The decomposition of the higher-order homology embedding constructed from the $k$-Laplacian
Authors: Yu-Chia Chen, Marina Meila
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Lastly, we support our theoretical claims with numerous empirical results from point clouds and images. |
| Researcher Affiliation | Academia | Yu-Chia Chen Electrical & Computer Engineering University of Washington Seattle, WA 98195 yuchaz@uw.edu Marina Meila Department of Statistics University of Washington Seattle, WA 98195 mmp2@uw.edu |
| Pseudocode | Yes | Algorithm 1: Subspace identification |
| Open Source Code | Yes | New codes are attached in the supplemental material codes.zip; they can also be found at https://github.com/yuchaz/homology_emb. |
| Open Datasets | Yes | RNA single-cell sequencing data [7]. |
| Dataset Splits | No | The paper does not explicitly provide training/test/validation dataset splits, such as specific percentages or sample counts for each split. |
| Hardware Specification | Yes | We perform our analysis on a desktop running Linux with 32GB RAM and an 8-Core 4.20GHz Intel Core i7-7700K CPU |
| Software Dependencies | No | The paper mentions tools and algorithms like "Infomax ICA [6]" and "Dijkstra", but does not specify version numbers for these or other software dependencies. |
| Experiment Setup | Yes | For all the point clouds, we build the VR complex SC from the Ck NN kernel [8] so that the resulting L1 is sparse and the topological information is preserved. [...] The cubical complex is constructed by intensity thresholding (also called the sub-level set method in TDA [58]) and then applying morphological closing on the binary image to remove small cavities. The weight for every rectangle w2(σ) is set to 1; [...] We chose to keep n1/β1 by treating each homology class equally, i.e., each class has roughly n1/β1 edges. |