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Redundancy

R(X_1,...X_n)=sum_(i=1)^nH(X_i)-H(X_1,...,X_n),

where H(x_i) is the entropy and H(X_1,...,X_n) is the joint entropy. Linear redundancy is defined as

L(X_1,...,X_n)=-1/2sum_(i=1)^nlog_2sigma_i,

where sigma_i are eigenvalues of the correlation matrix.

See also

Predictability

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References

Fraser, A. M. "Reconstructing Attractors from Scalar Time Series: A Comparison of Singular System and Redundancy Criteria." Phys. D 34, 391-404, 1989.Paluš, M. "Identifying and Quantifying Chaos by Using Information-Theoretic Functionals." In Time Series Prediction: Forecasting the Future and Understanding the Past (Ed. A. S. Weigend and N. A. Gerschenfeld). Proc. NATO Advanced Research Workshop on Comparative Time Series Analysis held in Sante Fe, NM, May 14-17, 1992. Reading, MA: Addison-Wesley, pp. 387-413, 1994.

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Redundancy

Cite this as:

Weisstein, Eric W. "Redundancy." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Redundancy.html

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