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Register a new userDRGraph: An Efficient Graph Layout Algorithm for Large-scale Graphs by Dimensionality Reduction
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Added by
Minfeng Zhu
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Efficient layout of large-scale graphs remains a challenging problem: the force-directed and dimensionality reduction-based methods suffer from high overhead for graph distance and gradient computation. In this paper, we present a new graph layout algorithm, called DRGraph, that enhances the nonlinear dimensionality reduction process with three schemes: approximating graph distances by means of a sparse distance matrix, estimating the gradient by using the negative sampling technique, and accelerating the optimization process through a multi-level layout scheme. DRGraph achieves a linear complexity for the computation and memory consumption, and scales up to large-scale graphs with millions of nodes. Experimental results and comparisons with state-of-the-art graph layout methods demonstrate that DRGraph can generate visually comparable layouts with a faster running time and a lower memory requirement.
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The subgraph-centric programming model is a promising approach and has been applied in many state-of-the-art distributed graph computing frameworks. However, traditional graph partition algorithms have significant difficulties in processing large-scale power-law graphs. The major problem is the communication bottleneck found in many subgraph-centric frameworks. Detailed analysis indicates that the communication bottleneck is caused by the huge communication volume or the extreme message imbalance among partitioned subgraphs. The traditional partition algorithms do not consider both factors at the same time, especially on power-law graphs. In this paper, we propose a novel efficient and balanced vertex-cut graph partition algorithm (EBV) which grants appropriate weights to the overall communication cost and communication balance. We observe that the number of replicated vertices and the balance of edge and vertex assignment have a great influence on communication patterns of distributed subgraph-centric frameworks, which further affect the overall performance. Based on this insight, We design an evaluation function that quantifies the proportion of replicated vertices and the balance of edges and vertices assignments as important parameters. Besides, we sort the order of edge processing by the sum of end-vertices degrees from small to large. Experiments show that EBV reduces replication factor and communication by at least 21.8% and 23.7% respectively than other self-based partition algorithms. When deployed in the subgraph-centric framework, it reduces the running time on power-law graphs by an average of 16.8% compared with the state-of-the-art partition algorithm. Our results indicate that EBV has a great potential in improving the performance of subgraph-centric frameworks for the parallel large-scale power-law graph processing.
Force-directed algorithms are widely used to generate aesthetically pleasing layouts of graphs or networks arisen in many scientific disciplines. To visualize large-scale graphs, several parallel algorithms have been discussed in the literature. However, existing parallel algorithms do not utilize memory hierarchy efficiently and often offer limited parallelism. This paper addresses these limitations with BatchLayout, an algorithm that groups vertices into minibatches and processes them in parallel. BatchLayout also employs cache blocking techniques to utilize memory hierarchy efficiently. More parallelism and improved memory accesses coupled with force approximating techniques, better initialization, and optimized learning rate make BatchLayout significantly faster than other state-of-the-art algorithms such as ForceAtlas2 and OpenOrd. The visualization quality of layouts from BatchLayout is comparable or better than similar visualization tools. All of our source code, links to datasets, results and log files are available at https://github.com/khaled-rahman/BatchLayout.
Multiple-input multiple-output (MIMO) detection is a fundamental problem in wireless communications and it is strongly NP-hard in general. Massive MIMO has been recognized as a key technology in the fifth generation (5G) and beyond communication networks, which on one hand can significantly improve the communication performance, and on the other hand poses new challenges of solving the corresponding optimization problems due to the large problem size. While various efficient algorithms such as semidefinite relaxation (SDR) based approaches have been proposed for solving the small-scale MIMO detection problem, they are not suitable to solve the large-scale MIMO detection problem due to their high computational complexities. In this paper, we propose an efficient sparse quadratic programming (SQP) relaxation based algorithm for solving the large-scale MIMO detection problem. In particular, we first reformulate the MIMO detection problem as an SQP problem. By dropping the sparse constraint, the resulting relaxation problem shares the same global minimizer with the SQP problem. In sharp contrast to the SDRs for the MIMO detection problem, our relaxation does not contain any (positive semidefinite) matrix variable and the numbers of variables and constraints in our relaxation are significantly less than those in the SDRs, which makes it particularly suitable for the large-scale problem. Then we propose a projected Newton based quadratic penalty method to solve the relaxation problem, which is guaranteed to converge to the vector of transmitted signals under reasonable conditions. By extensive numerical experiments, when applied to solve large-scale problems, the proposed algorithm achieves better detection performance than a recently proposed generalized power method.
This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of learning tasks such as classification, clustering, and visualization, these methods have focused primarily on Riemannian manifolds in Euclidean space. While sufficient for many applications, there are many high-dimensional signals which have no straightforward and meaningful Euclidean representation. In these cases, signals may be more appropriately represented as a realization of some distribution lying on a statistical manifold, or a manifold of probability density functions (PDFs). We present a framework for dimensionality reduction that uses information geometry for both statistical manifold reconstruction as well as dimensionality reduction in the data domain.
The movement of large quantities of data during the training of a Deep Neural Network presents immense challenges for machine learning workloads. To minimize this overhead, especially on the movement and calculation of gradient information, we introduce streaming batch principal component analysis as an update algorithm. Streaming batch principal component analysis uses stochastic power iterations to generate a stochastic k-rank approximation of the network gradient. We demonstrate that the low rank updates produced by streaming batch principal component analysis can effectively train convolutional neural networks on a variety of common datasets, with performance comparable to standard mini batch gradient descent. These results can lead to both improvements in the design of application specific integrated circuits for deep learning and in the speed of synchronization of machine learning models trained with data parallelism.
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