arXiv subjects

Ping Li

Publications and source records attributed to Ping Li.

At least 307 records · Page 17Linked to original sources

arXiv2020

A hybridizable discontinuous Galerkin method for simulation of electrostatic problems with floating potential conductors

In an electrostatic simulation, an equipotential condition with an undefined/floating potential value has to be enforced on the surface of an isolated conductor. If this conductor is charged, a nonzero charge condition is also required. While implementation of these conditions using a traditional finite element method (FEM) is not straightforward, they can be easily discretized and incorporated within a discontinuous Galerkin (DG) method. However, DG discretization results in a larger number of unknowns as compared to FEM. In this work, a hybridizable DG (HDG) method is proposed to alleviate this problem. Floating potential boundary conditions, possibly with different charge values, are introduced on surfaces of each isolated conductor and are weakly enforced in the global problem of HDG. The unknowns of the global HDG problem are those only associated with the nodes on the mesh skeleton and their number is much smaller than the total number of unknowns required by DG. Numerical examples show that the proposed method is as accurate as DG while it improves the computational efficiency significantly.

math.NA↗

arXiv2020

Exploring global diverse attention via pairwise temporal relation for video summarization

Video summarization is an effective way to facilitate video searching and browsing. Most of existing systems employ encoder-decoder based recurrent neural networks, which fail to explicitly diversify the system-generated summary frames while requiring intensive computations. In this paper, we propose an efficient convolutional neural network architecture for video SUMmarization via Global Diverse Attention called SUM-GDA, which adapts attention mechanism in a global perspective to consider pairwise temporal relations of video frames. Particularly, the GDA module has two advantages: 1) it models the relations within paired frames as well as the relations among all pairs, thus capturing the global attention across all frames of one video; 2) it reflects the importance of each frame to the whole video, leading to diverse attention on these frames. Thus, SUM-GDA is beneficial for generating diverse frames to form satisfactory video summary. Extensive experiments on three data sets, i.e., SumMe, TVSum, and VTW, have demonstrated that SUM-GDA and its extension outperform other competing state-of-the-art methods with remarkable improvements. In addition, the proposed models can be run in parallel with significantly less computational costs, which helps the deployment in highly demanding applications.

cs.CV↗

arXiv2020

Monochromatic disconnection: Erdős-Gallai-type problems and product graphs

For an edge-colored graph $G$, we call an edge-cut $M$ of $G$ monochromatic if the edges of $M$ are colored with a same color. The graph $G$ is called monochromatically disconnected if any two distinct vertices of $G$ are separated by a monochromatic edge-cut. The monochromatic disconnection number, denoted by $md(G)$, of a connected graph $G$ is the maximum number of colors that are allowed to make $G$ monochromatically disconnected. In this paper, we solve the Erdős-Gallai-type problems for the monochromatic disconnection, and give the monochromatic disconnection numbers for four graph products, i.e., Cartesian, strong, lexicographic, and tensor products.

math.CO↗

arXiv2020

Upper bounds for the $MD$-numbers and characterization of extremal graphs

For an edge-colored graph $G$, we call an edge-cut $M$ of $G$ monochromatic if the edges of $M$ are colored with the same color. The graph $G$ is called monochromatic disconnected if any two distinct vertices of $G$ are separated by a monochromatic edge-cut. For a connected graph $G$, the monochromatic disconnection number (or $MD$-number for short) of $G$, denoted by $md(G)$, is the maximum number of colors that are allowed in order to make $G$ monochromatic disconnected. For graphs with diameter one, they are complete graphs and so their $MD$-numbers are $1$. For graphs with diameter at least 3, we can construct $2$-connected graphs such that their $MD$-numbers can be arbitrarily large; whereas for graphs $G$ with diameter two, we show that if $G$ is a $2$-connected graph then $md(G)\leq 2$, and if $G$ has a cut-vertex then $md(G)$ is equal to the number of blocks of $G$. So, we will focus on studying $2$-connected graphs with diameter two, and give two upper bounds of their $MD$-numbers depending on their connectivity and independent numbers, respectively. We also characterize the $\left\lfloor\frac{n}{2}\right\rfloor$-connected graphs (with large connectivity) whose $MD$-numbers are $2$ and the $2$-connected graphs (with small connectivity) whose $MD$-numbers archive the upper bound $\left\lfloor\frac{n}{2}\right\rfloor.$ For graphs with connectivity less than $\frac n 2$, we show that if the connectivity of a graph is in linear with its order $n$, then its $MD$-number is upper bounded by a constant, and this suggests us to leave a conjecture that for a $k$-connected graph $G$, $md(G)\leq \left\lfloor\frac{n}{k}\right\rfloor$.

