Structure-adaptive Manifold Estimation
Authors: Nikita Puchkin, Vladimir Spokoiny
JMLR 2022 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we carry out simulations to illustrate the performance of SAME. For convenience, theoretical results were obtained for manifolds without a boundary (which is a common assumption in the manifold learning literature) but we use some well-known surfaces with boundary in the experiments. The source code of all the numerical experiments described in this section is available on Git Hub (link). Data set MSE of SAME, 102 MSE of MBMS, 102 Swiss Roll 67.4 69.3 S-shape 3.9 4.7 Table 1: Mean squared errors (MSE, (5)) of SAME and MBMS algorithms. Best results are boldfaced. |
| Researcher Affiliation | Academia | Nikita Puchkin EMAIL National Research University Higher School of Economics, Pokrovsky boulevard 11, 109028 Moscow, Russian Federation and Institute for Information Transmission Problems RAS, Bolshoy Karetny per. 19, build.1, 127051 Moscow, Russian Federation Vladimir Spokoiny EMAIL Weierstrass Institute and Humboldt University, Mohrenstrasse 39, 10117 Berlin, Germany and National Research University Higher School of Economics, Pokrovsky boulevard 11, 109028 Moscow, Russian Federation and Institute for Information Transmission Problems RAS, Bolshoy Karetny per. 19, build.1, 127051 Moscow, Russian Federation |
| Pseudocode | Yes | Algorithm 1 Structure-adaptive manifold estimator (SAME) Algorithm 2 Manifold blurring mean shift algorithm (with full graph), Wang and Carreira Perpinan (2010) |
| Open Source Code | Yes | The source code of all the numerical experiments described in this section is available on Git Hub (link). |
| Open Datasets | Yes | First, we show how our estimator denoises the manifold. We start with the description of the experiment with the Swiss Roll. We sampled n = 2500 points on a two-dimensional manifold in R3 and then embedded the surface into R20 adding 17 dummy coordinates. We take two artificial data sets g241c and g241n, which are described in (Chapelle et al., 2010). |
| Dataset Splits | Yes | We split the data sets into 100 train points and 1400 test points. |
| Hardware Specification | No | The paper describes the datasets and experimental procedure but does not specify any particular hardware used for running the simulations or experiments. |
| Software Dependencies | No | The paper describes various algorithms and methods but does not provide specific software dependencies or their version numbers used in the numerical experiments. |
| Experiment Setup | Yes | We sampled n = 2500 points on a two-dimensional manifold in R3 and then embedded the surface into R20 adding 17 dummy coordinates. After that, we added a uniform noise with a magnitude 0.75 to each coordinate (thus, the noise magnitude M was equal to 0.75 20). In our algorithm, we initialized bΠ(0) i = I20 for all i from 1 to n and made 6 iterations with h2 k = h2 0 1.25 k, 0 k 5, τ = h0, and γ = 4. For MBMS, we took σ = 2.6/ 2, k = 150 and only 1 iteration. The dimension d was set to 2. In the case of g241c data set, we took d = 10, τ = 22, γ = 4 and hk = 20 1.2 k, 0 k 1. In the case of g241n data set, we took d = 6, τ = 21, γ = 4 and hk = 20 1.2 k, 0 k 2. |