An Information Geometry of Statistical Manifold Learning
Authors: Ke Sun, Stéphane Marchand-Maillet
ICML 2014 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Table 1. Estimated intrinsic dimension (avg. std.) for each k {5, 10, . . . , 100}. Figure 2. Local dimension estimation. Figure 3. Performance measurements of different embeddings. In each sub-figure, the color-map shows the local densities vol(a, b)dσ(a, b) over Ω. From left to right (resp. bottom to up), the input (resp. output) observation radius expands from 5 to 50. |
| Researcher Affiliation | Academia | Ke Sun KE.SUN@UNIGE.CH Stéphane Marchand-Maillet STEPHANE.MARCHAND-MAILLET@UNIGE.CH Viper Group, Computer Vision & Multimedia Laboratory, University of Geneva, Switzerland |
| Pseudocode | No | The paper describes algorithms and derivations in text and mathematical formulas but does not include any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any statements about releasing code or links to source code repositories for the described methodology. |
| Open Datasets | Yes | Table 1 shows its performance compared to the maximum likelihood estimator (MLE) (Levina & Bickel, 2005) on several benchmark datasets, including a spiral with one intrinsic dimension, a Swiss roll with two intrinsic dimensions, an artificial face dataset2 rendered with different light directions and different orientations (three degrees of freedom), an image sequence3 recording a hand holding a bowl and rotating (around two degrees of freedom), and MNIST hand-written digits 4. (Footnotes: 2http://isomap.stanford.edu/datasets.html, 3http://vasc.ri.cmu.edu//idb/html/motion/hand/index.html, 4http://yann.lecun.com/exdb/mnist) |
| Dataset Splits | No | The paper mentions using specific datasets and discusses sample sizes (e.g., "Swiss roll (n = 103) and MNIST (n = 5 103; five classes)"), but it does not provide explicit training, validation, or test split percentages, sample counts, or methodology for partitioning the data. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used to conduct the experiments, such as GPU/CPU models or memory. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers, such as programming languages, libraries, or frameworks used for implementation. |
| Experiment Setup | Yes | The parameters k, κ and ks are empirically set to 100, 50 and 5, respectively. |