scholarly journals Calculation of Average Mutual Information (AMI) and False-Nearest Neighbors (FNN) for the Estimation of Embedding Parameters of Multidimensional Time Series in Matlab

2018 ◽  
Vol 9 ◽  
Author(s):  
Sebastian Wallot ◽  
Dan Mønster
Keyword(s):  
Time Series ◽  
Mutual Information ◽  
Nearest Neighbors ◽  
Average Mutual Information ◽  
Multidimensional Time Series ◽  
False Nearest Neighbors

Statistical Characterization of Nearest Neighbors to Reliably Estimate Minimum Embedding Dimension

2014 ◽  
Author(s):  
David Chelidze
Keyword(s):  
Time Series ◽  
Nearest Neighbor ◽  
Nearest Neighbors ◽  
Surrogate Data ◽  
Original Method ◽  
Random Time ◽  
Embedding Dimension ◽  
Statistical Characterization ◽  
False Nearest Neighbors ◽  
Coordinate Embedding

False nearest neighbors (FNN) is one of the essential methods used in estimating the minimally sufficient embedding dimension in delay coordinate embedding of deterministic time series. Its use for stochastic and noisy deterministic time series is problematic and erroneously indicates a finite embedding dimension. Various modifications to the original method have been proposed to mitigate this problem, but those are still not reliable for noisy time series. Nearest neighbor statistics are studied for uncorrelated random time series and contrasted with the deterministic statistics. A new FNN metric is constructed and its performance is evaluated for deterministic, stochastic, and random time series. The results are also contrasted with surrogate data analysis and show that the new metric is robust to noise. It also clearly identifies random time series as not having a finite embedding dimension and provides information about the deterministic part of stochastic processes. The new metric can also be used for differentiating between chaotic and random time series.

scholarly journals Reliable Estimation of Minimum Embedding Dimension Through Statistical Analysis of Nearest Neighbors

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
David Chelidze
Keyword(s):  
Time Series ◽  
Data Analysis ◽  
Nearest Neighbor ◽  
Nearest Neighbors ◽  
Surrogate Data ◽  
Original Method ◽  
Random Time ◽  
Embedding Dimension ◽  
False Nearest Neighbors ◽  
Coordinate Embedding

False nearest neighbors (FNN) is one of the essential methods used in estimating the minimally sufficient embedding dimension in delay-coordinate embedding of deterministic time series. Its use for stochastic and noisy deterministic time series is problematic and erroneously indicates a finite embedding dimension. Various modifications to the original method have been proposed to mitigate this problem, but those are still not reliable for noisy time series. Here, nearest-neighbor statistics are studied for uncorrelated random time series and contrasted with the corresponding deterministic and stochastic statistics. New composite FNN metrics are constructed and their performance is evaluated for deterministic, correlates stochastic, and white random time series. In addition, noise-contaminated deterministic data analysis shows that these composite FNN metrics are robust to noise. All FNN results are also contrasted with surrogate data analysis to show their robustness. The new metrics clearly identify random time series as not having a finite embedding dimension and provide information about the deterministic part of correlated stochastic processes. These metrics can also be used to differentiate between chaotic and random time series.

False-nearest-neighbors algorithm and noise-corrupted time series

1997 ◽  
Vol 55 (5) ◽  
pp. 6162-6170 ◽  
Author(s):  
Carl Rhodes ◽  
Manfred Morari
Keyword(s):  
Time Series ◽  
Nearest Neighbors ◽  
False Nearest Neighbors

Capacity Analysis for Correlated Multi-Hop MIMO Channels under Colored Noise

2015 ◽  
Vol 1 ◽  
pp. 41
Author(s):  
Nguyen N. Tran ◽  
Ha X. Nguyen
Keyword(s):  
Computational Complexity ◽  
Mutual Information ◽  
Closed Form Solution ◽  
Optimal Solution ◽  
Form Solution ◽  
Maximization Problem ◽  
Capacity Analysis ◽  
Mimo Channels ◽  
Average Mutual Information ◽  
Channel Output

A capacity analysis for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels is presented in this paper. The channel at each hop is spatially correlated, the source symbols are mutually correlated, and the additive Gaussian noises are colored. First, by invoking Karush-Kuhn-Tucker condition for the optimality of convex programming, we derive the optimal source symbol covariance for the maximum mutual information between the channel input and the channel output when having the full knowledge of channel at the transmitter. Secondly, we formulate the average mutual information maximization problem when having only the channel statistics at the transmitter. Since this problem is almost impossible to be solved analytically, the numerical interior-point-method is employed to obtain the optimal solution. Furthermore, to reduce the computational complexity, an asymptotic closed-form solution is derived by maximizing an upper bound of the objective function. Simulation results show that the average mutual information obtained by the asymptotic design is very closed to that obtained by the optimal design, while saving a huge computational complexity.

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