Tensor-Based Machine Learning : Modeling, Algorithms and Applications

概要

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Tensors are a generalization of vectors and matrices to higher dimensions that can naturally represent the multidimensional structured data. Based on multilinear algebra, tensor factorizations enable us to effectively capture the hidden structure of the data, which is usually available as a priori information on the data nature. Hence it attracts much interest on unsupervised learning and data exploratory. In this paper, we firstly present some basic concept of tensor factorization and multilinear algebra, then a novel framework for tensor variate Gaussian processes (GP) regression is introduced, which exploits a covariance function defined on tensor representation of data inputs. In this way, we bring together the powerful GP methods supported by Bayesian inference and higher-order tensor analysis techniques into one framework. This enables us to account for the underlying data structure within the model, providing a powerful framework for structural data analysis, such as 3D video sequences. Simulation results on both the synthetic data and a real world application of estimating the crowd size in videos, without the necessarity of the typical segmentations and feature extractions, demonstrate the effectiveness of the proposed approach.
一般社団法人電子情報通信学会の論文
2013-08-22