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Knowl. Discov. Data"],"published-print":{"date-parts":[[2019,6,30]]},"abstract":"Restricted Boltzmann machine (RBM) is a famous model for feature extraction and can be used as an initializer for neural networks. When applying the classic RBM to multidimensional data such as 2D\/3D tensors, one needs to vectorize such as high-order data. Vectorizing will result in dimensional disaster and valuable spatial information loss. As RBM is a model with fully connected layers, it requires a large amount of memory. Therefore, it is difficult to use RBM with high-order data on low-end devices. In this article, to utilize classic RBM on tensorial data directly, we propose a new tensorial RBM model parameterized by the tensor train format (TTRBM). In this model, both visible and hidden variables are in tensorial form, which are connected by a parameter matrix in tensor train format. The biggest advantage of the proposed model is that TTRBM can obtain comparable performance compared with the classic RBM with much fewer model parameters and faster training process. To demonstrate the advantages of TTRBM, we conduct three real-world applications, face reconstruction, handwritten digit recognition, and image super-resolution in the experiments.<\/jats:p>","DOI":"10.1145\/3321517","type":"journal-article","created":{"date-parts":[[2019,6,10]],"date-time":"2019-06-10T12:10:51Z","timestamp":1560168651000},"page":"1-16","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Tensorizing Restricted Boltzmann Machine"],"prefix":"10.1145","volume":"13","author":[{"given":"Fujiao","family":"Ju","sequence":"first","affiliation":[{"name":"Beijing University of Technology, Beijing, China"}]},{"given":"Yanfeng","family":"Sun","sequence":"additional","affiliation":[{"name":"Beijing University of Technology, Beijing, China"}]},{"given":"Junbin","family":"Gao","sequence":"additional","affiliation":[{"name":"The University of Sydney, Sydney, NSW, Australia"}]},{"given":"Michael","family":"Antolovich","sequence":"additional","affiliation":[{"name":"Charles Sturt University, Bathurst, NSW, Australia"}]},{"given":"Junliang","family":"Dong","sequence":"additional","affiliation":[{"name":"Beijing University of Technology, Beijing, China"}]},{"given":"Baocai","family":"Yin","sequence":"additional","affiliation":[{"name":"Dalian University of Technology, Dalian, China"}]}],"member":"320","published-online":{"date-parts":[[2019,6,7]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"N. 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Salakhutdinov. 2009. Replicated softmax: An undirected topic model. In Proceedings of the Advances in Neural Information Processing Systems. 1607--1614."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2017.2665555"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1137\/07070111X"},{"volume-title":"Proceedings of the International Conference on Artificial Intelligence and Statistics. 621--628","author":"Krizhevsky A.","key":"e_1_2_1_12_1","unstructured":"A. Krizhevsky and G. E. Hinton . 2010. Factored 3-way restricted Boltzmann machines for modeling natural images . In Proceedings of the International Conference on Artificial Intelligence and Statistics. 621--628 . A. Krizhevsky and G. E. Hinton. 2010. Factored 3-way restricted Boltzmann machines for modeling natural images. In Proceedings of the International Conference on Artificial Intelligence and Statistics. 621--628."},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00371-013-0868-3"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00371-015-1087-x"},{"volume-title":"Proceedings of the Association for the Advancement of Artificial Intelligence. 2887--2893","author":"Nguyen T. D.","key":"e_1_2_1_15_1","unstructured":"T. D. Nguyen , T. Tran , D. Phung , and S. Venkatesh . 2015. Tensor-variate restricted Boltzmann machines . In Proceedings of the Association for the Advancement of Artificial Intelligence. 2887--2893 . T. D. Nguyen, T. Tran, D. Phung, and S. Venkatesh. 2015. Tensor-variate restricted Boltzmann machines. In Proceedings of the Association for the Advancement of Artificial Intelligence. 2887--2893."},{"volume-title":"Proceedings of the Advances in Neural Information Processing Systems. 442--450","author":"Novikov A.","key":"e_1_2_1_16_1","unstructured":"A. Novikov , D. Podoprikhin , A. Osokin , and D. P. Vetrov . 2015. Tensorizing neural networks . In Proceedings of the Advances in Neural Information Processing Systems. 442--450 . A. Novikov, D. Podoprikhin, A. Osokin, and D. P. Vetrov. 2015. Tensorizing neural networks. In Proceedings of the Advances in Neural Information Processing Systems. 442--450."},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1137\/090752286"},{"key":"e_1_2_1_18_1","doi-asserted-by":"crossref","unstructured":"E. Papalexakis C. Faloutsos and N. D. Sidiropoulos. 2015. ParCube: Sparse parallelizable CANDECOMP-PARAFAC tensor decomposition. ACM Transactions on Knowledge Discovery from Data 10 1 (2015) 3:1--3:25. E. Papalexakis C. Faloutsos and N. D. 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In Proceedings of the ACM International Conference on Multimedia. 187--196 . H. Zhang, Y. Yang, H. Luan, S. Yang, and T. Chua. 2014. Start from scratch: Towards automatically identifying, modeling, and naming visual attributes. 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