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Bayesian network based label correlation analysis for multi-label classifier chain

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arXiv 2019年

作者： Wang, Ran Ye, Suhe Li, Ke Kwong, Sam College of Mathematics and Statistics Shenzhen University Shenzhen518060 China Shenzhen Key Laboratory of Advanced Machine Learning and Applications Shenzhen University Shenzhen518060 China Department of Computer Science University of Exeter ExeterEX4 4QF United Kingdom Department of Computer Science City University of Hong Kong 83 Tat Chee Avenue Kowloon Hong Kong

Classifier chain (CC) is a multi-label learning approach that constructs a sequence of binary classifiers according to a label order. Each classifier in the sequence is responsible for predicting the relevance of one label. When training the classifier for a label, proceeding labels will be taken as extended features. If the extended features are highly correlated to the label, the performance will be improved, otherwise, the performance will not be influenced or even degraded. How to discover label correlation and determine the label order is critical for CC approach. This paper employs Bayesian network (BN) to model the label correlations and proposes a new BN-based CC method (BNCC). First, conditional entropy is used to describe the dependency relations among labels. Then, a BN is built up by taking nodes as labels and weights of edges as their dependency relations. A new scoring function is proposed to evaluate a BN structure, and a heuristic algorithm is introduced to optimize the BN. At last, by applying topological sorting on the nodes of the optimized BN, the label order for constructing CC model is derived. Experimental comparisons demonstrate the feasibility and effectiveness of the proposed method. Copyright © 2019, The Authors. All rights reserved.

关键词： Bayesian networks

Analysis of a Direct Separation Method Based on Adaptive Chirplet Transform for Signals with Crossover Instantaneous Frequencies

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arXiv 2022年

作者： Chui, Charles K. Jiang, Qingtang Li, Lin Lu, Jian Menlo Park residence CA94025 United States Department of Mathematics & Statistics University of Missouri-St. Louis St. LouisMO63121 United States School of Electronic Engineering Xidian University Xi'An710071 China Shenzhen Key Laboratory of Advanced Machine Learning and Applications College of Mathematics & Statistics Shenzhen University Shenzhen518060 China

In many applications, it is necessary to retrieve the sub-signal building blocks of a multicomponent signal, which is usually non-stationary in real-world and real-life applications. Empirical mode decomposition (EMD), synchrosqueezing transform (SST), signal separation operation (SSO), and iterative filtering decomposition (IFD) have been proposed and developed for this purpose. However, these computational methods are restricted by the specification of well-separation of the sub-signal frequency curves for multi-component signals. On the other hand, the chirplet transform-based signal separation scheme (CT3S) that extends SSO from the two-dimensional "time-frequency" plane to the three-dimensional "time-frequency-chirp rate" space was recently proposed in our recent work to remove the frequency-separation specification, and thereby allowing "frequency crossing". The main objective of this present paper is to carry out an in-depth error analysis study of instantaneous frequency estimation and component recovery for the CT3S method. Copyright © 2022, The Authors. All rights reserved.

关键词： Specifications

A deep network for sinogram and CT image reconstruction

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arXiv 2020年

作者： Wang, Wei Xia, Xiang-Gen He, Chuanjiang Ren, Zemin Lu, Jian Wang, Tianfu Lei, Baiying School of Biomedical Engineering Shenzhen University National-Regional Key Technology Engineering Laboratory for Medical Ultrasound Guangdong Key Laboratory for Biomedical Measurements and Ultrasound Imaging School of Biomedical Engineering Health Science Center Shenzhen University Shenzhen China College of Information Engineering Shenzhen University Shenzhen China College of Electrical and Computer Engineering University of Delaware NewarkDE19716 United States College of Mathematics and Statistics Chongqing University Chongqing China College of Mathematics and Physics Chongqing University of Science and Technology Chongqing China Shenzhen Key Laboratory of Advanced Machine Learning and Applications Shenzhen University Shenzhen China

A CT image can be well reconstructed when the sampling rate of the sinogram satisfies the Nyquist criteria and the sampled signal is noise-free. However, in practice, the sinogram is usually contaminated by noise, which degrades the quality of a reconstructed CT image. In this paper, we design a deep network for sinogram and CT image reconstruction. The network consists of two cascaded blocks that are linked by a filter backprojection (FBP) layer, where the former block is responsible for denoising and completing the sinograms while the latter is used to removing the noise and artifacts of the CT images. Experimental results show that the reconstructed CT images by our methods have the highest PSNR and SSIM in average compared to state of the art methods. Copyright © 2020, The Authors. All rights reserved.

