# embedding

(redirected from Embedding dimension)
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Related to Embedding dimension: Correlation dimension

## embedding

[em′bed·iŋ]
(mathematics)
An injective homomorphism between two algebraic systems of the same type.

## embedding

(mathematics)
One instance of some mathematical object contained with in another instance, e.g. a group which is a subgroup.

## embedding

(theory)
(domain theory) A complete partial order F in [X -> Y] is an embedding if

(1) For all x1, x2 in X, x1 <= x2 <=> F x1 <= F x2 and

(2) For all y in Y, x | F x <= y is directed.

("<=" is written in LaTeX as \sqsubseteq).
References in periodicals archive ?
During the prediction process of the chaotic time series, the selection of the embedding dimension and delay time is the basis of chaotic time series prediction.
In Section 3, a practical method is proposed to determine the minimum embedding dimension and get the recurrence formula, with which a capacity model is built for the prediction.
The appropriate embedding dimension delay time can be estimated according to Taken's embedding theorem.
The embedding dimension d is computed by false nearest neighbors [22].
20] analysed the embedding dimension of normal and epileptic EEG time series.
For more on the embedding dimension for Stein spaces see [Sch97].
If the correlation exponents increase as a function of embedding dimension, then the considered system can be thought of as stochastic, otherwise it is chaotic.
It should be noted that the findings of this study are not conclusive for two reasons: firstly, some contradictory results were obtained when comparing the BDS statistic with the other analyses; and secondly, neither the optimum value of the lag nor that of the embedding dimension were taken into account.
Causation is detected by partial autocorrelation and by consecutive recurrence at low embedding dimensions.
The Correlation Dimension in embedding dimension M is given by
The key in detecting nonlinearities with the Grassberger and Procaccia test is to observe the changes in the CD as we increase the embedding dimension.

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