Adaptive Geometric Multiscale Approximations for Intrinsically Low-dimensional Data
Authors: Wenjing Liao, Mauro Maggioni
JMLR 2019 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We include several numerical experiments on both synthetic and real data, confirming our theoretical results and demonstrating the effectiveness of Adaptive GMRA. |
| Researcher Affiliation | Academia | Wenjing Liao EMAIL School of Mathematics Georgia Institute of Technology, Atlanta, GA, 30313, USA. Mauro Maggioni EMAIL Department of Mathematics, Department of Applied Mathematics and Statistics, Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218, USA |
| Pseudocode | Yes | Algorithm 1 Adaptive GMRA Input: data X2n = X n Xn, intrinsic dimension d, threshold κ Output: T n, {Cj,k}, b PbΛτn : multiscale tree, corresponding cells and adaptive piecewise linear projectors on an adaptive partition. 1: Construct T n and {Cj,k} from X n 2: Now use Xn. Compute b Pj,k and b j,k on every node Cj,k T n. 3: b Tτn smallest proper subtree of T n containing all Cj,k T n : b j,k 2 jτn where τn = κ p 4: bΛτn the partition associated with outer leaves of b Tτn 5: b PbΛτn P Cj,k bΛτn b Pj,k1j,k. |
| Open Source Code | No | The paper does not provide an explicit statement or link for open-source code. |
| Open Datasets | Yes | We consider the MNIST data set from http://yann.lecun.com/exdb/mnist/, We use the Caltech 101 dataset from https://www.vision.caltech.edu/Image_Datasets/Caltech101/ (see F. Li and Perona, 2006), multiscale patches from CIFAR 10 from https://www.cs.toronto.edu/~kriz/cifar.html (see Krizhevsky and Hinton, 2009) |
| Dataset Splits | Yes | We randomly split the data into two disjoint groups such that X2n = X n Xn where X n = {x 1, . . . , x n} and Xn = {x1, . . . , xn}, We evenly split the samples to the training set and the test set. |
| Hardware Specification | No | The paper does not provide specific hardware details (exact GPU/CPU models, processor types with speeds, memory amounts, or detailed computer specifications) used for running its experiments. It only generally states: 'We are grateful to Duke University for donated computing time and equipment used for part of the numerical experiments of this paper.' |
| Software Dependencies | No | The paper mentions 'matlab toolbox' but does not provide specific version numbers for any software, libraries, or frameworks used in the experiments. |
| Experiment Setup | Yes | In Figure 6, we set the noise level σ = 0 (a,c) and σ = 0.05 (b,d), We let κ {0.3, 0.4} when σ = 0 and κ {1, 2} when σ = 0.05., we set GMRA to pick the dimension of b Vj,k adaptively, as the smallest dimension needed to capture 50% of the energy of the data in Cj,k., we set the diameter of cells at scale j to be O(0.9j) and the dimension of b Vj,k to be the smallest dimension needed to capture 50% of the energy of the data in Cj,k. |