关键词： Computerized tomography

A new weighting scheme for fan-beam and circle cone-beam CT reconstructions

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arXiv 2021年

作者： Wang, Wei Xia, Xiang-Gen He, Chuanjiang Ren, Zemin Lu, Jian Wang, Tianfu Lei, Baiying The School of Biomedical Engineering Shenzhen University National-Regional Key Technology Engineering Laboratory for Medical Ultrasound Guangdong Key Laboratory for Biomedical Measurements and Ultrasound Imaging School of Biomedical Engineering Health Science Center Shenzhen University Shenzhen China The Department of Electrical and Computer Engineering University of Delaware NewarkDE19716 United States The College of Mathematics and Statistics Chongqing University Chongqing China The College of Mathematics and Physics Chongqing University of Science and Technology Chongqing China The Shenzhen Key Laboratory of Advanced Machine Learning and Applications Shenzhen University Shenzhen China

In this paper, we first present an arc based algorithm for fan-beam computed tomography (CT) reconstruction via applying Katsevich’s helical CT formula to 2D fan-beam CT reconstruction. Then, we propose a new weighting function to deal with the redundant projection data. By extending the weighted arc based fan-beam algorithm to circle cone-beam geometry, we also obtain a new FDK-similar algorithm for circle cone-beam CT reconstruction. Experiments show that our methods can obtain higher PSNR and SSIM compared to the Parker-weighted conventional fan-beam algorithm and the FDK algorithm for super-short-scan trajectories. Copyright © 2021, The Authors. All rights reserved.

关键词： Computerized tomography

A model-guided deep network for limited-angle computed tomography

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arXiv 2020年

作者： Wang, Wei Xia, Xiang-Gen He, Chuanjiang Ren, Zemin Lu, Jian Wang, Tianfu Lei, Baiying School of Biomedical Engineering Shenzhen University National-Regional Key Technology Engineering Laboratory for Medical Ultrasound Guangdong Key Laboratory for Biomedical Measurements and Ultrasound Imaging School of Biomedical Engineering Health Science Center Shenzhen University Shenzhen China Department of Electrical and Computer Engineering University of Delaware NewarkDE19716 United States College of Mathematics and Statistics Chongqing University Chongqing China College of Mathematics and Physics Chongqing University of Science and Technology Chongqing China Shenzhen Key Laboratory of Advanced Machine Learning and Applications Shenzhen University Shenzhen China

In this paper, we first propose a variational model for the limited-angle computed tomography (CT) image reconstruction and then convert the model into an end-to-end deep network. We use the penalty method to solve the model and divide it into three iterative subproblems, where the first subproblem completes the sinograms by utilizing the prior information of sinograms in the frequency domain and the second refines the CT images by using the prior information of CT images in the spatial domain, and the last merges the outputs of the first two subproblems. In each iteration, we use the convolutional neural networks (CNNs) to approxiamte the solutions of the first two subproblems and, thus, obtain an end-to-end deep network for the limited-angle CT image reconstruction. Our network tackles both the sinograms and the CT images, and can simultaneously suppress the artifacts caused by the incomplete data and recover fine structural information in the CT images. Experimental results show that our method outperforms the existing algorithms for the limited-angle CT image reconstruction. Copyright © 2020, The Authors. All rights reserved.

关键词： Computerized tomography

A signal separation method based on adaptive continuous wavelet transform and its analysis

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arXiv 2020年

作者： Chui, Charles K. Jiang, Qingtang Li, Lin Lu, Jian College of Mathematics & Statistics Shenzhen University Shenzhen518060 China Department of Mathematics Hong Kong Baptist University Hong Kong Department of Mathematics & Statistics University of Missouri-St. Louis St. LouisMO63121 United States School of Electronic Engineering Xidian University Xi'an710071 China Shenzhen Key Laboratory of Advanced Machine Learning and Applications College of Mathematics & Statistics Shenzhen University Shenzhen518060 China

In nature and engineering world, the measured signals are usually affected by multiple complicated factors and they appear as multicomponent non-stationary modes. In many situations we need to separate these signals to a finite number of mono-components to represent the intrinsic modes and underlying dynamics implicated in the source signals. Recently the synchrosqueezing transform (SST) was developed as an empirical mode decomposition (EMD)-like tool to enhance the time-frequency resolution and energy concentration of a multicomponent non-stationary signal and provides more accurate component recovery. To recover individual components, the SST method consists of two steps. First the instantaneous frequency (IF) of a component is estimated from the SST plane. Secondly, after IF is recovered, the associated component is computed by a definite integral along the estimated IF curve on the SST plane. The reconstruction accuracy for a component depends heavily on the accuracy of the IFs estimation carried out in the first step. More recently, a direct method of the time-frequency approach, called signal separation operation (SSO), was introduced for multicomponent signal separation. While both SST and SSO are mathematically rigorous on IF estimation, SSO avoids the second step of the two-step SST method in component recovery (mode retrieval). The SSO method is based the short-time Fourier transform. In this paper we propose a direct method of signal separation based on the adaptive continuous wavelet transform (CWT). We introduce two models of the adaptive CWT-based approach for signal separation: the sinusoidal signal-based model and the linear chirp-based model, which are derived respectively from sinusoidal signal approximation and the linear chirp approximation at any local time. A more accurate component recovery formula is derived from linear chirp local approximation. We present the theoretical analysis of our approach. For each model, we establish the error bound