math.CO↗

arXiv2020

Adaptive Randomization in Network Data

Network data have appeared frequently in recent research. For example, in comparing the effects of different types of treatment, network models have been proposed to improve the quality of estimation and hypothesis testing. In this paper, we focus on efficiently estimating the average treatment effect using an adaptive randomization procedure in networks. We work on models of causal frameworks, for which the treatment outcome of a subject is affected by its own covariate as well as those of its neighbors. Moreover, we consider the case in which, when we assign treatments to the current subject, only the subnetwork of existing subjects is revealed. New randomized procedures are proposed to minimize the mean squared error of the estimated differences between treatment effects. In network data, it is usually difficult to obtain theoretical properties because the numbers of nodes and connections increase simultaneously. Under mild assumptions, our proposed procedure is closely related to a time-varying inhomogeneous Markov chain. We then use Lyapunov functions to derive the theoretical properties of the proposed procedures. The advantages of the proposed procedures are also demonstrated by extensive simulations and experiments on real network data.

stat.ME↗

arXiv2020

Understanding and Detecting Convergence for Stochastic Gradient Descent with Momentum

Convergence detection of iterative stochastic optimization methods is of great practical interest. This paper considers stochastic gradient descent (SGD) with a constant learning rate and momentum. We show that there exists a transient phase in which iterates move towards a region of interest, and a stationary phase in which iterates remain bounded in that region around a minimum point. We construct a statistical diagnostic test for convergence to the stationary phase using the inner product between successive gradients and demonstrate that the proposed diagnostic works well. We theoretically and empirically characterize how momentum can affect the test statistic of the diagnostic, and how the test statistic captures a relatively sparse signal within the gradients in convergence. Finally, we demonstrate an application to automatically tune the learning rate by reducing it each time stationarity is detected, and show the procedure is robust to mis-specified initial rates.

cs.LG↗

arXiv2020

Cluster-Adaptive Network A/B Testing: From Randomization to Estimation

A/B testing is an important decision-making tool in product development for evaluating user engagement or satisfaction from a new service, feature or product. The goal of A/B testing is to estimate the average treatment effects (ATE) of a new change, which becomes complicated when users are interacting. When the important assumption of A/B testing, the Stable Unit Treatment Value Assumption (SUTVA), which states that each individual's response is affected by their own treatment only, is not valid, the classical estimate of the ATE usually leads to a wrong conclusion. In this paper, we propose a cluster-adaptive network A/B testing procedure, which involves a sequential cluster-adaptive randomization and a cluster-adjusted estimator. The cluster-adaptive randomization is employed to minimize the cluster-level Mahalanobis distance within the two treatment groups, so that the variance of the estimate of the ATE can be reduced. In addition, the cluster-adjusted estimator is used to eliminate the bias caused by network interference, resulting in a consistent estimation for the ATE. Numerical studies suggest our cluster-adaptive network A/B testing achieves consistent estimation with higher efficiency. An empirical study is conducted based on a real world network to illustrate how our method can benefit decision-making in application.

stat.ME↗

arXiv2020

FedSKETCH: Communication-Efficient and Private Federated Learning via Sketching

Communication complexity and privacy are the two key challenges in Federated Learning where the goal is to perform a distributed learning through a large volume of devices. In this work, we introduce FedSKETCH and FedSKETCHGATE algorithms to address both challenges in Federated learning jointly, where these algorithms are intended to be used for homogeneous and heterogeneous data distribution settings respectively. The key idea is to compress the accumulation of local gradients using count sketch, therefore, the server does not have access to the gradients themselves which provides privacy. Furthermore, due to the lower dimension of sketching used, our method exhibits communication-efficiency property as well. We provide, for the aforementioned schemes, sharp convergence guarantees. Finally, we back up our theory with various set of experiments.

stat.ML↗

arXiv2020

Complexity results for two kinds of colored disconnections of graphs

The concept of rainbow disconnection number of graphs was introduced by Chartrand et al. in 2018. Inspired by this concept, we put forward the concepts of rainbow vertex-disconnection and proper disconnection in graphs. In this paper, we first show that it is $NP$-complete to decide whether a given edge-colored graph $G$ with maximum degree $Δ(G)=4$ is proper disconnected. Then, for a graph $G$ with $Δ(G)\leq 3$ we show that $pd(G)\leq 2$ and determine the graphs with $pd(G)=1$ and $2$, respectively. Furthermore, we show that for a general graph $G$, deciding whether $pd(G)=1$ is $NP$-complete, even if $G$ is bipartite. We also show that it is $NP$-complete to decide whether a given vertex-colored graph $G$ is rainbow vertex-disconnected, even though the graph $G$ has $Δ(G)=3$ or is bipartite.

