Estimating manifold dimension with nearest neighbor graphs

We introduce a new algorithm to estimate the manifold dimension of datasets. Our technique is based on the idea that the manifold structure should be preserved as far as possible after dimension reduction. Computing the structure errors of nearest neighbor graphs before and after dimension reduction, we gain the manifold dimension by seeking the smallest value of dimension when the structure error is equal to zero. Experiments show that our results is consistent with the results obtained by other methods, but our method doesn't depend on the success of both the dimensionality reduction algorithm and the method used to discover the inverse map.