arXiv subjects

Hanyu Li

Publications and source records attributed to Hanyu Li.

At least 73 records · Page 4Linked to original sources

arXiv2022

Sketch-and-project methods for tensor linear systems

For tensor linear systems with respect to the popular t-product, we first present the sketch-and-project method and its adaptive variants. Their Fourier domain versions are also investigated. Then, considering that the existing sketching tensor or way for sampling has some limitations, we propose two improved strategies. Convergence analyses for the methods mentioned above are provided. We compare our methods with the existing ones using synthetic and real data. Numerical results show that they have quite decent performance in terms of the number of iterations and running time.

math.NA↗

arXiv2022

Splitting-based randomized iterative methods for solving indefinite least squares problem

The indefinite least squares (ILS) problem is a generalization of the famous linear least squares problem. It minimizes an indefinite quadratic form with respect to a signature matrix. For this problem, we first propose an impressively simple and effective splitting (SP) method according to its own structure and prove that it converges 'unconditionally' for any initial value. Further, to avoid implementing some matrix multiplications and calculating the inverse of large matrix and considering the acceleration and efficiency of the randomized strategy, we develop two randomized iterative methods on the basis of the SP method as well as the randomized Kaczmarz, Gauss-Seidel and coordinate descent methods, and describe their convergence properties. Numerical results show that our three methods all have quite decent performance in both computing time and iteration numbers compared with the latest iterative method of the ILS problem, and also demonstrate that the two randomized methods indeed yield significant acceleration in term of computing time.

math.NA↗

arXiv2022

Rope3D: TheRoadside Perception Dataset for Autonomous Driving and Monocular 3D Object Detection Task

Concurrent perception datasets for autonomous driving are mainly limited to frontal view with sensors mounted on the vehicle. None of them is designed for the overlooked roadside perception tasks. On the other hand, the data captured from roadside cameras have strengths over frontal-view data, which is believed to facilitate a safer and more intelligent autonomous driving system. To accelerate the progress of roadside perception, we present the first high-diversity challenging Roadside Perception 3D dataset- Rope3D from a novel view. The dataset consists of 50k images and over 1.5M 3D objects in various scenes, which are captured under different settings including various cameras with ambiguous mounting positions, camera specifications, viewpoints, and different environmental conditions. We conduct strict 2D-3D joint annotation and comprehensive data analysis, as well as set up a new 3D roadside perception benchmark with metrics and evaluation devkit. Furthermore, we tailor the existing frontal-view monocular 3D object detection approaches and propose to leverage the geometry constraint to solve the inherent ambiguities caused by various sensors, viewpoints. Our dataset is available on https://thudair.baai.ac.cn/rope.

cs.CV↗

arXiv2021

AxonEM Dataset: 3D Axon Instance Segmentation of Brain Cortical Regions

Electron microscopy (EM) enables the reconstruction of neural circuits at the level of individual synapses, which has been transformative for scientific discoveries. However, due to the complex morphology, an accurate reconstruction of cortical axons has become a major challenge. Worse still, there is no publicly available large-scale EM dataset from the cortex that provides dense ground truth segmentation for axons, making it difficult to develop and evaluate large-scale axon reconstruction methods. To address this, we introduce the AxonEM dataset, which consists of two 30x30x30 um^3 EM image volumes from the human and mouse cortex, respectively. We thoroughly proofread over 18,000 axon instances to provide dense 3D axon instance segmentation, enabling large-scale evaluation of axon reconstruction methods. In addition, we densely annotate nine ground truth subvolumes for training, per each data volume. With this, we reproduce two published state-of-the-art methods and provide their evaluation results as a baseline. We publicly release our code and data at https://connectomics-bazaar.github.io/proj/AxonEM/index.html to foster the development of advanced methods.

cs.CV↗

arXiv2021

Convergence directions of the randomized Gauss--Seidel method and its extension

The randomized Gauss--Seidel method and its extension have attracted much attention recently and their convergence rates have been considered extensively. However, the convergence rates are usually determined by upper bounds, which cannot fully reflect the actual convergence. In this paper, we make a detailed analysis of their convergence behaviors. The analysis shows that the larger the singular value of $A$ is, the faster the error decays in the corresponding singular vector space, and the convergence directions are mainly driven by the large singular values at the beginning, then gradually driven by the small singular values, and finally by the smallest nonzero singular value. These results explain the phenomenon found in the extensive numerical experiments appearing in the literature that these two methods seem to converge faster at the beginning. Numerical examples are provided to confirm the above findings.

