Persistence weighted Gaussian kernel for topological data analysis
Authors: Genki Kusano, Yasuaki Hiraoka, Kenji Fukumizu
ICML 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate the performance of the proposed kernel method with synthesized and real-world data, including protein datasets (taken by NMR and X-ray crystallography experiments) and oxide glasses (taken by molecular dynamics simulations). In Section 4, we apply KG for SVM, kernel PCA, and kernel change point detection. |
| Researcher Affiliation | Academia | Genki Kusano1 GENKSN@GMAIL.COM Kenji Fukumizu2 FUKUMIZU@ISM.AC.JP Yasuaki Hiraoka1 HIRAOKA@WPI-AIMR.TOHOKU.AC.JP 1Tohoku University, 2The Institute of Statistical Mathematics |
| Pseudocode | No | The paper does not contain any 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 mentions protein datasets (taken by NMR and X-ray crystallography experiments) and oxide glasses from molecular dynamics simulations, and refers to "data used in (Nakamura et al., 2015a;b)" for the Si O2 data. However, it does not provide concrete access information (links, DOIs, or explicit public availability statements) for these datasets in the paper itself. |
| Dataset Splits | Yes | The hyper-parameters (σ, C) in the PWGK and t in the PSSK are chosen by the 10-fold crossvalidation, and the degree p in the weight of the PWGK is set to be 5. SVMs are trained with persistence diagrams given by 100 data sets, and evaluated with 99 independent test data sets. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, memory amounts) used for running its experiments. |
| Software Dependencies | No | The paper mentions that "all persistence diagrams are 1-dimensional (i.e., rings) and computed by CGAL (Da et al., 2015) and PHAT (Bauer et al., 2014)", but it does not specify version numbers for these software components. |
| Experiment Setup | Yes | In this paper, since all points of data are in R3, we set p = 5 from the assumption p > d + 1 in Theorem 3.2. For the parameter C, we also set C = (median{pers(Dℓ) | ℓ= 1, . . . , n}) p, where pers(D) = median{pers(xi) | xi D}. Similarly, τ is defined by median{dwarc k G (Di, Dj) | 1 i < j n}. |