arXiv subjects

Wenjian Yu

Publications and source records attributed to Wenjian Yu.

45 records · Page 3Linked to original sources

arXiv2017

Single-Pass PCA of Large High-Dimensional Data

Principal component analysis (PCA) is a fundamental dimension reduction tool in statistics and machine learning. For large and high-dimensional data, computing the PCA (i.e., the singular vectors corresponding to a number of dominant singular values of the data matrix) becomes a challenging task. In this work, a single-pass randomized algorithm is proposed to compute PCA with only one pass over the data. It is suitable for processing extremely large and high-dimensional data stored in slow memory (hard disk) or the data generated in a streaming fashion. Experiments with synthetic and real data validate the algorithm's accuracy, which has orders of magnitude smaller error than an existing single-pass algorithm. For a set of high-dimensional data stored as a 150 GB file, the proposed algorithm is able to compute the first 50 principal components in just 24 minutes on a typical 24-core computer, with less than 1 GB memory cost.

cs.DS↗

arXiv2017

A Fast Implementation of Singular Value Thresholding Algorithm using Recycling Rank Revealing Randomized Singular Value Decomposition

In this paper, we present a fast implementation of the Singular Value Thresholding (SVT) algorithm for matrix completion. A rank-revealing randomized singular value decomposition (R3SVD) algorithm is used to adaptively carry out partial singular value decomposition (SVD) to fast approximate the SVT operator given a desired, fixed precision. We extend the R3SVD algorithm to a recycling rank revealing randomized singular value decomposition (R4SVD) algorithm by reusing the left singular vectors obtained from the previous iteration as the approximate basis in the current iteration, where the computational cost for partial SVD at each SVT iteration is significantly reduced. A simulated annealing style cooling mechanism is employed to adaptively adjust the low-rank approximation precision threshold as SVT progresses. Our fast SVT implementation is effective in both large and small matrices, which is demonstrated in matrix completion applications including image recovery and movie recommendation system.

math.NA↗

arXiv2016

A Rank Revealing Randomized Singular Value Decomposition (R3SVD) Algorithm for Low-rank Matrix Approximations

In this paper, we present a Rank Revealing Randomized Singular Value Decomposition (R3SVD) algorithm to incrementally construct a low-rank approximation of a potentially large matrix while adaptively estimating the appropriate rank that can capture most of the actions of the matrix. Starting from a low-rank approximation with an initial guessed rank, R3SVD adopts an orthogonal Gaussian sampling approach to obtain the dominant subspace within the leftover space, which is used to add up to the existing low-rank approximation. Orthogonal Gaussian sampling is repeated until an appropriate low-rank approximation with satisfactory accuracy, measured by the overall energy percentage of the original matrix, is obtained. While being a fast algorithm, R3SVD is also a memory-aware algorithm where the computational process can be decomposed into a series of sampling tasks that use constant amount of memory. Numerical examples in image compression and matrix completion are used to demonstrate the effectiveness of R3SVD in low-rank approximation.

math.NA↗

arXiv2016

Simulation Algorithms with Exponential Integration for Time-Domain Analysis of Large-Scale Power Delivery Networks

We design an algorithmic framework using matrix exponentials for time-domain simulation of power delivery network (PDN). Our framework can reuse factorized matrices to simulate the large-scale linear PDN system with variable stepsizes. In contrast, current conventional PDN simulation solvers have to use fixed step-size approach in order to reuse factorized matrices generated by the expensive matrix decomposition. Based on the proposed exponential integration framework, we design a PDN solver R-MATEX with the flexible time-stepping capability. The key operation of matrix exponential and vector product (MEVP) is computed by the rational Krylov subspace method. To further improve the runtime, we also propose a distributed computing framework DR-MATEX. DR-MATEX reduces Krylov subspace generations caused by frequent breakpoints from a large number of current sources during simulation. By virtue of the superposition property of linear system and scaling invariance property of Krylov subspace, DR-MATEX can divide the whole simulation task into subtasks based on the alignments of breakpoints among those sources. The subtasks are processed in parallel at different computing nodes without any communication during the computation of transient simulation. The final result is obtained by summing up the partial results among all the computing nodes after they finish the assigned subtasks. Therefore, our computation model belongs to the category known as Embarrassingly Parallel model. Experimental results show R-MATEX and DR-MATEX can achieve up to around 14.4X and 98.0X runtime speedups over traditional trapezoidal integration based solver with fixed timestep approach.

cs.CE↗

arXiv2015

An Algorithmic Framework for Efficient Large-Scale Circuit Simulation Using Exponential Integrators