math.NA↗

arXiv2021

Preconvergence of the randomized extended Kaczmarz method

In this paper, we analyze the convergence behavior of the randomized extended Kaczmarz (REK) method for all types of linear systems (consistent or inconsistent, overdetermined or underdetermined, full-rank or rank-deficient). The analysis shows that the larger the singular value of $A$ is, the faster the error decays in the corresponding right singular vector space, and as $k\rightarrow\infty$, $x_{k}-x_{\star}$ tends to the right singular vector corresponding to the smallest singular value of $A$, where $x_{k}$ is the $k$th approximation of the REK method and $x_{\star}$ is the minimum $\ell_2 $-norm least squares solution. These results explain the phenomenon found in the extensive numerical experiments appearing in the literature that the REK method seems to converge faster in the beginning. A simple numerical example is provided to confirm the above findings.

math.NA↗

arXiv2021

Optimal Sampling Algorithms for Block Matrix Multiplication

In this paper, we investigate the randomized algorithms for block matrix multiplication from random sampling perspective. Based on the A-optimal design criterion, the optimal sampling probabilities and sampling block sizes are obtained. To improve the practicability of the block sizes, two modified ones with less computation cost are provided. With respect to the second one, a two step algorithm is also devised. Moreover, the probability error bounds for the proposed algorithms are given. Extensive numerical results show that our methods outperform the existing one in the literature.

math.NA↗

arXiv2020

Greedy Motzkin-Kaczmarz methods for solving linear systems

The famous greedy randomized Kaczmarz (GRK) method uses the greedy selection rule on maximum distance to determine a subset of the indices of working rows. In this paper, with the greedy selection rule on maximum residual, we propose the greedy randomized Motzkin-Kaczmarz (GRMK) method for linear systems. The block version of the new method is also presented. We analyze the convergence of the two methods and provide the corresponding convergence factors. Extensive numerical experiments show that the GRMK method has almost the same performance as the GRK method for dense matrices and the former performs better in computing time for some sparse matrices, and the block versions of the GRMK and GRK methods always have almost the same performance.

math.NA↗

arXiv2020

Block sampling Kaczmarz-Motzkin methods for consistent linear systems

The sampling Kaczmarz-Motzkin (SKM) method is a generalization of the randomized Kaczmarz and Motzkin methods. It first samples some rows of coefficient matrix randomly to build a set and then makes use of the maximum violation criterion within this set to determine a constraint. Finally, it makes progress by enforcing this single constraint. In this paper, on the basis of the framework of the SKM method and considering the greedy strategies, we present two block sampling Kaczmarz-Motzkin methods for consistent linear systems. Specifically, we also first sample a subset of rows of coefficient matrix and then determine an index in this set using the maximum violation criterion. Unlike the SKM method, in the rest of the block methods, we devise different greedy strategies to build index sets. Then, the new methods make progress by enforcing the corresponding multiple constraints simultaneously. Theoretical analyses demonstrate that these block methods converge at least as quickly as the SKM method, and numerical experiments show that, for the same accuracy, our methods outperform the SKM method in terms of the number of iterations and computing time.

math.NA↗

arXiv2020

Toward an Automated HPC Pipeline for Processing Large Scale Electron Microscopy Data

We present a fully modular and scalable software pipeline for processing electron microscope (EM) images of brain slices into 3D visualization of individual neurons and demonstrate an end-to-end segmentation of a large EM volume using a supercomputer. Our pipeline scales multiple packages used by the EM community with minimal changes to the original source codes. We tested each step of the pipeline individually, on a workstation, a cluster, and a supercomputer. Furthermore, we can compose workflows from these operations using a Balsam database that can be triggered during the data acquisition or with the use of different front ends and control the granularity of the pipeline execution. We describe the implementation of our pipeline and modifications required to integrate and scale up existing codes. The modular nature of our environment enables diverse research groups to contribute to the pipeline without disrupting the workflow, i.e. new individual codes can be easily integrated for each step on the pipeline.

cs.DC↗

arXiv2020

On the condition number theory of the equality constrained indefinite least squares problem

In this paper, within a unified framework of the condition number theory we present the explicit expression of the projected condition number of the equality constrained indefinite least squares problem. By setting specific norms and parameters, some widely used condition numbers, like the normwise, mixed and componentwise condition numbers follow as its special cases. Considering practical applications and computation, some new compact forms or upper bounds of the projected condition numbers are given to improve the computational efficiency. The new compact forms are of particular interest in calculating the exact value of the 2-norm projected condition numbers. When the equality constrained indefinite least squares problem degenerates into some specific least squares problems, our results give some new findings on the condition number theory of these specific least squares problems. Numerical experiments are given to illustrate our theoretical results.

math.NA↗

arXiv2020

A novel greedy Gauss-Seidel method for solving large linear least squares problem

