Legendre Decomposition for Tensors
Authors: Mahito Sugiyama, Hiroyuki Nakahara, Koji Tsuda
NeurIPS 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We empirically show that Legendre decomposition can more accurately reconstruct tensors than other nonnegative tensor decomposition methods. We empirically examine performance of our method in Section 3 |
| Researcher Affiliation | Academia | Mahito Sugiyama National Institute of Informatics JST, PRESTO mahito@nii.ac.jp Hiroyuki Nakahara RIKEN Center for Brain Science hiro@brain.riken.jp Koji Tsuda The University of Tokyo NIMS; RIKEN AIP tsuda@k.u-tokyo.ac.jp |
| Pseudocode | Yes | Algorithm 1: Legendre decomposition by gradient descent. Algorithm 2: Legendre decomposition by natural gradient. |
| Open Source Code | Yes | Implementation is available at: https://github.com/mahito-sugiyama/Legendre-decomposition |
| Open Datasets | Yes | We used the MNIST dataset (Le Cun et al., 1998)... URL http://yann.lecun.com/exdb/mnist/. We picked up the first entry from the fourth mode (corresponds to lighting) from the dataset... This dataset is originally distributed at http://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html and also available from the R r Tensor package (https://CRAN.R-project.org/package=r Tensor). |
| Dataset Splits | No | The paper mentions using synthetic and real-world datasets (face images, MNIST) and describes how subsets were created (e.g., |
| Hardware Specification | Yes | We used Amazon Linux AMI release 2018.03 and ran all experiments on 2.3 GHz Intel Xeon CPU E5-2686 v4 with 256 GB of memory. |
| Software Dependencies | Yes | The Legendre decomposition was implemented in C++ and compiled with icpc 18.0.0. We used the Tensor Ly implementation (Kossaifiet al., 2016) for the nonnegative Tucker and CP decompositions and the tensor toolbox (Bader et al., 2017; Bader and Kolda, 2007) for CP-APR. |
| Experiment Setup | Yes | We set B = B3(l) and varied the number of parameters |B| with increasing l. In Algorithm 2, we used the outer loop (from line 3 to 8) as one iteration for fair comparison and fixed the learning rate ε = 0.1. |