arXiv subjects

Yicong He

Publications and source records attributed to Yicong He.

8 recordsLinked to original sources

arXiv2023

Scalable and Robust Tensor Ring Decomposition for Large-scale Data

Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is hindered by prevalent large data sizes, missing entries, and corruption with outliers. In this work, we propose a scalable and robust TR decomposition algorithm capable of handling large-scale tensor data with missing entries and gross corruptions. We first develop a novel auto-weighted steepest descent method that can adaptively fill the missing entries and identify the outliers during the decomposition process. Further, taking advantage of the tensor ring model, we develop a novel fast Gram matrix computation (FGMC) approach and a randomized subtensor sketching (RStS) strategy which yield significant reduction in storage and computational complexity. Experimental results demonstrate that the proposed method outperforms existing TR decomposition methods in the presence of outliers, and runs significantly faster than existing robust tensor completion algorithms.

cs.LG↗

arXiv2022

Robust Low-tubal-rank Tensor Completion based on Tensor Factorization and Maximum Correntopy Criterion

The goal of tensor completion is to recover a tensor from a subset of its entries, often by exploiting its low-rank property. Among several useful definitions of tensor rank, the low-tubal-rank was shown to give a valuable characterization of the inherent low-rank structure of a tensor. While some low-tubal-rank tensor completion algorithms with favorable performance have been recently proposed, these algorithms utilize second-order statistics to measure the error residual, which may not work well when the observed entries contain large outliers. In this paper, we propose a new objective function for low-tubal-rank tensor completion, which uses correntropy as the error measure to mitigate the effect of the outliers. To efficiently optimize the proposed objective, we leverage a half-quadratic minimization technique whereby the optimization is transformed to a weighted low-tubal-rank tensor factorization problem. Subsequently, we propose two simple and efficient algorithms to obtain the solution and provide their convergence and complexity analysis. Numerical results using both synthetic and real data demonstrate the robust and superior performance of the proposed algorithms.

cs.LG↗

arXiv2022

Patch Tracking-based Streaming Tensor Ring Completion for Visual Data Recovery

Tensor completion aims to recover the missing entries of a partially observed tensor by exploiting its low-rank structure, and has been applied to visual data recovery. In applications where the data arrives sequentially such as streaming video completion, the missing entries of the tensor need to be dynamically recovered in a streaming fashion. Traditional streaming tensor completion algorithms treat the entire visual data as a tensor, which may not work satisfactorily when there is a big change in the tensor subspace along the temporal dimension, such as due to strong motion across the video frames. In this paper, we develop a novel patch tracking-based streaming tensor ring completion framework for visual data recovery. Given a newly incoming frame, small patches are tracked from the previous frame. Meanwhile, for each tracked patch, a patch tensor is constructed by stacking similar patches from the new frame. Patch tensors are then completed using a streaming tensor ring completion algorithm, and the incoming frame is recovered using the completed patch tensors. We propose a new patch tracking strategy that can accurately and efficiently track the patches with missing data. Further, a new streaming tensor ring completion algorithm is proposed which can efficiently and accurately update the latent core tensors and complete the missing entries of the patch tensors. Extensive experimental results demonstrate the superior performance of the proposed algorithms compared with both batch and streaming state-of-the-art tensor completion methods.

cs.CV↗

arXiv2022

Coarse to Fine Two-Stage Approach to Robust Tensor Completion of Visual Data

Tensor completion is the problem of estimating the missing values of high-order data from partially observed entries. Data corruption due to prevailing outliers poses major challenges to traditional tensor completion algorithms, which catalyzed the development of robust algorithms that alleviate the effect of outliers. However, existing robust methods largely presume that the corruption is sparse, which may not hold in practice. In this paper, we develop a two-stage robust tensor completion approach to deal with tensor completion of visual data with a large amount of gross corruption. A novel coarse-to-fine framework is proposed which uses a global coarse completion result to guide a local patch refinement process. To efficiently mitigate the effect of a large number of outliers on tensor recovery, we develop a new M-estimator-based robust tensor ring recovery method which can adaptively identify the outliers and alleviate their negative effect in the optimization. The experimental results demonstrate the superior performance of the proposed approach over state-of-the-art robust algorithms for tensor completion.

cs.LG↗

arXiv2019

Robust Matrix Completion via Maximum Correntropy Criterion and Half Quadratic Optimization

