3,243 research outputs found

    Multilevel refinement based on neighborhood similarity

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    The multilevel graph partitioning strategy aims to reduce the computational cost of the partitioning algorithm by applying it on a coarsened version of the original graph. This strategy is very useful when large-scale networks are analyzed. To improve the multilevel solution, refinement algorithms have been used in the uncorsening phase. Typical refinement algorithms exploit network properties, for example minimum cut or modularity, but they do not exploit features from domain specific networks. For instance, in social networks partitions with high clustering coefficient or similarity between vertices indicate a better solution. In this paper, we propose a refinement algorithm (RSim) which is based on neighborhood similarity. We compare RSim with: 1. two algorithms from the literature and 2. one baseline strategy, on twelve real networks. Results indicate that RSim is competitive with methods evaluated for general domains, but for social networks it surpasses the competing refinement algorithms.CNPq (grant 151836-/2013-2)FAPESP (grants 2011/22749-8, 11/20451-1 and 2013/12191-5)CAPE

    Spectrally approximating large graphs with smaller graphs

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    How does coarsening affect the spectrum of a general graph? We provide conditions such that the principal eigenvalues and eigenspaces of a coarsened and original graph Laplacian matrices are close. The achieved approximation is shown to depend on standard graph-theoretic properties, such as the degree and eigenvalue distributions, as well as on the ratio between the coarsened and actual graph sizes. Our results carry implications for learning methods that utilize coarsening. For the particular case of spectral clustering, they imply that coarse eigenvectors can be used to derive good quality assignments even without refinement---this phenomenon was previously observed, but lacked formal justification.Comment: 22 pages, 10 figure

    Memetic Multilevel Hypergraph Partitioning

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    Hypergraph partitioning has a wide range of important applications such as VLSI design or scientific computing. With focus on solution quality, we develop the first multilevel memetic algorithm to tackle the problem. Key components of our contribution are new effective multilevel recombination and mutation operations that provide a large amount of diversity. We perform a wide range of experiments on a benchmark set containing instances from application areas such VLSI, SAT solving, social networks, and scientific computing. Compared to the state-of-the-art hypergraph partitioning tools hMetis, PaToH, and KaHyPar, our new algorithm computes the best result on almost all instances

    Visual Saliency Based on Multiscale Deep Features

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    Visual saliency is a fundamental problem in both cognitive and computational sciences, including computer vision. In this CVPR 2015 paper, we discover that a high-quality visual saliency model can be trained with multiscale features extracted using a popular deep learning architecture, convolutional neural networks (CNNs), which have had many successes in visual recognition tasks. For learning such saliency models, we introduce a neural network architecture, which has fully connected layers on top of CNNs responsible for extracting features at three different scales. We then propose a refinement method to enhance the spatial coherence of our saliency results. Finally, aggregating multiple saliency maps computed for different levels of image segmentation can further boost the performance, yielding saliency maps better than those generated from a single segmentation. To promote further research and evaluation of visual saliency models, we also construct a new large database of 4447 challenging images and their pixelwise saliency annotation. Experimental results demonstrate that our proposed method is capable of achieving state-of-the-art performance on all public benchmarks, improving the F-Measure by 5.0% and 13.2% respectively on the MSRA-B dataset and our new dataset (HKU-IS), and lowering the mean absolute error by 5.7% and 35.1% respectively on these two datasets.Comment: To appear in CVPR 201
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