Statistical Analysis of Metric Graph Reconstruction
Authors: Fabrizio Lecci, Alessandro Rinaldo, Larry Wasserman
JMLR 2014 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Example 1 A Neuron in Three-Dimensions. We return to the neuron example and we try to apply Propositions 4 to the 3D data of Figure 1, namely the neuron cr22e from the hippocampus of a rat (Guly as et al., 1999). The data were obtained from Neuro Morpho.Org (Ascoli et al., 2007). The total length of the graph is 1750.86µm. We assume the smallest edge has length 100µm, the smallest angle π/3, the local reach 30µm and ξ = 50µm. The conditions of Proposition 4 are satisfied for δ = 2.00µm. Algorithm 1 reconstructs the topology of the metric graph starting from a δ/2-dense sample. Figure 1b shows the reconstructed graph. |
| Researcher Affiliation | Academia | Fabrizio Lecci EMAIL Alessandro Rinaldo EMAIL Larry Wasserman EMAIL Department of Statistics Carnegie Mellon University Pittsburgh, PA 15213, USA |
| Pseudocode | Yes | Algorithm 1 Metric Graph Reconstruction Algorithm Input: sample Y, d Y, r, p11. 1: Labeling points as edge or vertex 2: for all y Y do 3: Sy B(y, r + δ)\B(y, r) 4: degr(y) Number of connected components of Rips-Vietoris graph Rδ(Sy) 5: if degr(y) = 2 then 6: Label y as a edge point 7: else 8: Label y as a preliminary vertex point. 9: end if 10: end for. 11: Label all points within Euclidean distance p11 from a preliminary vertex point as vertices. 12: Let E be the point of Y labeled as edge points. 13: Let V be the point of Y labeled as vertices. 14: Reconstructing the graph structure 15: Compute the connected components of the Rips-Vietoris graphs Rδ(E) and Rδ(V). 16: Let the connected components of Rδ(V) be the vertices of of the reconstructed graph b G. 17. Let there be an edge between vertices of b G if their corresponding connected components in Rδ(V) contain points at distance less than δ from the same connected component of Rδ(E). Output: b G. |
| Open Source Code | No | The paper does not provide explicit statements about the release of source code for the methodology described in this paper, nor does it provide links to a code repository. It uses an algorithm from a cited external paper. |
| Open Datasets | Yes | The data were obtained from Neuro Morpho.Org (Ascoli et al., 2007). |
| Dataset Splits | No | The paper discusses reconstructing a metric graph from a 'random sample' or 'δ/2-dense sample' but does not specify any training, test, or validation splits for experimental reproduction. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used to run the analysis or the example (e.g., GPU/CPU models, memory specifications). |
| Software Dependencies | No | The paper does not provide specific software dependencies, such as library names with version numbers, used in the analysis or for the example. |
| Experiment Setup | Yes | Example 1 A Neuron in Three-Dimensions. We return to the neuron example and we try to apply Propositions 4 to the 3D data of Figure 1, namely the neuron cr22e from the hippocampus of a rat (Guly as et al., 1999). The data were obtained from Neuro Morpho.Org (Ascoli et al., 2007). The total length of the graph is 1750.86µm. We assume the smallest edge has length 100µm, the smallest angle π/3, the local reach 30µm and ξ = 50µm. The conditions of Proposition 4 are satisfied for δ = 2.00µm. |