Understanding and modeling complex network processes is an important task in many real-world applications. The first challenge is to discover patterns in such complex data. In this work, our goal is to summarize diffe...
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ISBN:
(纸本)9781538691595
Understanding and modeling complex network processes is an important task in many real-world applications. The first challenge is to discover patterns in such complex data. In this work, our goal is to summarize different processes in a network by a small yet interpretable set of network patterns, each of which represents a local community of connected nodes frequently participating in the same network processes. We formulate this problem as a Boolean Matrix Factorization with a networkconstraint, which we prove to be NP-hard. We then propose an efficient algorithm that incrementally adds the best patterns and achieve scalability with two further improvements. First, to decide which network processes contain which network patterns, we introduce two mapping algorithms with linear costs. Second, to systematically mine the exponential subgraph search space for good patterns, we devise two sampling algorithms based on Monte Carlo Markov Chain. Experimental results on both synthetic and real-world datasets show that our solutions are scalable and find network patterns that effectively summarize network processes.
Classic multinomial logit model, commonly used in multiclass regression problem, is restricted to few predictors and does not take into account the relationship among variables. It has limited use for genomic data, wh...
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Classic multinomial logit model, commonly used in multiclass regression problem, is restricted to few predictors and does not take into account the relationship among variables. It has limited use for genomic data, where the number of genomic features far exceeds the sample size. Genomic features such as gene expressions are usually related by an underlying biological network. Efficient use of the network information is important to improve classification performance as well as the biological interpretability. We proposed a multinomial logit model that is capable of addressing both the high dimensionality of predictors and the underlying network information. Group lasso was used to induce model sparsity, and a network-constraint was imposed to induce the smoothness of the coefficients with respect to the underlying network structure. To deal with the non-smoothness of the objective function in optimization, we developed a proximal gradient algorithm for efficient computation. The proposed model was compared to models with no prior structure information in both simulations and a problem of cancer subtype prediction with real TCGA (the cancer genome atlas) gene expression data. The network-constrained mode outperformed the traditional ones in both cases.
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