Computing Kantorovich-Wasserstein Distances on $d$-dimensional histograms using $(d+1)$-partite graphs
Authors: Gennaro Auricchio, Federico Bassetti, Stefano Gualandi, Marco Veneroni
NeurIPS 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | On these types of instances, our approach is competitive with state-of-the-art optimal transport algorithms. ... In this section, we report the results obtained on two different set of instances. The goal of our experiments is to show how our approach scales with the size of the histogram N and with the dimension of the histogram d. As problem instances, we use the gray scale images (i.e., 2-dimensional histograms) proposed by the DOTMark benchmark [26], and a set of d-dimensional histograms obtained by bio medical data measured by flow cytometer [9]. |
| Researcher Affiliation | Academia | Gennaro Auricchio, Stefano Gualandi, Marco Veneroni Università degli Studi di Pavia, Dipartimento di Matematica F. Casorati |
| Pseudocode | No | The paper does not contain structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | The C++ and Matlab code we used for this paper is freely available at http://stegua.github.io/dpartion-nips2018. |
| Open Datasets | Yes | As problem instances, we use the gray scale images (i.e., 2-dimensional histograms) proposed by the DOTMark benchmark [26], and a set of d-dimensional histograms obtained by bio medical data measured by flow cytometer [9]. ... available at http://flowrepository.org/id/FR-FCM-ZZYA |
| Dataset Splits | No | The paper describes how instances were created for evaluation (e.g., 'we compute the distance between every possible pair of images within the same class: the first image plays the role of the source distribution µ, and the second image gives the target distribution ν. Considering all pairs within a class, it gives 45 instances for each class.'), but it does not specify train/validation splits in the typical machine learning sense with percentages or explicit counts for model training. |
| Hardware Specification | Yes | The tests are executed on a gaming laptop with Windows 10 (64 bit), equipped with an Intel i7-6700HQ CPU and 16 GB of Ram. |
| Software Dependencies | Yes | We run our experiments using the Network Simplex as implemented in the Lemon C++ graph library1, since it provides the fastest implementation of the Network Simplex algorithm to solve uncapacitated minimum cost flow problems [16]. ... The code was compiled with MS Visual Studio 2017, using the ANSI standard C++17. |
| Experiment Setup | Yes | As cost distance c(x, y), with x, y Rd, we use the squared ℓ2 norm. ... In our tests, we used λ = 1 and λ = 1.5. ... The Matlab implementation of the Sinkhorn s algorithm [11] runs in parallel on the CPU cores, but we do not use any GPU in our test. The C++ and Matlab code we used for this paper is freely available at http://stegua.github.io/dpartion-nips2018. |