Data driven estimation of Laplace-Beltrami operator
Authors: Frederic Chazal, Ilaria Giulini, Bertrand Michel
NeurIPS 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | A numerical illustration and a discussion about the proposed method are given in Sections 5 and 6 respectively. In this section we illustrate the results of the previous section on a simple example. We sample n1 = 10^6 points on the sphere for computing the graph Laplacians and we use n = 10^3 points for approximating the norms... |
| Researcher Affiliation | Academia | Frédéric Chazal Inria Saclay Palaiseau France frederic.chazal@inria.fr; Ilaria Giulini Inria Saclay Palaiseau France ilaria.giulini@me.com; Bertrand Michel Ecole Centrale de Nantes Laboratoire de Mathématiques Jean Leray (UMR 6629 CNRS) Nantes France bertrand.michel@ec-nantes.fr |
| Pseudocode | No | The paper does not contain structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide concrete access to source code for the methodology described. |
| Open Datasets | No | The paper states 'We sample n1 = 10^6 points on the sphere for computing the graph Laplacians and we use n = 10^3 points for approximating the norms ( ˆ h ˆ h ) f 2 2,M.' and 'data points generated uniformly on the sphere S2 in R3', but provides no access information (link, DOI, repository, or citation) for this generated dataset. |
| Dataset Splits | Yes | Regarding the first issue, we can approximate 2,M by splitting the data into two samples: an estimation sample X1 for computing the estimators and a validation sample X2 for evaluating this norm. More precisely, given two estimators ˆ hf and ˆ h f computed using X1, the quantity ( ˆ h ˆ h )f 2 2,M/µ(M) is approximated by the averaged sum 1 n2 P x X2 | ˆ hf(x) ˆ h f(x)|2, where n2 is the number of points in X2. |
| Hardware Specification | No | The paper does not provide specific hardware details (like exact GPU/CPU models or processor types) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details (e.g., library or solver names with version numbers) needed to replicate the experiment. |
| Experiment Setup | Yes | We sample n1 = 10^6 points on the sphere for computing the graph Laplacians and we use n = 10^3 points for approximating the norms... We compute the graph Laplacians for bandwidths in a grid H between 0.001 and 0.8. |