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.