IEEE Trans Image Process - Tensor learning for regression.

Tópicos

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Resumo

In this paper, we exploit the advantages of tensorial representations and propose several tensor learning models for regression. The model is based on the canonical/parallel-factor decomposition of tensors of multiple modes and allows the simultaneous projections of an input tensor to more than one direction along each mode. Two empirical risk functions are studied, namely, the square loss and e -insensitive loss functions. The former leads to higher rank tensor ridge regression (TRR), and the latter leads to higher rank support tensor regression (STR), both formulated using the Frobenius norm for regularization. We also use the group-sparsity norm for regularization, favoring in that way the low rank decomposition of the tensorial weight. In that way, we achieve the automatic selection of the rank during the learning process and obtain the optimal-rank TRR and STR. Experiments conducted for the problems of head-pose, human-age, and 3-D body-pose estimations using real data from publicly available databases, verified not only the superiority of tensors over their vector counterparts but also the efficiency of the proposed algorithms.

Resumo Limpo

paper exploit advantag tensori represent propos sever tensor learn model regress model base canonicalparallelfactor decomposit tensor multipl mode allow simultan project input tensor one direct along mode two empir risk function studi name squar loss e insensit loss function former lead higher rank tensor ridg regress trr latter lead higher rank support tensor regress str formul use frobenius norm regular also use groupspars norm regular favor way low rank decomposit tensori weight way achiev automat select rank learn process obtain optimalrank trr str experi conduct problem headpos humanag d bodypos estim use real data public avail databas verifi superior tensor vector counterpart also effici propos algorithm

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