Diffusion Representation for Asymmetric Kernels via Magnetic Transform
Authors: Mingzhen He, FAN He, Ruikai Yang, Xiaolin Huang
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | 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 mingzhen_he@sjtu.edu.cn Fan He Department of Electrical Engineering (ESAT-STADIUS) KU Leuven, Leuven, Belgium fan.he@esat.kuleuven.be Ruikai Yang, Xiaolin Huang Institute of Image Processing and Pattern Recognition Shanghai Jiao Tong University, Shanghai, China {ruikai.yang, xiaolinhuang}@sjtu.edu.cn |
| 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. |