name: CorrelationDimension : public AlgorithmBase

synopsis:

g++ [flags ...] file ... -l /isip/tools/lib/$ISIP_BINARY/lib_algo.a

#include <CorrelationDimension.h>

CorrelationDimension(ALGORITHM algorithm = DEF_ALGORITHM, IMPLEMENTATION implementation = DEF_IMPLEMENTATION, SCALING scaling = DEF_SCALING, float epsilon_min = DEF_EPSILON_MIN, float epsilon_max = DEF_EPSILON_MAX, float epsilon_res = DEF_EPSILON_RES, float delta = DEF_DELTA, long theiler_correction = DEF_THEILER_CORRECTION);
boolean eq(const CorrelationDimension& arg) const;
boolean compute(VectorFloat& output, const MatrixFloat& input);
quick start:

MatrixFloat input;
VectorFloat output;
CorrelationDimension cdim;
cdim.compute(output, input);
description:

The CorrelationDimension class computes the invariant of chaotic system, CorrelationDimension, given Rps of the time series. The dimension of an attractor is a measure of its geometric scaling properties. Many definitions of dimension exist. We implement the widely used correlation dimension. In chaos theory, the correlation dimension is a measure of the dimensionality of the space occupied by a set of random points. The major utility of the correlation dimension is in determining the dimensions of fractal objects. The idea is to construct a function proportional to the probability that two arbitrary points on the orbit in the state space are closer than epsilon. We use CorrelationIntegral for calculating the dimension. For a limited range of epsilon, correlation integral is proportional to epsilon ^ dimension. There are two scaling options for epsilon spacing. User may specify epsilons to be linearly equally spaced or logarithmically equally spaced.
CorrelationIntegral class. Dimension is well explained here: Three implementations are supported: backward differentiation, central differentiation and smooth differentiation. The backward differentiation method of implementation is described in: The smooth differentiation approach is accurate and is described in: dependencies:

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