【摘 要】
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Two major tools in the study of multi-relational datasets are (i) higher-order Markov chains and (ii) linear algebra-inspired computations on hypermatrices
【出 处】
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2016年张量和矩阵学术研讨会(International conference on Tensor, Matrix a
论文部分内容阅读
Two major tools in the study of multi-relational datasets are (i) higher-order Markov chains and (ii) linear algebra-inspired computations on hypermatrices including low-rank factorization and eigenvectors. We unify these ideas through a new type of stochastic process called a spacey random walk that combines a higher-order Markov chain with a vertex-reinforced random walk. Their stationary distributions, if they exist, correspond to the solution of a tensor eigenvector problem. Thus, we provide a solid probabilistic foundation for tensor eigenvectors as well as a new analytical tool for data problems with higher-order structure. We provide several potential applications of the spacey random walk model in population genetics, ranking, and data clustering, and we use the process to analyze taxi trajectory data in New York. This example shows defi-nite non-Markovian, and higher-order, structure. We will also see clusters in text and transportation data.
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