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The Renyi dimension spectrum of a points set can be estimated using information about
the distribution of the interpoint distances. Since we are interested in the scaling behaviour
of the Renyi information for small distances, we don't need to compute all interpoint distances,
the distances to k nearest neighbors for each reference point are sufficient [150].
Robust estimation is used instead of mean square error fitting.
Syntax:
- [dimensions, moments] = gendimest(dists, gammas, kmin_low, kmin_high, kmax)
Input arguments:
- dists - a matrix of size R by k which
contains distances from reference points to their k nearest neighbors,
sorted in increasing order. This matrix can be obtained by calling
nn_search (cf. Section 6.14) or fnearneigh (cf. Section 6.9) on the point set
whose dimension spectrum is to be investigated.
- gammas - vector of the moment orders
- kmin_low - first kmin, 1
kmin_low
- kmin_high - last kmin, kmin_low
kmin_high
kmax
- kmax - highest neigbor order up to which, kmax
k
Output arguments:
- dimensions - matrix of size length(gammas) by kmin_upper-kmin_lower+1, holding the
dimension estimates
- moments (optional) - matrix of size k by length(gammas), storing the computed
moments of the neigbor distances
Example:
x = chaosys(25000, 0.025, [0.1 -0.1 0.02], 0); % generate data from Lorenz system
x = x(5001:end,:); % discard first 5000 samples due to transient
[nn, dist] = fnearneigh(x, randref(1, 20000, 1000), 128, 0);
gammas = -5:0.5:5;
gedims = gendimest(dist, gammas, 8, 8, 128);
plot(1-gammas./gedims', gedims)
xlabel('q');ylabel('D_q');title('Renyi dimension')
Next: 6.11 henon - Generate
Up: 6. Mex-Function Reference
Previous: 6.9 fnearneigh - Fast
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