arXiv subjects

Yuqing Liu

Publications and source records attributed to Yuqing Liu.

41 records · Page 3Linked to original sources

arXiv2022

Reduce the rank calculation of a high-dimensional sparse matrix based on network controllability theory

Numerical computing of the rank of a matrix is a fundamental problem in scientific computation. The datasets generated by the internet often correspond to the analysis of high-dimensional sparse matrices. Notwithstanding recent advances in the promotion of traditional singular value decomposition (SVD), an efficient estimation algorithm for the rank of a high-dimensional sparse matrix is still lacking. Inspired by the controllability theory of complex networks, we converted the rank of a matrix into maximum matching computing. Then, we established a fast rank estimation algorithm by using the cavity method, a powerful approximate technique for computing the maximum matching, to estimate the rank of a sparse matrix. In the merit of the natural low complexity of the cavity method, we showed that the rank of a high-dimensional sparse matrix can be estimated in a much faster way than SVD with high accuracy. Our method offers an efficient pathway to quickly estimate the rank of the high-dimensional sparse matrix when the time cost of computing the rank by SVD is unacceptable.

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arXiv2022

Cross-SRN: Structure-Preserving Super-Resolution Network with Cross Convolution

It is challenging to restore low-resolution (LR) images to super-resolution (SR) images with correct and clear details. Existing deep learning works almost neglect the inherent structural information of images, which acts as an important role for visual perception of SR results. In this paper, we design a hierarchical feature exploitation network to probe and preserve structural information in a multi-scale feature fusion manner. First, we propose a cross convolution upon traditional edge detectors to localize and represent edge features. Then, cross convolution blocks (CCBs) are designed with feature normalization and channel attention to consider the inherent correlations of features. Finally, we leverage multi-scale feature fusion group (MFFG) to embed the cross convolution blocks and develop the relations of structural features in different scales hierarchically, invoking a lightweight structure-preserving network named as Cross-SRN. Experimental results demonstrate the Cross-SRN achieves competitive or superior restoration performances against the state-of-the-art methods with accurate and clear structural details. Moreover, we set a criterion to select images with rich structural textures. The proposed Cross-SRN outperforms the state-of-the-art methods on the selected benchmark, which demonstrates that our network has a significant advantage in preserving edges.

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arXiv2022

Iterative Network for Image Super-Resolution

Single image super-resolution (SISR), as a traditional ill-conditioned inverse problem, has been greatly revitalized by the recent development of convolutional neural networks (CNN). These CNN-based methods generally map a low-resolution image to its corresponding high-resolution version with sophisticated network structures and loss functions, showing impressive performances. This paper provides a new insight on conventional SISR algorithm, and proposes a substantially different approach relying on the iterative optimization. A novel iterative super-resolution network (ISRN) is proposed on top of the iterative optimization. We first analyze the observation model of image SR problem, inspiring a feasible solution by mimicking and fusing each iteration in a more general and efficient manner. Considering the drawbacks of batch normalization, we propose a feature normalization (F-Norm, FN) method to regulate the features in network. Furthermore, a novel block with FN is developed to improve the network representation, termed as FNB. Residual-in-residual structure is proposed to form a very deep network, which groups FNBs with a long skip connection for better information delivery and stabling the training phase. Extensive experimental results on testing benchmarks with bicubic (BI) degradation show our ISRN can not only recover more structural information, but also achieve competitive or better PSNR/SSIM results with much fewer parameters compared to other works. Besides BI, we simulate the real-world degradation with blur-downscale (BD) and downscale-noise (DN). ISRN and its extension ISRN+ both achieve better performance than others with BD and DN degradation models.

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arXiv2020

Power Cyber-Physical System Risk Area Prediction Using Dependent Markov Chain and Improved Grey Wolf Optimization

Existing power cyber-physical system (CPS) risk prediction results are inaccurate as they fail to reflect the actual physical characteristics of the components and the specific operational status. A new method based on dependent Markov chain for power CPS risk area prediction is proposed in this paper. The load and constraints of the non-uniform power CPS coupling network are first characterized, and can be utilized as a node state judgment standard. Considering the component node isomerism and interdependence between the coupled networks, a power CPS risk regional prediction model based on dependent Markov chain is then constructed. A cross-adaptive gray wolf optimization algorithm improved by adaptive position adjustment strategy and cross-optimal solution strategy is subsequently developed to optimize the prediction model. Simulation results using the IEEE 39-BA 110 test system verify the effectiveness and superiority of the proposed method.

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arXiv2018

The realization problem for discrete Morse functions on trees

We introduce a new notion of equivalence of discrete Morse functions on graphs called persistence equivalence. Two functions are considered persistence equivalent if and only if they induce the same persistence diagram. We compare this notion of equivalence to other notions of equivalent discrete Morse functions. We then compute an upper bound for the number of persistence equivalent discrete Morse functions on a fixed graph and show that this upper bound is sharp in the case where our graph is a tree. This is a version of the "realization problem" of the persistence map. We conclude with an example illustrating our construction.

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