Li Chen

Li Chen, Feng Luo

In computer graphics, smooth data reconstruction on 2D or 3D manifolds usually refers to subdivision problems. Such a method is only valid based on dense sample points. The manifold usually needs to be triangulated into meshes (or patches) and each node on the mesh will have an initial value. While the mesh is refined the algorithm will provide a smooth function on the redefined manifolds. However, when data points are not dense and the original mesh is not allowed to be changed, how is the "continuous and/or smooth" reconstruction possible? This paper will present a new method using harmonic functions to solve the problem. Our method contains the following steps: (1) Partition the boundary surfaces of the 3D manifold based on sample points so that each sample point is on the edge of the partition. (2) Use gradually varied interpolation on the edges so that each point on edge will be assigned a value. In addition, all values on the edge are gradually varied. (3) Use discrete harmonic function to fit the unknown points, i.e. the points inside each partition patch. The fitted function will be a harmonic or a local harmonic function in each partitioned area. The function on edge will be "near" continuous (or "near" gradually varied). If we need a smoothed surface on the manifold, we can apply subdivision algorithms. This paper has also a philosophical advantage over triangulation meshes. People usually use triangulation for data reconstruction. This paper employs harmonic functions, a generalization of triangulation because linearity is a form of harmonic. Therefore, local harmonic initialization is more sophisticated then triangulation. This paper is a conceptual and methodological paper. This paper does not focus on detailed mathematical analysis nor fine algorithm design.

Li Chen, Ruo Li, Chengbao Yao

We propose an approximate solver for multi-medium Riemann problems with materials described by a family of general Mie-Grüneisen equations of state, which are widely used in practical applications. The solver provides the interface pressure and normal velocity by an iterative method. The well-posedness and convergence of the solver is verified with mild assumptions on the equations of state. To validate the solver, it is employed in computing the numerical flux on phase interfaces of a numerical scheme on Eulerian grids that was developed recently for compressible multi-medium flows. Numerical examples are presented for Riemann problems, air blast and underwater explosion applications.

Li Chen

This paper presents some applications using recently developed algorithms for smooth-continuous data reconstruction based on the digital-discrete method. The classical discrete method for data reconstruction is based on domain decomposition according to guiding (or sample) points. Then the Spline method (for polynomial) or finite elements method (for PDE) is used to fit the data. Our method is based on the gradually varied function that does not assume the property of being linearly separable among guiding points, i.e. no domain decomposition methods are needed. We also demonstrate the flexibility of the new method and its potential to solve a variety of problems. The examples include some real data from water well logs and harmonic functions on closed 2D manifolds. This paper presents the results from six different algorithms. This method can be easily extended to higher multi-dimensions. We also include an advanced consideration related to the use of gradually varied mapping.

Runduo Han, Yanxin Hu, Yihui Fu et al.

Separating overlapping speech from multiple speakers is crucial for effective human-vehicle interaction. This paper proposes CabinSep, a lightweight neural mask-based minimum variance distortionless response (MVDR) speech separation approach, to reduce speech recognition errors in back-end automatic speech recognition (ASR) models. Our contributions are threefold: First, we utilize channel information to extract spatial features, which improves the estimation of speech and noise masks. Second, we employ MVDR during inference, reducing speech distortion to make it more ASR-friendly. Third, we introduce a data augmentation method combining simulated and real-recorded impulse responses (IRs), improving speaker localization at zone boundaries and further reducing speech recognition errors. With a computational complexity of only 0.4 GMACs, CabinSep achieves a 17.5% relative reduction in speech recognition error rate in a real-recorded dataset compared to the state-of-the-art DualSep model. Demos are available at: https://cabinsep.github.io/cabinsep/.

Wei Liu, Li Chen, Wenyi Zhang

Decentralized stochastic gradient descent (SGD) is a driving engine for decentralized federated learning (DFL). The performance of decentralized SGD is jointly influenced by inter-node communications and local updates. In this paper, we propose a general DFL framework, which implements both multiple local updates and multiple inter-node communications periodically, to strike a balance between communication efficiency and model consensus. It can provide a general decentralized SGD analytical framework. We establish strong convergence guarantees for the proposed DFL algorithm without the assumption of convex objectives. The convergence rate of DFL can be optimized to achieve the balance of communication and computing costs under constrained resources. For improving communication efficiency of DFL, compressed communication is further introduced to the proposed DFL as a new scheme, named DFL with compressed communication (C-DFL). The proposed C-DFL exhibits linear convergence for strongly convex objectives. Experiment results based on MNIST and CIFAR-10 datasets illustrate the superiority of DFL over traditional decentralized SGD methods and show that C-DFL further enhances communication efficiency.

Li Chen, Richard Peng, Di Wang

Diffusion is a fundamental graph procedure and has been a basic building block in a wide range of theoretical and empirical applications such as graph partitioning and semi-supervised learning on graphs. In this paper, we study computationally efficient diffusion primitives beyond random walk. We design an $\widetilde{O}(m)$-time randomized algorithm for the $\ell_2$-norm flow diffusion problem, a recently proposed diffusion model based on network flow with demonstrated graph clustering related applications both in theory and in practice. Examples include finding locally-biased low conductance cuts. Using a known connection between the optimal dual solution of the flow diffusion problem and the local cut structure, our algorithm gives an alternative approach for finding such cuts in nearly linear time. From a technical point of view, our algorithm contributes a novel way of dealing with inequality constraints in graph optimization problems. It adapts the high-level algorithmic framework of nearly linear time Laplacian system solvers, but requires several new tools: vertex elimination under constraints, a new family of graph ultra-sparsifiers, and accelerated proximal gradient methods with inexact proximal mapping computation.