We present a novel greedy Gauss-Seidel method for solving large linear least squares problem. This method improves the greedy randomized coordinate descent (GRCD) method proposed recently by Bai and Wu [Bai ZZ, and Wu WT. On greedy randomized coordinate descent methods for solving large linear least-squares problems. Numer Linear Algebra Appl. 2019;26(4):1--15], which in turn improves the popular randomized Gauss-Seidel method. Convergence analysis of the new method is provided. Numerical experiments show that, for the same accuracy, our method outperforms the GRCD method in term of the computing time.

math.NA↗

arXiv2020

Greedy Block Gauss-Seidel Methods for Solving Large Linear Least Squares Problem

With a greedy strategy to construct control index set of coordinates firstly and then choosing the corresponding column submatrix in each iteration, we present a greedy block Gauss-Seidel (GBGS) method for solving large linear least squares problem. Theoretical analysis demonstrates that the convergence factor of the GBGS method can be much smaller than that of the greedy randomized coordinate descent (GRCD) method proposed recently in the literature. On the basis of the GBGS method, we further present a pseudoinverse-free greedy block Gauss-Seidel method, which doesn't need to calculate the Moore-Penrose pseudoinverse of the column submatrix in each iteration any more and hence can be achieved greater acceleration. Moreover, this method can also be used for distributed implementations. Numerical experiments show that, for the same accuracy, our methods can far outperform the GRCD method in terms of the iteration number and computing time.

math.NA↗

arXiv2020

A Count Sketch Kaczmarz Method For Solving Large Overdetermined Linear Systems

In this paper, combining count sketch and maximal weighted residual Kaczmarz method, we propose a fast randomized algorithm for large overdetermined linear systems. Convergence analysis of the new algorithm is provided. Numerical experiments show that, for the same accuracy, our method behaves better in computing time compared with the state-of-the-art algorithm.

math.NA↗

arXiv2020

A Novel Greedy Kaczmarz Method For Solving Consistent Linear Systems

With a quite different way to determine the working rows, we propose a novel greedy Kaczmarz method for solving consistent linear systems. Convergence analysis of the new method is provided. Numerical experiments show that, for the same accuracy, our method outperforms the greedy randomized Kaczmarz method and the relaxed greedy randomized Kaczmarz method introduced recently by Bai and Wu [Z.Z. BAI AND W.T. WU, On greedy randomized Kaczmarz method for solving large sparse linear systems, SIAM J. Sci. Comput., 40 (2018), pp. A592--A606; Z.Z. BAI AND W.T. WU, On relaxed greedy randomized Kaczmarz methods for solving large sparse linear systems, Appl. Math. Lett., 83 (2018), pp. 21--26] in term of the computing time.

math.NA↗

arXiv2020

Randomized block Krylov space methods for trace and log-determinant estimators

We present randomized algorithms based on block Krylov space method for estimating the trace and log-determinant of Hermitian positive semi-definite matrices. Using the properties of Chebyshev polynomial and Gaussian random matrix, we provide the error analysis of the proposed estimators and obtain the expectation and concentration error bounds. These bounds improve the corresponding ones given in the literature. Numerical experiments are presented to illustrate the performance of the algorithms and to test the error bounds.

math.NA↗

arXiv2019

Scaling Distributed Training of Flood-Filling Networks on HPC Infrastructure for Brain Mapping

Mapping all the neurons in the brain requires automatic reconstruction of entire cells from volume electron microscopy data. The flood-filling network (FFN) architecture has demonstrated leading performance for segmenting structures from this data. However, the training of the network is computationally expensive. In order to reduce the training time, we implemented synchronous and data-parallel distributed training using the Horovod library, which is different from the asynchronous training scheme used in the published FFN code. We demonstrated that our distributed training scaled well up to 2048 Intel Knights Landing (KNL) nodes on the Theta supercomputer. Our trained models achieved similar level of inference performance, but took less training time compared to previous methods. Our study on the effects of different batch sizes on FFN training suggests ways to further improve training efficiency. Our findings on optimal learning rate and batch sizes agree with previous works.

cs.DC↗

arXiv2019

A Fusion Adversarial Underwater Image Enhancement Network with a Public Test Dataset

Underwater image enhancement algorithms have attracted much attention in underwater vision task. However, these algorithms are mainly evaluated on different data sets and different metrics. In this paper, we set up an effective and pubic underwater test dataset named U45 including the color casts, low contrast and haze-like effects of underwater degradation and propose a fusion adversarial network for enhancing underwater images. Meanwhile, the well-designed the adversarial loss including Lgt loss and Lfe loss is presented to focus on image features of ground truth, and image features of the image enhanced by fusion enhance method, respectively. The proposed network corrects color casts effectively and owns faster testing time with fewer parameters. Experiment results on U45 dataset demonstrate that the proposed method achieves better or comparable performance than the other state-of-the-art methods in terms of qualitative and quantitative evaluations. Moreover, an ablation study demonstrates the contributions of each component, and the application test further shows the effectiveness of the enhanced images.

eess.IV↗