Tucker-TensorSketch provides Matlab functions for low-rank Tucker decomposition of tensors using TensorSketch. For further information about our methods, please see our paper:
O. A. Malik and S. Becker. Low-Rank Tucker Decomposition of Large Tensors Using TensorSketch. Advances in Neural Information Processing Systems 32, pages 10096-10106, 2018.
It is available at http://papers.nips.cc/paper/8213-low-rank-tucker-decomposition-of-large-tensors-using-tensorsketch.
Tucker-TensorSketch provides three functions, tucker_ts, tucker_ts_double_sketch and tucker_ttmts, for low-rank Tucker decomposition of tensors. These functions are variants of the standard alternating least-squares algorithm (higher-order orthogonal iteration) for the Tucker decomposition. They incorporate a sketching technique called TensorSketch, which is a form of CountSketch that can be applied efficiently to matrices which are Kronecker products of smaller matrices. Due to the properties of TensorSketch, our functions only require a single pass of the input tensor. They can handle streamed data in the sense that they can read tensor elements in any order, and do not need to have access to all elements at the same time. The functions tucker_ts and tucker_ttmts incorporate sketching in different ways. The function tucker_ts_double_sketch is a variant of tucker_ts which incorporates the idea presented in Remark 3.2 (c) of our paper.
The figure below shows an experiment where we compare our functions to other competing methods. The experiment is done for sparse 3-way tensors each containing about 1e+6 nonzero elements. All sides of each tensor are of equal length. The plots show how the relative error (in subplot (a)) and run time (in subplot (b)) vary as the size of the tensor sides is increased. Our functions are fast and can handle larger tensors than competing methods, while still maintaining good accuracy. However, our functions do not scale well with the target rank, which is why we recommend using them for low-rank decomposition only.
In our paper, we present an experiment where we apply one of our methods to a 3-way tensor representing a video and then use the resulting decomposition to classify frames that contain a distubance. Use the following link to view a video showing the results of this experiment: https://figshare.com/articles/media/Walking_Past_Camera/15135186?file=29084178
The original video which we used in this experiment is available for download here: https://figshare.com/articles/media/Walking_Past_Camera/15135186?file=29084181. In our experiment, we converted this video to grayscale and then treated the video as a 3-way tensor. The video in the link is 173 MB in size. After converting it to grayscale and then simply treating it as an array of doubles its size is about 38 GB. Feel free to use this video in your own experiments. If you do, please provide a reference to our paper.
Our code requires Tensor Toolbox version 2.6 by Bader, Kolda and others (available at https://www.tensortoolbox.org/).
Run the file compile_all_mex.m inside the folder help_functions. Alternatively, simply compile each C file individually by running "mex filename.c" inside Matlab.
The four demo files demonstrate our functions. Below is a brief description of each.
- Demo 1: This scrips gives a demo of tucker_ts and tucker_ttmts decomposing a sparse tensor. The script generates a sparse tensor and then decomposes it using both tucker_ts and tucker_ttmts, as well as tucker_als from Tensor Toolbox.
- Demo 2: This script gives a demo of tucker_ts and tucker_ttmts decomposing a dense tensor. The script generates a dense tensor and then decomposes it using both tucker_ts and tucker_ttmts, as well as tucker_als from Tensor Toolbox.
- Demo 3: This script gives a demo of tucker_ts and tucker_ttmts decomposing a dense tensor which is stored in a mat file on the hard drive. The result is compared to that produced by tucker_als in Tensor Toolbox applied to the same tensor stored in memory.
- Demo 4: This script gives a demo of tucker_ts and tucker_ts_double_sketch decomposing a sparse tensor. The script generates a sparse tensor and then decomposes it using both tucker_ts and tucker_ts_double_sketch. The idea is to demonstrate that the technique which we present in Remark 3.2 (c) of our paper improves the speed of the TUCKER-TS algorithm when the tensor dimension sizes are much larger than the sum of the two target sketch dimensions.
If you use our code in any of your own work, please reference our paper:
@inproceedings{malik-2018-low-rank-tucker,
title = {Low-Rank {T}ucker Decomposition of Large Tensors Using {T}ensor{S}ketch},
booktitle = {Advances in {Neural Information Processing Systems}},
author = {Malik, Osman Asif and Becker, Stephen},
year = {2018},
pages = {10096--10106},
}
Please feel free to contact me at any time if you have any questions or would like to provide feedback on this code or on our paper. I can be reached at [email protected].
This code uses the implementation of randomized SVD by Antoine Liutkus, which is available on MathWorks File Exchange. The license of that software is available in its original form in tucker-tensorsketch/help_functions/rsvd.
All other code in this project falls under the license in the root of this project.