关键词： Error analysis

Analysis of an Adaptive Short-Time Fourier Transform-Based Multicomponent Signal Separation Method Derived from Linear Chirp Local Approximation

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arXiv 2020年

作者： Chui, Charles K. Jiang, Qingtang Li, Lin Lu, Jian College of Mathematics & Statistics Shenzhen University Shenzhen518060 China Department of Mathematics Hong Kong Baptist University Hong Kong Department of Math & Computer Sci. Univ. of Missouri-St. Louis St. LouisMO63121 United States School of Electronic Engineering Xidian University Xian710071 China Shenzhen Key Laboratory of Advanced Machine Learning and Applications College of Mathematics & Statistics Shenzhen University Shenzhen518060 China

The synchrosqueezing transform (SST) has been developed as a powerful EMD-like tool for instantaneous frequency (IF) estimation and component separation of non-stationary multicomponent signals. Recently, a direct method of the time-frequency approach, called signal separation operation (SSO), was introduced to solving the problem of multicomponent signal separation. While both SST and SSO are mathematically rigorous on IF estimation, SSO avoids the second step of the two-step SST method in component recovery (mode retrieval). In addition, SSO is simple: the IF of a component is estimated by a time-frequency ridge of the SSO plane;and this component is recovered by simply plugging the time-frequency ridge to the SSO operation. In recent paper "Direct signal separation via extraction of local frequencies with adaptive time-varying parameters", after showing that the SSO operation is related to the adaptive short-time Fourier transform (STFT), the authors obtained a more accurate component recovery formula derived from the linear chirp (also called linear frequency modulation signal) approximation at any local time and they also proposed a recovery scheme to extract the signal components one by one with the time-varying window updated for each component. However the theoretical analysis of the recovery formula derived from linear chirp local approximation has not been studied there. In this paper, we carry out such analysis and obtain error bounds for IF estimation and component recovery. These results provide a mathematical guarantee to the proposed adaptive STFT-based non-stationary multicomponent signal separation method. Copyright © 2020, The Authors. All rights reserved.

关键词： Error analysis

A Review of Generalized Zero-Shot learning Methods

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arXiv 2020年

作者： Pourpanah, Farhad Abdar, Moloud Luo, Yuxuan Zhou, Xinlei Wang, Ran Lim, Chee Peng Wang, Xi-Zhao Jonathan Wu, Q.M. The Centre for Computer Vision and Deep Learning Department of Electrical and Computer Engineering University of Windsor WindsorONN9B 3P4 Canada Deakin University Australia The Department of Computer Science City University of Hong Kong Hong Kong The College of Mathematics and Statistics Shenzhen Key Lab. of Advanced Machine Learning and Applications Shenzhen University Shenzhen518060 China The College of Computer Science and Software Engineering Guangdong Key Lab. of Intelligent Information Processing Shenzhen University Shenzhen518060 China

Generalized zero-shot learning (GZSL) aims to train a model for classifying data samples under the condition that some output classes are unknown during supervised learning. To address this challenging task, GZSL leverages semantic information of the seen (source) and unseen (target) classes to bridge the gap between both seen and unseen classes. Since its introduction, many GZSL models have been formulated. In this review paper, we present a comprehensive review on GZSL. Firstly, we provide an overview of GZSL including the problems and challenges. Then, we introduce a hierarchical categorization for the GZSL methods and discuss the representative methods in each category. In addition, we discuss the available benchmark data sets and applications of GZSL, along with a discussion on the research gaps and directions for future investigations. Copyright © 2020, The Authors. All rights reserved.

关键词： Zero-shot learning

Partial regularity of suitable weak solutions of the Navier-Stokes-Planck-Nernst-Poisson equation

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arXiv 2019年

作者： Gong, Huajun Wang, Changyou Zhang, Xiaotao Shenzhen Key Laboratory of Advance Machine Learning and Applications College of Mathematics and Statistics Shenzhen University Shenzhen Guangdong518060 China Department of Mathematics Purdue University West LafayetteIN47907 United States South China Research Center for Applied Mathematics and Interdisciplinary Studies South China Normal University Zhong Shan Avenue West 55 Guangzhou510631 China

In this paper, inspired by the seminal work by Caffarelli-Kohn-Nirenberg [1] on the incompressible Navier-Stokes equation, we establish the existence of a suitable weak solution to the Navier-Stokes-Planck-Nernst-Poisson equation in dimension three, which is shown to be smooth away from a closed set whose 1-dimensional parabolic Hausdorff measure is zero. Copyright © 2019, The Authors. All rights reserved.

关键词： Navier Stokes equations