An efficient algorithm for estimating dimensionalities
R. L. Somorjai, Mazhar Ali · Canadian Journal of Chemistry · 1988
We present an algorithm for estimating dimensionality. It is based on a multivariate k nearest neighbor (k-NN) density estimator and shows explicitly that the dependence of k-NN distances on k does not follow pure power law behavior. We achieve very high efficiency (≤ 2000 points for up to 20 dimensions) by abandoning the distribution free feature of our algorithm; it is calibrated for two distributions and tested on a number of strange attractors, the discretized Mackay–Glass system, and trajectories of 3, 10, and 20 coupled harmonic oscillators. The danger of embedding in higher dimensional spaces is demonstrated.