Li Chen, Shuizheng Zhou, Jiajun Ma

Sparse random projection (RP) is a popular tool for dimensionality reduction that shows promising performance with low computational complexity. However, in the existing sparse RP matrices, the positions of non-zero entries are usually randomly selected. Although they adopt uniform sampling with replacement, due to large sampling variance, the number of non-zeros is uneven among rows of the projection matrix which is generated in one trial, and more data information may be lost after dimension reduction. To break this bottleneck, based on random sampling without replacement in statistics, this paper builds a stable sparse subspace embedded matrix (S-SSE), in which non-zeros are uniformly distributed. It is proved that the S-SSE is stabler than the existing matrix, and it can maintain Euclidean distance between points well after dimension reduction. Our empirical studies corroborate our theoretical findings and demonstrate that our approach can indeed achieve satisfactory performance.

Fan Ang, Li Chen, Nan Zhao et al.

Federated learning is a communication-efficient training process that alternates between local training at the edge devices and averaging the updated local model at the central server. Nevertheless, it is impractical to achieve a perfect acquisition of the local models in wireless communication due to noise, which also brings serious effects on federated learning. To tackle this challenge, we propose a robust design for federated learning to alleviate the effects of noise in this paper. Considering noise in the two aforementioned steps, we first formulate the training problem as a parallel optimization for each node under the expectation-based model and the worst-case model. Due to the non-convexity of the problem, a regularization for the loss function approximation method is proposed to make it tractable. Regarding the worst-case model, we develop a feasible training scheme which utilizes the sampling-based successive convex approximation algorithm to tackle the unavailable maxima or minima noise condition and the non-convex issue of the objective function. Furthermore, the convergence rates of both new designs are analyzed from a theoretical point of view. Finally, the improvement of prediction accuracy and the reduction of loss function are demonstrated via simulations for the proposed designs.

Wei Liu, Li Chen, Yunfei Chen et al.

Federated learning (FL) provides a communication-efficient approach to solve machine learning problems concerning distributed data, without sending raw data to a central server. However, existing works on FL only utilize first-order gradient descent (GD) and do not consider the preceding iterations to gradient update which can potentially accelerate convergence. In this paper, we consider momentum term which relates to the last iteration. The proposed momentum federated learning (MFL) uses momentum gradient descent (MGD) in the local update step of FL system. We establish global convergence properties of MFL and derive an upper bound on MFL convergence rate. Comparing the upper bounds on MFL and FL convergence rate, we provide conditions in which MFL accelerates the convergence. For different machine learning models, the convergence performance of MFL is evaluated based on experiments with MNIST dataset. Simulation results comfirm that MFL is globally convergent and further reveal significant convergence improvement over FL.

Cencheng Shen, Li Chen, Yuexiao Dong et al.

The sparse representation classifier (SRC) is shown to work well for image recognition problems that satisfy a subspace assumption. In this paper we propose a new implementation of SRC via screening, establish its equivalence to the original SRC under regularity conditions, and prove its classification consistency for random graphs drawn from stochastic blockmodels. The results are demonstrated via simulations and real data experiments, where the new algorithm achieves comparable numerical performance but significantly faster.

Li Chen, Shuisheng Zhou, Zhuan Zhang

In machine learning, nonconvex optimization problems with multiple local optimums are often encountered. Graduated Optimization Algorithm (GOA) is a popular heuristic method to obtain global optimums of nonconvex problems through progressively minimizing a series of convex approximations to the nonconvex problems more and more accurate. Recently, such an algorithm GradOpt based on GOA is proposed with amazing theoretical and experimental results, but it mainly studies the problem which consists of one nonconvex part. This paper aims to find the global solution of a nonconvex objective with a convex part plus a nonconvex part based on GOA. By graduating approximating non-convex part of the problem and minimizing them with the Stochastic Variance Reduced Gradient (SVRG) or proximal SVRG, two new algorithms, SVRG-GOA and PSVRG-GOA, are proposed. We prove that the new algorithms have lower iteration complexity ($O(1/\varepsilon)$) than GradOpt ($O(1/\varepsilon^2)$). Some tricks, such as enlarging shrink factor, using project step, stochastic gradient, and mini-batch skills, are also given to accelerate the convergence speed of the proposed algorithms. Experimental results illustrate that the new algorithms with the similar performance can converge to 'global' optimums of the nonconvex problems, and they converge faster than the GradOpt and the nonconvex proximal SVRG.

Cencheng Shen, Li Chen, Yuexiao Dong et al.

The sparse representation classifier (SRC) has been utilized in various classification problems, which makes use of L1 minimization and works well for image recognition satisfying a subspace assumption. In this paper we propose a new implementation of SRC via screening, establish its equivalence to the original SRC under regularity conditions, and prove its classification consistency under a latent subspace model and contamination. The results are demonstrated via simulations and real data experiments, where the new algorithm achieves comparable numerical performance and significantly faster.