494 research outputs found

    Temporal Clustering

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    We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological surveys and contagious disease surveillance. In this more general setting existing algorithms for classical (i.e. static) clustering problems are not applicable anymore. We propose a set of optimization problems which we collectively refer to as temporal clustering. The quality of a solution to a temporal clustering instance can be quantified using three parameters: the number of clusters k, the spatial clustering cost r, and the maximum cluster displacement delta between consecutive time steps. We consider spatial clustering costs which generalize the well-studied k-center, discrete k-median, and discrete k-means objectives of classical clustering problems. We develop new algorithms that achieve trade-offs between the three objectives k, r, and delta. Our upper bounds are complemented by inapproximability results

    Temporal Hierarchical Clustering

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    We study hierarchical clusterings of metric spaces that change over time. This is a natural geo- metric primitive for the analysis of dynamic data sets. Specifically, we introduce and study the problem of finding a temporally coherent sequence of hierarchical clusterings from a sequence of unlabeled point sets. We encode the clustering objective by embedding each point set into an ultrametric space, which naturally induces a hierarchical clustering of the set of points. We enforce temporal coherence among the embeddings by finding correspondences between successive pairs of ultrametric spaces which exhibit small distortion in the Gromov-Hausdorff sense. We present both upper and lower bounds on the approximability of the resulting optimization problems

    Tensor Regression with Applications in Neuroimaging Data Analysis

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    Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays (tensors). Traditional statistical and computational methods are proving insufficient for analysis of these high-throughput data due to their ultrahigh dimensionality as well as complex structure. In this article, we propose a new family of tensor regression models that efficiently exploit the special structure of tensor covariates. Under this framework, ultrahigh dimensionality is reduced to a manageable level, resulting in efficient estimation and prediction. A fast and highly scalable estimation algorithm is proposed for maximum likelihood estimation and its associated asymptotic properties are studied. Effectiveness of the new methods is demonstrated on both synthetic and real MRI imaging data.Comment: 27 pages, 4 figure

    The Reactome pathway Knowledgebase

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    The Reactome Knowledgebase (www.reactome.org) provides molecular details of signal transduction, transport, DNA replication, metabolism and other cellular processes as an ordered network of molecular transformations-an extended version of a classic metabolic map, in a single consistent data model. Reactome functions both as an archive of biological processes and as a tool for discovering unexpected functional relationships in data such as gene expression pattern surveys or somatic mutation catalogues from tumour cells. Over the last two years we redeveloped major components of the Reactome web interface to improve usability, responsiveness and data visualization. A new pathway diagram viewer provides a faster, clearer interface and smooth zooming from the entire reaction network to the details of individual reactions. Tool performance for analysis of user datasets has been substantially improved, now generating detailed results for genome-wide expression datasets within seconds. The analysis module can now be accessed through a RESTFul interface, facilitating its inclusion in third party applications. A new overview module allows the visualization of analysis results on a genome-wide Reactome pathway hierarchy using a single screen page. The search interface now provides auto-completion as well as a faceted search to narrow result lists efficiently

    Medico-Legal Findings, Legal Case Progression, and Outcomes in South African Rape Cases: Retrospective Review

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    Rachel Jewkes and colleagues examine the processing of rape cases by South African police and courts and show an association between documentation of ano-genital injuries, trials commencing, and convictions in rape cases
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