Talk:Correlation dimension

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"less than or equal" should be "less than"

I've just read the original 1983 paper, and noticed that the wikipedia definition is about finding the number of pairs separated by an amount "less than or equal to distance epsilon", whereas the 1983 definition just uses "less than" (i.e. equality doesn't count). It's a very minor point but I thought it worth noting just for future editors' reference. I'll change the article to reflect this. --mcld 21:33, 17 July 2007 (UTC)[reply]

So how is correlation dimension defined?

Can someone knowledgeable comment on how correlation dimension is defined?

So if I understand the article correctly, correlation dimension is defined only in the following case: "If the number of points is sufficiently large, and evenly distributed, a Log-log graph of the correlation integral versus \varepsilon will yield an estimate of ν." Right? 141.214.17.5 (talk) 16:36, 17 December 2008 (UTC)[reply]

I wouldn't include the "evenly distributed (homogeneous)" attribute. By definition of strange attractor, the points are not supposed to be homogeneous. Homogeneity is an indication of random process. Strange attractors however means that the points are fractal distributed. See Paladin & Vulpiani 1987 (Physics Reports v156: 147-225). Meson2439 (talk) 07:48, 10 September 2009 (UTC)[reply]

NN or N(N-1)

Is there a really 1/N*N multiplier in original definition? I am cand remember 2/N(N-1) in many papers, and the latter have more sense to me. Lqp (talk) 06:40, 18 April 2009 (UTC)[reply]

N*(N-1) are used for computing the correlation sum. The original paper in 1983 actually used N*N. It was removed for computational purpose because when i=j, |x_i - x_j| = 0 which do not contributes to the counting of points.Meson2439 (talk) 07:38, 10 September 2009 (UTC)[reply]

Weak level of rigor

The article gives a vague definition of ν. For example, what object is ν a property of? Is it

1) A sequence of N points?

2) An infinite sequence of points?

3) An infinite sequence of samples of a probability distribution?

4) An infinite sequence of samples of a probability distribution supported on a fractal?

If so, is it a property of the fractal? The language used suggests each of these at various points.

In general, the language of the article is sloppy.

For example, it says "The technique can be used to distinguish between (deterministic) chaotic and truly random behavior". What technique? A number is not a technique.

144.200.0.157 (talk) 04:19, 22 April 2022 (UTC)[reply]

"less than or equal" should be "less than"

So how is correlation dimension defined?

N*N or N*(N-1)

Weak level of rigor

NN or N(N-1)