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.