Last update: 08/09/2014
Matlab Tensor Tools (MTT) is a lightweight MATLAB library providing a comprehensive set of functions for manipulating and decomposing tensors, aimed especially at applications in computer vision and multidimensional signal processing. It includes utilities for tensor unfolding/folding, slicing, fiber extraction, n-mode products, tensor–tensor operations, and demos covering key decompositions such as HoSVD/iHoSVD, Tucker via ALS, CP/PARAFAC via ALS, t-SVD, non-negative tensor factorization, and incremental tensor learning. The repo is stable, compact, and example-driven, making it easy for researchers and students to explore tensor algebra workflows in MATLAB.
See also: Presentation about Matrix and Tensor Tools for Computer Vision http://www.slideshare.net/andrewssobral/matrix-and-tensor-tools-for-computer-vision LRSLibrary: Low-Rank and Sparse Tools for Background Modeling and Subtraction in Videos https://github.com/andrewssobral/lrslibrary IMTSL: Incremental and Multi-feature Tensor Subspace Learning https://github.com/andrewssobral/imtsl If you use this code for your publications, please cite it as:
@misc{asobral2014, author = "Sobral, Andrews", title = "Matlab Tensor Tools", year = "2014", url = "https://github.com/andrewssobral/mtt/" } tensor_demo_operations.m - Basic operations tensor_demo_hosvd_ihosvd.m - High-order singular value decomposition (Tucker decomposition) tensor_demo_parafac_als.m - CP decomposition via ALS (Alternating Least-Squares) tensor_demo_tucker_als.m - Tucker decomposition via ALS (Alternating Least-Squares) tensor_demo_tsvd.m - t-SVD and inverse t-svd tensor_demo_ntf.m - Non-Negative Tensor Factorization tensor_demo_subtensors_ntf_hals.m - Low-rank approximation based Non-Negative Tensor(CP) factorization tensor_demo_inclearn.m - Incremental tensor learning A = reshape(1:12,[2,2,3]); B = reshape(1:12,[2,2,3]); %% Basic operations [A1,A2,A3] = tensor_matricization(A); M22 = reshape(1:4,[2,2]); M33 = reshape(1:9,[3,3]); B1 = tensor_nmodeproduct(A,M22,1); B2 = tensor_nmodeproduct(A,M22,2); B3 = tensor_nmodeproduct(A,M33,3); Au = tensor_unfold(A); A_hat = tensor_fold(Au,size(A)); [A1_] = tensor_slices_frontal(A); [A2_] = tensor_slices_lateral(A); [A3_] = tensor_slices_horizontal(A); [At1_] = tensor_fibers_column(A); [At2_] = tensor_fibers_row(A); [At3_] = tensor_fibers_tube(A); Bt = tensor_transpose(B); [C] = tensor_product(A,B); %% HoSVD and iHoSVD decomposition T = tensor(A); [core,U] = tensor_hosvd(T); [T_hat] = tensor_ihosvd(core,U); %% t-SVD decomposition [U,S,V] = tensor_t_svd(A); [C] = tensor_product(U,S); [A_hat] = tensor_product(C,tensor_transpose(V)); %% Tucker ALS decomposition r = 10; T_hat = tucker_als(T,[r r r]); %% PARAFAC/CP ALS decomposition T_hat = cp_als(T, r);