We propose an efficient algorithmic framework for time domain circuit simulation using exponential integrator. This work addresses several critical issues exposed by previous matrix exponential based circuit simulation research, and makes it capable of simulating stiff nonlinear circuit system at a large scale. In this framework, the system's nonlinearity is treated with exponential Rosenbrock-Euler formulation. The matrix exponential and vector product is computed using invert Krylov subspace method. Our proposed method has several distinguished advantages over conventional formulations (e.g., the well-known backward Euler with Newton-Raphson method). The matrix factorization is performed only for the conductance/resistance matrix G, without being performed for the combinations of the capacitance/inductance matrix C and matrix G, which are used in traditional implicit formulations. Furthermore, due to the explicit nature of our formulation, we do not need to repeat LU decompositions when adjusting the length of time steps for error controls. Our algorithm is better suited to solving tightly coupled post-layout circuits in the pursuit for full-chip simulation. Our experimental results validate the advantages of our framework.

cs.CE↗

arXiv2010

The Future of Social Experimenting

Recent lab experiments by Traulsen et al. for the spatial prisoner's dilemma suggest that exploratory behavior of human subjects prevents cooperation through neighborhood interactions over experimentally accessible time spans. This indicates that new theoretical and experimental efforts are needed to explore the mechanisms underlying a number of famous puzzles in the social sciences.

physics.soc-ph↗

arXiv2009

The outbreak of cooperation among success-driven individuals under noisy conditions

According to Thomas Hobbes' Leviathan [1651; 2008 (Touchstone, New York), English Ed], "the life of man [is] solitary, poor, nasty, brutish, and short," and it would need powerful social institutions to establish social order. In reality, however, social cooperation can also arise spontaneously, based on local interactions rather than centralized control. The self-organization of cooperative behavior is particularly puzzling for social dilemmas related to sharing natural resources or creating common goods. Such situations are often described by the prisoner's dilemma. Here, we report the sudden outbreak of predominant cooperation in a noisy world dominated by selfishness and defection, when individuals imitate superior strategies and show success-driven migration. In our model, individuals are unrelated, and do not inherit behavioral traits. They defect or cooperate selfishly when the opportunity arises, and they do not know how often they will interact or have interacted with someone else. Moreover, our individuals have no reputation mechanism to form friendship networks, nor do they have the option of voluntary interaction or costly punishment. Therefore, the outbreak of prevailing cooperation, when directed motion is integrated in a game-theoretical model, is remarkable, particularly when random strategy mutations and random relocations challenge the formation and survival of cooperative clusters. Our results suggest that mobility is significant for the evolution of social order, and essential for its stabilization and maintenance.

physics.soc-ph↗

arXiv2009

Game Theoretical Interactions of Moving Agents

Game theory has been one of the most successful quantitative concepts to describe social interactions, their strategical aspects, and outcomes. Among the payoff matrix quantifying the result of a social interaction, the interaction conditions have been varied, such as the number of repeated interactions, the number of interaction partners, the possibility to punish defective behavior etc. While an extension to spatial interactions has been considered early on such as in the "game of life", recent studies have focussed on effects of the structure of social interaction networks. However, the possibility of individuals to move and, thereby, evade areas with a high level of defection, and to seek areas with a high level of cooperation, has not been fully explored so far. This contribution presents a model combining game theoretical interactions with success-driven motion in space, and studies the consequences that this may have for the degree of cooperation and the spatio-temporal dynamics in the population. It is demonstrated that the combination of game theoretical interactions with motion gives rise to many self-organized behavioral patterns on an aggregate level, which can explain a variety of empirically observed social behaviors.

physics.soc-ph↗

arXiv2007

Modeling Crowd Turbulence by Many-Particle Simulations

A recent study [D. Helbing, A. Johansson and H. Z. Al-Abideen, {\it Phys. Rev. E} 75, 046109 (2007)] has revealed a "turbulent" state of pedestrian flows, which is characterized by sudden displacements and causes the falling and trampling of people. However, turbulent crowd motion is not reproduced well by current many-particle models due to their insufficient representation of the local interactions in areas of extreme densities. In this contribution, we extend the repulsive force term of the social force model to reproduce crowd turbulence. We perform numerical simulations of pedestrians moving through a bottleneck area with this new model. The transitions from laminar to stop-and-go and turbulent flows are observed. The empirical features characterizing crowd turbulence, such as the structure function and the probability density function of velocity increments are reproduced well, i.e. they are well compatible with an analysis of video data during the annual Muslim pilgrimage.

physics.soc-ph↗