wireless communication networks uses the advantages of Massive Multiple-Input Multiple-Output (MIMO) technologies to improve network coverage, increase data speeds, and enhance reliability...
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In this paper, we explore the interplay between code obfuscation techniques and performance counter traces to undermine Hardware Malware Detectors (HMDs) that rely on Machine Learning (ML) models. By crafting various ...
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This study investigates the impact of automobile air conditioning systems on fuel consumption and gas emissions in hybrid and internal combustion engine vehicles using machine learning algorithms. Dynamic and static d...
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Healthcare is a fundamental part of every individual’s *** healthcare industry is developing very rapidly with the help of advanced *** researchers are trying to build cloud-based healthcare applications that can be ...
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Healthcare is a fundamental part of every individual’s *** healthcare industry is developing very rapidly with the help of advanced *** researchers are trying to build cloud-based healthcare applications that can be accessed by healthcare professionals from their premises,as well as by patients from their mobile devices through communication *** systems promote reliable and remote interactions between patients and healthcare ***,there are several limitations to these innovative cloud computing-based systems,namely network availability,latency,battery life and resource *** propose a hybrid mobile cloud computing(HMCC)architecture to address these ***,we also evaluate the performance of heuristic and dynamic machine learning based task scheduling and load balancing algorithms on our proposed *** compare them,to identify the strengths and weaknesses of each algorithm;and provide their comparative results,to show latency and energy consumption *** issues for cloudbased healthcare systems are discussed in detail.
Perusing web data items such as shopping products is a core online user activity. To prevent information overload, the content associated with data items is typically dispersed across multiple webpage sections over mu...
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In the event of a disaster or emergency, it is not uncommon for the dedicated communication infrastructure to become damaged or weakened. This is not just an inconvenience but rather a monumental problem for first res...
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Chaos is a deterministic phenomenon that occurs in a non-linear dynamic system under specific condition when the trajectories of the state vector become periodic and extremely sensitive to the initial conditions. Whil...
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