When Locally Linear Embedding Hits Boundary
Authors: Hau-Tieng Wu, Nan Wu
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Third, through a series of numerical simulations, we explore the impact of the hyperbolic part of the operator... Numerical simulations of the clipped LLE are provided... At last, in Figure 2, we provide a visualization of the augmented vector field in a 2-dim manifold parametrized by (x,y,x2 y3), where x2 + y2 1. We sample the manifold in the following way. First, uniformly sample 20,000 points independently on [ 1,1] [ 1,1], and keep points with norm less and equal to 1. The i-th point is then constructed by the parametrization... The LLE matrix is constructed with the ε-radius ball nearest neighbor search scheme with ε = 0.2. |
| Researcher Affiliation | Academia | Hau-Tieng Wu EMAIL Department of Mathematics and Department of Statistical Science, Duke University, Durham, NC 27708, United States; Nan Wu EMAIL Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, TX 75080, United States |
| Pseudocode | No | The paper describes the LLE algorithm and its modifications using mathematical equations and textual descriptions (e.g., Section 2: 'Review locally linear embedding', Section 7: 'Clipped LLE matrix'), but it does not include any clearly labeled pseudocode or algorithm blocks with structured steps. |
| Open Source Code | Yes | For reproducibility purposes, the Matlab code to reproduce figures in this paper can be downloaded from http://hautiengwu.wordpress.com/code/. |
| Open Datasets | No | The paper does not use publicly available datasets. Instead, it describes generating synthetic data by sampling points from various manifolds for its numerical simulations, for example: 'First, uniformly sample 20,000 points independently on [ 1,1] [ 1,1], and keep points with norm less and equal to 1. The i-th point is then constructed by the parametrization.' (Figure 2 description) or 'We uniformly and independently sample points from M1 := [0,1] R1.' |
| Dataset Splits | No | The paper describes methods for sampling data from defined manifolds for simulations but does not discuss training, validation, or test dataset splits, as its numerical experiments do not involve such typical machine learning data partitioning. |
| Hardware Specification | No | The paper does not provide specific details about the hardware (e.g., CPU, GPU models, memory) used to run the numerical simulations or generate the figures. It only mentions that 'Matlab code' is available. |
| Software Dependencies | No | The paper mentions 'Matlab code' for reproducibility but does not specify a version number for Matlab or any other software libraries or dependencies with their respective versions. |
| Experiment Setup | Yes | The LLE matrix is constructed with the ε-radius ball nearest neighbor search scheme with ε = 0.2... The LLE matrix is constructed with the ε-radius ball nearest neighbor search scheme, where ε = 0.1... The LLE matrix is constructed with the ε-radius scheme, where ε = 0.01... Then, establish the LLE matrix and the clipped LLE matrix with ε = 0.3. |