Dimension Estimation Using Random Connection Models
Authors: Paulo Serra, Michel Mandjes
JMLR 2017 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | A simulation study on both real and simulated data shows that our approach compares favourably with some competing methods from the literature, including approaches that rely on distance information. In Section 7 we present some numerical illustrations for our method, and we propose our bias corrected estimator. |
| Researcher Affiliation | Academia | Paulo Serra EMAIL Department of Mathematics and Computer Science Groene Loper 5 Meta Forum Building Eindhoven University of Technology 5612 AZ Eindhoven, the Netherlands; Michel Mandjes EMAIL Korteweg-de Vries Institute for Mathematics Science Park 105 107 University of Amsterdam 1098 XG Amsterdam, the Netherlands |
| Pseudocode | No | The paper describes the estimation process and formulas in detail, particularly in Section 4 'Estimation of the Intrinsic Dimension', but does not include a distinct pseudocode block or algorithm listing. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code, nor does it provide links to a code repository or supplementary materials for code. |
| Open Datasets | Yes | We consider twelve data sets; seven consist of simulated data, and five of real data. The Isomap faces data set4 contains 698 images (D = 64 × 64 pixels) of a rendered face of a sculpture taken from different angles, under different lighting conditions. The Hands data set5 contains 481 frames (D = 512 × 480 pixels) from a video of a hand holding a rice bowl and revolving it while moving from right to left. The MNIST data sets6 contain 7141, 6824, and 6313 images (D = 28 × 28 pixels) of handwritten digits 3, 4, and 5, respectively. |
| Dataset Splits | No | The paper mentions using simulated data and real datasets (Isomap faces, Hands, MNIST) but does not specify training/test/validation splits. For the MNIST dataset, it states the total number of images for specific digits (e.g., '7141, 6824, and 6313 images'), but no split methodology is described. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used to run the experiments, such as GPU or CPU models, or memory specifications. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers used for the implementation or experiments. |
| Experiment Setup | Yes | We set the distribution of the design points X ~ Nd(0, I), for d ∈ {1, 2, 3, 4, 5, 10}, and chose n ∈ {10^3, 10^4, 10^5, 10^6, 10^7}; irrespectively of the dimension we always set ϵ = ϵn = 4/(log n)^1/2. Based on the discussion from the previous section, the parameter mn was set to max(1, log n). |