Robust matrix completion aims to recover a low-rank matrix from a subset of noisy entries perturbed by complex noises, where traditional methods for matrix completion may perform poorly due to utilizing $l_2$ error norm in optimization. In this paper, we propose a novel and fast robust matrix completion method based on maximum correntropy criterion (MCC). The correntropy based error measure is utilized instead of using $l_2$-based error norm to improve the robustness to noises. Using the half-quadratic optimization technique, the correntropy based optimization can be transformed to a weighted matrix factorization problem. Then, two efficient algorithms are derived, including alternating minimization based algorithm and alternating gradient descend based algorithm. The proposed algorithms do not need to calculate singular value decomposition (SVD) at each iteration. Further, the adaptive kernel selection strategy is proposed to accelerate the convergence speed as well as improve the performance. Comparison with existing robust matrix completion algorithms is provided by simulations, showing that the new methods can achieve better performance than existing state-of-the-art algorithms.

cs.IT↗

arXiv2018

Diffusion Adaptation Framework for Compressive Sensing Reconstruction

Compressive sensing(CS) has drawn much attention in recent years due to its low sampling rate as well as high recovery accuracy. As an important procedure, reconstructing a sparse signal from few measurement data has been intensively studied. Many reconstruction algorithms have been proposed and shown good reconstruction performance. However, when dealing with large-scale sparse signal reconstruction problem, the storage requirement will be high, and many algorithms also suffer from high computational cost. In this paper, we propose a novel diffusion adaptation framework for CS reconstruction, where the reconstruction is performed in a distributed network. The data of measurement matrix are partitioned into small parts and are stored in each node, which assigns the storage load in a decentralized manner. The local information interaction provides the reconstruction ability. Then, a simple and efficient gradient-descend based diffusion algorithm has been proposed to collaboratively recover the sparse signal over network. The convergence of the proposed algorithm is analyzed. To further increase the convergence speed, a mini-batch based diffusion algorithm is also proposed. Simulation results show that the proposed algorithms can achieve good reconstruction accuracy as well as fast convergence speed.

cs.IT↗

arXiv2018

Maximum Total Correntropy Diffusion Adaptation over Networks with Noisy Links

Distributed estimation over networks draws much attraction in recent years. In many situations, due to imperfect information communication among nodes, the performance of traditional diffusion adaptive algorithms such as the diffusion LMS (DLMS) may degrade. To deal with this problem, several modified DLMS algorithms have been proposed. However, these DLMS based algorithms still suffer from biased estimation and are not robust to impulsive link noise. In this paper, we focus on improving the performance of diffusion adaptation with noisy links from two aspects: accuracy and robustness. A new algorithm called diffusion maximum total correntropy (DMTC) is proposed. The new algorithm is theoretically unbiased in Gaussian noise, and can efficiently handle the link noises in the presence of large outliers. The adaptive combination rule is applied to further improve the performance. The stability analysis of the proposed algorithm is given. Simulation results show that the DMTC algorithm can achieve good performance in both Gaussian and non-Gaussian noise environments.

cs.IT↗

arXiv2017

Maximum Correntropy Adaptive Filtering Approach for Robust Compressive Sensing Reconstruction

Robust compressive sensing(CS) reconstruction has become an attractive research topic in recent years. Robust CS aims to reconstruct the sparse signals under non-Gaussian(i.e. heavy tailed) noises where traditional CS reconstruction algorithms may perform very poorly due to utilizing $l_2$ norm of the residual vector in optimization. Most of existing robust CS reconstruction algorithms are based on greedy pursuit method or convex relaxation approach. Recently, the adaptive filtering framework has been introduced to deal with the CS reconstruction, which shows desirable performance in both efficiency and reconstruction performance under Gaussian noise. In this paper, we propose an adaptive filtering based robust CS reconstruction algorithm, called $l_0$ regularized maximum correntropy criterion($l_0$-MCC) algorithm, which combines the adaptive filtering framework and maximum correntropy criterion(MCC). MCC has recently been successfully used in adaptive filtering due to its robustness to impulsive non-Gaussian noises and low computational complexity. We analyze theoretically the stability of the proposed $l_0$-MCC algorithm. A mini-batch based $l_0$-MCC(MB-$l_0$-MCC) algorithm is further developed to speed up the convergence. Comparison with existing robust CS reconstruction algorithms is conducted via simulations, showing that the proposed $l_0$-MCC and MB-$l_0$-MCC can achieve significantly better performance than other algorithms.

cs.IT↗