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The proposed methodology allows one to automatically perform three tasks: the identification of single batches within the entire data-sequence of the historical dataset, the identification of distinct operating phases within each batch, and the characterization of a batch with respect to an assigned multivariate set of operating characteristics.
The S-estimator indirectly measures the synchronization-induced contraction of the embedding dimension by determining the dispersion (entropy) of the eigenvalues of the correlation matrix of a multivariate set of measurements.
The S estimator indirectly measures the synchronization-induced contraction of the embedding dimension by measuring the dispersion (entropy) of the eigenvalues of the correlation matrix of a multivariate set of measurements.
A multivariate set of predictors comprised of epidemiological, diabetes, and depression characteristics were identified.
Multivariate mixed models enabled us to estimate the genetic covariance between expression traits in a variance-component form that has a standard interpretation for any pair in a multivariate set of quantitative traits and has well-known statistical properties (Lynch and Walsh 1998).
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Towards this goal, we selected the best multivariate sets of candidate genes for prognosis, by means of exhaustive feature selection (all possible combinations) of single, pairs and triplets of genes out of the pre-filtered set of 1981 genes, using Linear Discrimination Analysis as the classification rule, and bolstered resubstitution as the error estimator (see the Methods section).
GC has some useful properties including a decomposition of causal influence by frequency [ 15 ] and formulation in an 'ensemble' form, allowing evaluation of GC between multivariate sets of responses [ 22].
The innovation and the main contribution of this paper consists of building a 2-dimensional equispaced and convex Pareto Frontier for rotated factor scores representing the original multivariate set, reducing the number of objective functions without inverting the correlation among the original responses.
Finally, a critical discussion, giving some practical advices and pointing out the most common issues involved in multivariate set-up of CE methods, is provided.
In an earlier paper the author has defined joint capacity and joint containment functionals which are multivariate set functions describing the joint distribution of random sets.
Unfortunately, in this multivariate setting, the verification of the above assumptions is often neglected.
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