605 research outputs found

    An application of Hoffman graphs for spectral characterizations of graphs

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    In this paper, we present the first application of Hoffman graphs for spectral characterizations of graphs. In particular, we show that the 22-clique extension of the (t+1)×(t+1)(t+1)\times(t+1)-grid is determined by its spectrum when tt is large enough. This result will help to show that the Grassmann graph J2(2D,D)J_2(2D,D) is determined by its intersection numbers as a distance regular graph, if DD is large enough

    Gradient descent for sparse rank-one matrix completion for crowd-sourced aggregation of sparsely interacting workers

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    We consider worker skill estimation for the singlecoin Dawid-Skene crowdsourcing model. In practice skill-estimation is challenging because worker assignments are sparse and irregular due to the arbitrary, and uncontrolled availability of workers. We formulate skill estimation as a rank-one correlation-matrix completion problem, where the observed components correspond to observed label correlation between workers. We show that the correlation matrix can be successfully recovered and skills identifiable if and only if the sampling matrix (observed components) is irreducible and aperiodic. We then propose an efficient gradient descent scheme and show that skill estimates converges to the desired global optima for such sampling matrices. Our proof is original and the results are surprising in light of the fact that even the weighted rank-one matrix factorization problem is NP hard in general. Next we derive sample complexity bounds for the noisy case in terms of spectral properties of the signless Laplacian of the sampling matrix. Our proposed scheme achieves state-of-art performance on a number of real-world datasets.Published versio
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