This repository is based and supplements the paper
Díaz, M., Quiroz, A., & Velasco, M. (2018). Local angles and dimension estimation from data on manifolds.
We implemented functions for both our local and global estimators and can be found in 'ANOVA_local_estimator.m' and 'ANOVA_global_estimator.m', respectively. Each one of these files contains instructions on how to use them. The user can set parameters such as the number of neighbors, number of centers, maximum possible dimension and whether to use the naive or the kernel-based estimator.
Additionally, we include code for the experiments described in the paper. That is, we have two scripts named 'benchmark_experiment.m' and 'normal_conjecture_experiment.m'.
/utils This folder contains all the necessary functions to run the estimators.
/data This folder includes a .mat file with the data to run the kernel-based estimator (The code will create it again if it doesn't exist).
/results The experiment scripts paste all their results here (both figures and .mat files).
In order to run the experiments one need to add to path some dependencies.
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To run the benchmark experiment one needs to add to path code for DANCo and the data generator.
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One can run the last two experiments without any extra code, nonetheless we added sections that make better-than-standard plots and save them. To run those one needs to add to path code for linspecer and export_fig.