167,451 research outputs found

    Tensor Spectral Clustering for Partitioning Higher-order Network Structures

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    Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. Spectral methods are based on a first-order Markov chain derived from a random walk on the graph and thus they cannot take advantage of important higher-order network substructures such as triangles, cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework. Our TSC algorithm allows the user to specify which higher-order network structures (cycles, feed-forward loops, etc.) should be preserved by the network clustering. Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method. Our framework can be applied to discovering layered flows in networks as well as graph anomaly detection, which we illustrate on synthetic networks. In directed networks, a higher-order structure of particular interest is the directed 3-cycle, which captures feedback loops in networks. We demonstrate that our TSC algorithm produces large partitions that cut fewer directed 3-cycles than standard spectral clustering algorithms.Comment: SDM 201

    Employment conditions in the scottish social care voluntary sector : impact of public funding constraints in the context of economic recession

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    This report uses data to assess the impact of public funding constraints on employment conditions in the Scottish social care voluntary sector, in the context of the recent economic recessionand future public expenditure cuts

    Follow up evaluation of self-directed support test sites in Scotland

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