2,360 research outputs found

    Sampling Large Data on Graphs

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    We consider the problem of sampling from data defined on the nodes of a weighted graph, where the edge weights capture the data correlation structure. As shown recently, using spectral graph theory one can define a cut-off frequency for the bandlimited graph signals that can be reconstructed from a given set of samples (i.e., graph nodes). In this work, we show how this cut-off frequency can be computed exactly. Using this characterization, we provide efficient algorithms for finding the subset of nodes of a given size with the largest cut-off frequency and for finding the smallest subset of nodes with a given cut-off frequency. In addition, we study the performance of random uniform sampling when compared to the centralized optimal sampling provided by the proposed algorithms.Comment: To be presented at GlobalSIP 201

    Active search in intensionally specified structured spaces

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    We consider an active search problem in intensionally specified structured spaces. The ultimate goal in this setting is to discover structures from structurally different partitions of a fixed but unknown target class. An example of such a process is that of computer-aided de novo drug design. In the past 20 years several Monte Carlo search heuristics have been developed for this process. Motivated by these hand-crafted search heuristics, we devise a Metropolis--Hastings sampling scheme where the acceptance probability is given by a probabilistic surrogate of the target property, modeled with a max entropy conditional model. The surrogate model is updated in each iteration upon the evaluation of a selected structure. The proposed approach is consistent and the empirical evidence indicates that it achieves a large structural variety of discovered targets

    Interpolation of Sparse Graph Signals by Sequential Adaptive Thresholds

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    This paper considers the problem of interpolating signals defined on graphs. A major presumption considered by many previous approaches to this problem has been lowpass/ band-limitedness of the underlying graph signal. However, inspired by the findings on sparse signal reconstruction, we consider the graph signal to be rather sparse/compressible in the Graph Fourier Transform (GFT) domain and propose the Iterative Method with Adaptive Thresholding for Graph Interpolation (IMATGI) algorithm for sparsity promoting interpolation of the underlying graph signal.We analytically prove convergence of the proposed algorithm. We also demonstrate efficient performance of the proposed IMATGI algorithm in reconstructing randomly generated sparse graph signals. Finally, we consider the widely desirable application of recommendation systems and show by simulations that IMATGI outperforms state-of-the-art algorithms on the benchmark datasets in this application.Comment: 12th International Conference on Sampling Theory and Applications (SAMPTA 2017
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