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In multilinear algebra, a tensor decomposition is any scheme for expressing a "data tensor" as a sequence of elementary operations acting on other, often simpler tensors. Many tensor decompositions generalize some matrix decompositions.
In multilinear algebra, the higher-order singular value decomposition (HOSVD) of a tensor is a specific orthogonal Tucker decomposition. It may be regarded as one type of generalization of the matrix singular value decomposition. It has applications in computer vision, computer graphics, machine learning, scientific computing, and signal processing. Some aspects can be traced as far back as F. L. Hitchcock in 1928, but it was L. R. Tucker who developed for third-order tensors the general Tucker decomposition in the 1960s, further advocated by L. De Lathauwer et al. in their Multilinear SVD work that employs the power method, or advocated by Vasilescu and Terzopoulos that developed M-mode SVD a parallel algorithm that employs the matrix SVD.
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Igor Mezić is a mechanical engineer, mathematician, and Distinguished Professor of mechanical engineering and mathematics at the University of California, Santa Barbara. He is best known for his contributions to operator theoretic, data driven approach to dynamical systems theory that he advanced via articles based on Koopman operator theory, and his work on theory of mixing, that culminated in work on microfluidic mixer design, and mapping oil refuse from the Deepwater Horizon oil spill in the Gulf of Mexico to aid in cleaning efforts.
Gordon L. Kindlmann is an American computer scientist who works on information visualization and image analysis. He is recognized for his contributions in developing tools for tensor data visualization.
Dacheng Tao is an Australian engineer and academic. He is currently a professor of computer science at the University of Sydney, Australia. He received a PhD in 2007 from the University of London under Stephen Maybank, with a thesis titled Discriminative linear and multilinear subspace methods. He was named a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) in 2015 for his contributions to pattern recognition and visual analytics. He was awarded an Australian Laureate Fellowship in 2017. In 2018, Tao was also elected a Fellow of the Australian Academy of Science (FAA) for his "ground-breaking contributions in artificial intelligence, computer vision image processing and machine learning. He was elected as an ACM Fellow in 2019 "for contributions to representation learning and its applications". He was selected to the Global Young Academy. Tao won the Australian Museum's Eureka Prize for Excellence in Data Science in 2020. He has written over 1200 publications across various Artificial Intelligence fields, including pattern recognition, visual analytics, and statistical learning theory.
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Daniel Kressner is a German numerical analyst. He has a Chair of Numerical Algorithms and High Performance Computing in the Institute of Mathematics at EPF Lausanne.
Tensor informally refers in machine learning to two different concepts that organize and represent data. Data may be organized in a multidimensional array (M-way array) that is informally referred to as a "data tensor"; however in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector space. Observations, such as images, movies, volumes, sounds, and relationships among words and concepts, stored in an M-way array ("data tensor") may be analyzed either by artificial neural networks or tensor methods.
References
- ↑ "Lieven De Lathauwer". STADIUS. Retrieved 31 August 2022.
- ↑ "2015 elevated fellow" (PDF). IEEE Fellows Directory. Archived from the original (PDF) on March 30, 2015.
- ↑ SIAM Fellows: Class of 2017, retrieved 2017-04-25.
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