math.CO↗

arXiv2020

RGB-D SLAM in Dynamic Environments Using Point Correlations

In this paper, a simultaneous localization and mapping (SLAM) method that eliminates the influence of moving objects in dynamic environments is proposed. This method utilizes the correlation between map points to separate points that are part of the static scene and points that are part of different moving objects into different groups. A sparse graph is first created using Delaunay triangulation from all map points. In this graph, the vertices represent map points, and each edge represents the correlation between adjacent points. If the relative position between two points remains consistent over time, there is correlation between them, and they are considered to be moving together rigidly. If not, they are considered to have no correlation and to be in separate groups. After the edges between the uncorrelated points are removed during point-correlation optimization, the remaining graph separates the map points of the moving objects from the map points of the static scene. The largest group is assumed to be the group of reliable static map points. Finally, motion estimation is performed using only these points. The proposed method was implemented for RGB-D sensors, evaluated with a public RGB-D benchmark, and tested in several additional challenging environments. The experimental results demonstrate that robust and accurate performance can be achieved by the proposed SLAM method in both slightly and highly dynamic environments. Compared with other state-of-the-art methods, the proposed method can provide competitive accuracy with good real-time performance.

cs.CV↗

arXiv2020

Characterization on projective submanifolds of codimensions 2 and 3

In this article we give a necessary and sufficient condition to characterize projective submanifolds in ${\mathbb P}^N$ with codimensions 2 and 3. The conditions involve the Chern classes of the manifold and a very ample line bundle on the manifold. This generalizes our earlier characterization for hypersurfaces. The higher codimensional cases are proposed as a general question.

math.DG↗

arXiv2020

MeDaS: An open-source platform as service to help break the walls between medicine and informatics

In the past decade, deep learning (DL) has achieved unprecedented success in numerous fields including computer vision, natural language processing, and healthcare. In particular, DL is experiencing an increasing development in applications for advanced medical image analysis in terms of analysis, segmentation, classification, and furthermore. On the one hand, tremendous needs that leverage the power of DL for medical image analysis are arising from the research community of a medical, clinical, and informatics background to jointly share their expertise, knowledge, skills, and experience. On the other hand, barriers between disciplines are on the road for them often hampering a full and efficient collaboration. To this end, we propose our novel open-source platform, i.e., MeDaS -- the MeDical open-source platform as Service. To the best of our knowledge, MeDaS is the first open-source platform proving a collaborative and interactive service for researchers from a medical background easily using DL related toolkits, and at the same time for scientists or engineers from information sciences to understand the medical knowledge side. Based on a series of toolkits and utilities from the idea of RINV (Rapid Implementation aNd Verification), our proposed MeDaS platform can implement pre-processing, post-processing, augmentation, visualization, and other phases needed in medical image analysis. Five tasks including the subjects of lung, liver, brain, chest, and pathology, are validated and demonstrated to be efficiently realisable by using MeDaS.

cs.CV↗

arXiv2020

The Benefits of Diversity: Permutation Recovery in Unlabeled Sensing from Multiple Measurement Vectors

In "Unlabeled Sensing", one observes a set of linear measurements of an underlying signal with incomplete or missing information about their ordering, which can be modeled in terms of an unknown permutation. Previous work on the case of a single noisy measurement vector has exposed two main challenges: 1) a high requirement concerning the \emph{signal-to-noise ratio} ($\snr$), i.e., approximately of the order of $n^{5}$, and 2) a massive computational burden in light of NP-hardness in general. In this paper, we study the case of \emph{multiple} noisy measurement vectors (MMVs) resulting from a \emph{common} permutation and investigate to what extent the number of MMVs $m$ facilitates permutation recovery by "borrowing strength". The above two challenges have at least partially been resolved within our work. First, we show that a large stable rank of the signal significantly reduces the required snr which can drop from a polynomial in $n$ for $m = 1$ to a constant for $m = Ω(\log n)$, where $m$ denotes the number of MMVs and $n$ denotes the number of measurements per MV. This bound is shown to be sharp and is associated with a phase transition phenomenon. Second, we propose a computational scheme for recovering the unknown permutation in practice. For the "oracle case" with the known signal, the maximum likelihood (ML) estimator reduces to a linear assignment problem whose global optimum can be obtained efficiently. For the case in which both the signal and permutation are unknown, the problem is reformulated as a bi-convex optimization problem with an auxiliary variable, which can be solved by the Alternating Direction Method of Multipliers (ADMM). Numerical experiments based on the proposed computational scheme confirm the tightness of our theoretical analysis.

cs.IT↗

arXiv2020

A Two-Stage Approach to Multivariate Linear Regression with Sparsely Mismatched Data

