correlation dimension meaning

• [Finance]
  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.

• Method of computing correlation dimension based on wavelet packet transform
• correlation dimension of pressure fluctuation in gas-liquid-solid three phase co-current up-flow system
• Application of correlation dimension in fan fault diagnosis based on wavelet coefficient region relativity
• The chaotic invariants of measured time series of dams such as correlation dimension, the lyapunov exponent and the kolmogorov entropy, are calculated
• Yet another measure of fractal dimension is the correlation dimension.
• Note : It can be shown that the correlation dimension is certainly between 0 . 4926 and 0 . 5024.
• Where " mod " is the Grassberger ( 1983 ) questions this value based on their difficulties measuring the correlation dimension.
• D ( Q = 1 ) is equal to the information dimension, and D ( Q = 2 ) to the correlation dimension.
• But in the presence of complicated deterministic systems they may not have very high power to detect it ( see note 4 in Correlation dimension ).
• Numerical estimates yield a correlation dimension of 0 . 500 � 0 . 005 ( Grassberger 1983 ) for r \ simeq 3 . 5699456 . . . ( onset of chaos ).

• "correlation dimension" meaning in Chinese: 关联维数