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However, they have two serious drawbacks. Firstly, TSA and DTSA iteratively compute the left and right projection matrices. At each iteration, two generalized eigenvalue problems are required to solve, which makes them inapplicable for high dimensional image data. Secondly, the metric structure of the facial image space cannot be preserved since the left and right projection matrices are not usually orthonormal. In this paper, we propose the orthogonal TSA (OTSA) and orthogonal DTSA (ODTSA). In contrast to TSA and DTSA, two trace ratio optimization problems are required to be solved at each iteration. Thus, OTSA and ODTSA have much less computational cost than their nonorthogonal counterparts since the trace ratio optimization problem can be solved by the inexpensive Newton-Lanczos method. Experimental results show that the proposed methods achieve much higher recognition accuracy and have much lower training cost.<\/jats:p>","DOI":"10.1155\/2014\/871565","type":"journal-article","created":{"date-parts":[[2014,1,9]],"date-time":"2014-01-09T11:04:16Z","timestamp":1389265456000},"page":"1-11","source":"Crossref","is-referenced-by-count":3,"title":["Fast Second-Order Orthogonal Tensor Subspace Analysis for Face Recognition"],"prefix":"10.1155","volume":"2014","author":[{"given":"Yujian","family":"Zhou","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computational Science, Institute of Computational Mathematics, Hunan University of Science and Engineering, Yongzhou 425100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liang","family":"Bao","sequence":"additional","affiliation":[{"name":"Department of Mathematics, East China University of Science and Technology, Shanghai 200237, 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