Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Diffusion Representation for Asymmetric Kernels via Magnetic Transform
Authors: Mingzhen He, FAN He, Ruikai Yang, Xiaolin Huang
NeurIPS 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We present experiments that demonstrate the effectiveness and robustness of the Mag DM algorithm on three synthetic datasets and two real-world trophic networks. In this section, we demonstrate the capability of the Mag DM method to extract asymmetric information on three synthetic and two real-world trophic datasets. The results of the quantitative experiments evaluating the performance of the proposed Mag DM are presented in Tab. Ape.1 of the attached PDF file. |
| Researcher Affiliation | Academia | Mingzhen He Institute of Image Processing and Pattern Recognition Shanghai Jiao Tong University, Shanghai, China EMAIL Fan He Department of Electrical Engineering (ESAT-STADIUS) KU Leuven, Leuven, Belgium EMAIL Ruikai Yang, Xiaolin Huang Institute of Image Processing and Pattern Recognition Shanghai Jiao Tong University, Shanghai, China EMAIL |
| Pseudocode | Yes | Algorithm 1 Mag DM for asymmetric kernels Input: The Gram matrix K of dataset X endowed with an asymmetric kernel K, the scaling parameter q and a preset accuracy δ. Output: The diffusion map ψt,(q) of X. 1: Calculate the Hermitian Gram matrix H of the asymmetric Gram matrix K by (3) and (4). 2: Calculate the t-powers kernel matrix Ht. 3: Run eigen-decomposition of Ht and denote its eigen-system as {λ(q) n , ϕ(q) n }. 4: s(δ, t) max{n N : |λ(q) n | > δ|λ(q) 1 |}. 5: Return the diffusion map ψt,(q) by (8). |
| Open Source Code | Yes | Codes are available at https://github.com/Alex He123/Mag DM |
| Open Datasets | Yes | To further illustrate the concept, we have chosen two specific real-world trophic networks from the Pajek datasets1: the Mondego network [32], which records trophic exchanges at the Mondego estuary, and the Florida network [33], which records trophic exchanges in Florida Bay during the wet season. 1http://vlado.fmf.uni-lj.si/pub/networks/data/bio/foodweb/foodweb.htm |
| Dataset Splits | No | The paper uses synthetic datasets and real-world networks for dimension reduction and clustering, but does not specify explicit training/validation/test dataset splits or cross-validation methods for the model learning process. |
| Hardware Specification | Yes | The experiments were conducted using MATLAB on a PC with an Intel i7-10700K CPU (3.8GHz) and 32GB of memory. |
| Software Dependencies | No | The experiments were conducted using MATLAB on a PC with an Intel i7-10700K CPU (3.8GHz) and 32GB of memory. |
| Experiment Setup | Yes | In this experiment, we choose 5 probabilities for the backward running flow, P {0, 0.2, 0.5, 0.8, 1}. with q = 1/4. with q = 1/3. ρ = 5 and q = 0.09. The dimension reduction of the Florida network is shown using six methods (DM, ADM, KPCA, ME, MME, and Mag DM), with q = 0.045. Then we cluster the low-dimensional embeddings of the three methods using the k-means algorithm with k=3. |