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Arye Nehorai

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4 papers

2 author rows

NeurIPS Conference 2019 Conference Paper

KerGM: Kernelized Graph Matching

Zhen Zhang
Yijian Xiang
Lingfei Wu
Bing Xue
Arye Nehorai

Graph matching plays a central role in such fields as computer vision, pattern recognition, and bioinformatics. Graph matching problems can be cast as two types of quadratic assignment problems (QAPs): Koopmans-Beckmann's QAP or Lawler's QAP. In our paper, we provide a unifying view for these two problems by introducing new rules for array operations in Hilbert spaces. Consequently, Lawler's QAP can be considered as the Koopmans-Beckmann's alignment between two arrays in reproducing kernel Hilbert spaces (RKHS), making it possible to efficiently solve the problem without computing a huge affinity matrix. Furthermore, we develop the entropy-regularized Frank-Wolfe (EnFW) algorithm for optimizing QAPs, which has the same convergence rate as the original FW algorithm while dramatically reducing the computational burden for each outer iteration. We conduct extensive experiments to evaluate our approach, and show that our algorithm significantly outperforms the state-of-the-art in both matching accuracy and scalability.

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NeurIPS Conference 2018 Conference Paper

RetGK: Graph Kernels based on Return Probabilities of Random Walks

Zhen Zhang
Mianzhi Wang
Yijian Xiang
Yan Huang
Arye Nehorai

Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph kernels, based on return probabilities of random walks. The advantages of our proposed kernels are that they can effectively exploit various node attributes, while being scalable to large datasets. We conduct extensive graph classification experiments to evaluate our graph kernels. The experimental results show that our graph kernels significantly outperform other state-of-the-art approaches in both accuracy and computational efficiency.

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NeurIPS Conference 2014 Conference Paper

Fast Kernel Learning for Multidimensional Pattern Extrapolation

Andrew Wilson
Elad Gilboa
Arye Nehorai
John Cunningham

The ability to automatically discover patterns and perform extrapolation is an essential quality of intelligent systems. Kernel methods, such as Gaussian processes, have great potential for pattern extrapolation, since the kernel flexibly and interpretably controls the generalisation properties of these methods. However, automatically extrapolating large scale multidimensional patterns is in general difficult, and developing Gaussian process models for this purpose involves several challenges. A vast majority of kernels, and kernel learning methods, currently only succeed in smoothing and interpolation. This difficulty is compounded by the fact that Gaussian processes are typically only tractable for small datasets, and scaling an expressive kernel learning approach poses different challenges than scaling a standard Gaussian process model. One faces additional computational constraints, and the need to retain significant model structure for expressing the rich information available in a large dataset. In this paper, we propose a Gaussian process approach for large scale multidimensional pattern extrapolation. We recover sophisticated out of class kernels, perform texture extrapolation, inpainting, and video extrapolation, and long range forecasting of land surface temperatures, all on large multidimensional datasets, including a problem with 383, 400 training points. The proposed method significantly outperforms alternative scalable and flexible Gaussian process methods, in speed and accuracy. Moreover, we show that a distinct combination of expressive kernels, a fully non-parametric representation, and scalable inference which exploits existing model structure, are critical for large scale multidimensional pattern extrapolation.

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ICRA Conference 2005 Conference Paper

Information Based Distributed Control for Biochemical Source Detection and Localization

Panos Tzanos
Milos Zefran
Arye Nehorai

The paper proposes several improvements on the Direction of Gradient (DOG) algorithm proposed in [1] for detecting and localizing a biochemical source with moving sensors. In particular, we show that the DOG algorithm can be turned into a distributed control scheme for a mobile sensing network, and that the maximum likelihood estimation proposed in the original algorithm can be replaced with more computationally efficient numerical procedures. Simulations on a single sensor and on a group of mobile sensors are provided that show that the proposed modifications simplify the original algorithm and improve its performance.

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