A tacit assumption in linear regression is that (response, predictor)-pairs correspond to identical observational units. A series of recent works have studied scenarios in which this assumption is violated under terms such as ``Unlabeled Sensing and ``Regression with Unknown Permutation''. In this paper, we study the setup of multiple response variables and a notion of mismatches that generalizes permutations in order to allow for missing matches as well as for one-to-many matches. A two-stage method is proposed under the assumption that most pairs are correctly matched. In the first stage, the regression parameter is estimated by handling mismatches as contaminations, and subsequently the generalized permutation is estimated by a basic variant of matching. The approach is both computationally convenient and equipped with favorable statistical guarantees. Specifically, it is shown that the conditions for permutation recovery become considerably less stringent as the number of responses $m$ per observation increase. Particularly, for $m = Ω(\log n)$, the required signal-to-noise ratio no longer depends on the sample size $n$. Numerical results on synthetic and real data are presented to support the main findings of our analysis.

stat.ML↗

arXiv2020

Cooperative Rate-Splitting for Secrecy Sum-Rate Enhancement in Multi-antenna Broadcast Channels

In this paper, we employ Cooperative Rate-Splitting (CRS) technique to enhance the Secrecy Sum Rate (SSR) for the Multiple Input Single Output (MISO) Broadcast Channel (BC), consisting of two legitimate users and one eavesdropper, with perfect Channel State Information (CSI) available at all nodes. For CRS based on the three-node relay channel, the transmitter splits and encodes the messages of legitimate users into common and private streams based on Rate-Splitting (RS). With the goal of maximizing SSR, the proposed CRS strategy opportunistically asks the relaying legitimate user to forward its decoded common message. During the transmission, the eavesdropper keeps wiretapping silently. To ensure secure transmission, the common message is used for the dual purpose, serving both as a desired message and Artificial Noise (AN) without consuming extra transmit power comparing to the conventional AN design. Taking into account the total power constraint and the Physical Layer (PHY) security, the precoders and time-slot allocation are jointly optimized by solving the non-convex SSR maximization problem based on Sequential Convex Approximation (SCA) algorithm. Numerical results show that the proposed CRS secure transmission scheme outperforms existing Multi-User Linear Precoding (MU-LP) and Cooperative Non-Orthogonal Multiple Access (C-NOMA) strategies. Therefore, CRS is a promising strategy to enhance the PHY security in multi-antenna BC systems.

eess.SP↗

arXiv2020

Chern class inequalities on polarized manifolds and nef vector bundles

This article is concerned with Chern class and Chern number inequalities on polarized manifolds and nef vector bundles. For a polarized pair $(M,L)$ with $L$ very ample, our first main result is a family of sharp Chern class inequalities. Among them the first one is a variant of a classical result and the equality case of the second one is a characterization of hypersurfaces. The second main result is a Chern number inequality on it, which includes a reverse Miyaoka-Yau type inequality. The third main result is that the Chern numbers of a nef vector bundle over a compact Kähler manifold are bounded below by the Euler number. As an application, we classify compact Kähler manifolds with nonnegative bisectional curvature whose Chern numbers are all positive. A conjecture related to the Euler number of compact Kähler manifolds with nonpositive bisectional curvature is proposed, which can be regarded as a complex analogue to the Hopf conjecture.

math.DG↗

arXiv2020

Randomized Kernel Multi-view Discriminant Analysis

In many artificial intelligence and computer vision systems, the same object can be observed at distinct viewpoints or by diverse sensors, which raises the challenges for recognizing objects from different, even heterogeneous views. Multi-view discriminant analysis (MvDA) is an effective multi-view subspace learning method, which finds a discriminant common subspace by jointly learning multiple view-specific linear projections for object recognition from multiple views, in a non-pairwise way. In this paper, we propose the kernel version of multi-view discriminant analysis, called kernel multi-view discriminant analysis (KMvDA). To overcome the well-known computational bottleneck of kernel methods, we also study the performance of using random Fourier features (RFF) to approximate Gaussian kernels in KMvDA, for large scale learning. Theoretical analysis on stability of this approximation is developed. We also conduct experiments on several popular multi-view datasets to illustrate the effectiveness of our proposed strategy.

stat.ML↗

arXiv2020

IVFS: Simple and Efficient Feature Selection for High Dimensional Topology Preservation

Feature selection is an important tool to deal with high dimensional data. In unsupervised case, many popular algorithms aim at maintaining the structure of the original data. In this paper, we propose a simple and effective feature selection algorithm to enhance sample similarity preservation through a new perspective, topology preservation, which is represented by persistent diagrams from the context of computational topology. This method is designed upon a unified feature selection framework called IVFS, which is inspired by random subset method. The scheme is flexible and can handle cases where the problem is analytically intractable. The proposed algorithm is able to well preserve the pairwise distances, as well as topological patterns, of the full data. We demonstrate that our algorithm can provide satisfactory performance under a sharp sub-sampling rate, which supports efficient implementation of our proposed method to large scale datasets. Extensive experiments validate the effectiveness of the proposed feature selection scheme.

stat.ML↗