# correlation dimension

correlation dimension
An estimate of the fractal dimension which measures the probability that two points chosen at random will be within a certain distance of each other, and examines how this probability changes as the distance is increased. white noise will fill its space since its components are uncorrelated, and its correlation dimension is equal to whatever dimension it is placed in. A dependent system will be held together by its correlations and retain its dimension whatever embedding dimension it is placed in, as long as it is greater than its fractal dimension. Bloomberg Financial Dictionary

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• Correlation dimension — In chaos theory, the correlation dimension (denoted by ν) is a measure of the dimensionality of the space occupied by a set of random points, often referred to as a type of fractal dimension.[1][2][3] For example, if we have a set of random… …   Wikipedia

• Correlation sum — In chaos theory, the correlation sum is the estimator of the correlation integral, which reflects the mean probability that the states at two different times are close: where N is the number of considered states , ε is a threshold distance, a… …   Wikipedia

• Correlation integral — In chaos theory, the correlation integral is the mean probability that the states at two different times are close: where N is the number of considered states , ε is a threshold distance, a norm (e.g. Euclidean norm) and …   Wikipedia

• Dimension — 0d redirects here. For 0D, see 0d (disambiguation). For other uses, see Dimension (disambiguation). From left to right, the square, the cube, and the tesseract. The square is bounded by 1 dimensional lines, the cube by 2 dimensional areas, and… …   Wikipedia

• Dimension — Sur les autres projets Wikimedia : « Dimension », sur le Wiktionnaire (dictionnaire universel) Dans le sens commun, la notion de dimension renvoie à la taille ; les dimensions d une pièce sont sa longueur, sa largeur et sa… …   Wikipédia en Français

• Correlation Integral — The probability that two points are within a certain distance from one another. Used in the calculation of the correlation dimension. Bloomberg Financial Dictionary …   Financial and business terms

• Correlation spectroscopy — is one of several types of two dimensional nuclear magnetic resonance (NMR) spectroscopy. Other types of two dimensional NMR include J spectroscopy, exchange spectroscopy (EXSY), and Nuclear Overhauser effect spectroscopy (NOESY). Two dimensional …   Wikipedia

• Dimension fractale — Mesure de la dimension fractale de la côte de Grande Bretagne En géométrie fractale, la dimension fractale, D, est une grandeur qui a vocation à traduire la façon qu a un ensemble fractal de remplir l espace, à toutes les échelles. Dans le cas… …   Wikipédia en Français

• Dimension (data warehouse) — This article is about a dimension in a data warehouse. For other uses, see dimension (disambiguation). In a data warehouse, a dimension is a data element that categorizes each item in a data set into non overlapping regions. A data warehouse… …   Wikipedia

• Corrélation linéaire — Régression linéaire Pour les articles homonymes, voir Régression. Un exemple graphique En statistiques, étant donné un échantillon aléatoire …   Wikipédia en Français