Dynamic Mode Decomposition with Reproducing Kernels for Koopman Spectral Analysis
Authors: Yoshinobu Kawahara
NeurIPS 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We illustrate the method on the applications using synthetic and real-world data. |
| Researcher Affiliation | Academia | a The Institute of Scientific and Industrial Research, Osaka University b Center for Advanced Integrated Intelligence Research, RIKEN |
| Pseudocode | Yes | The procedure for the robustified variant of the DMD is summarized as follows.1 (1) Define Mτ and calculate the centered Gram matrix G = HM τMτH. (2) Calculate the eigendecomposition G B S B , which gives the kernel principal directions U. (3) Calculate ˆF as in Eq. (11) and its eigendecomposition ˆF = ˆT 1ˆΛ ˆT, where each diagonal element of ˆΛ gives λj. (4) Define φj to be the columns of MτH B S 1/2 ˆT 1. |
| Open Source Code | Yes | 1The Matlab code is available at http://en.44nobu.net/codes/kdmd.zip |
| Open Datasets | Yes | locomotion data from CMU Graphics Lab Motion Capture Database.2Available at http://mocap.cs.cmu.edu. |
| Dataset Splits | No | The paper describes the data sources used, such as synthetic data and 'locomotion data from CMU Graphics Lab Motion Capture Database,' and mentions generating samples with 'several initial conditions,' but it does not provide specific details on how these datasets were split into training, validation, or test sets for reproducibility. |
| Hardware Specification | No | The paper does not provide any specific hardware details such as CPU/GPU models, memory specifications, or cloud computing resources used for running the experiments. |
| Software Dependencies | No | The paper mentions that 'The Matlab code is available at http://en.44nobu.net/codes/kdmd.zip', implying the use of Matlab, but it does not specify the version number of Matlab or any other software dependencies (e.g., libraries, packages) with their specific versions. |
| Experiment Setup | Yes | We used the polynomial kernel of degree three for the toy system, and the Gaussian kernel with width 1 for the H enon map, respectively. We used the RBF Gaussian kernel, where the kernel width was set as the median of the distances from a data matrix. |