Towards the maximal number of components of a nonsingular surface of degree 5 in ℝℙ³

1996 ◽  
pp. 111-118 ◽  
Author(s):  
V. Kharlamov ◽  
I. Itenberg
Keyword(s):  
Number Of Components ◽  
Nonsingular Surface

scholarly journals Improved Predictive Ability of KPLS Regression with Memetic Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 506
Author(s):  
Jorge Daniel Mello-Román ◽  
Adolfo Hernández ◽  
Julio César Mello-Román
Keyword(s):  
Kernel Function ◽  
Linear Method ◽  
Predictive Ability ◽  
Feature Space ◽  
Memetic Algorithms ◽  
Least Squares Regression ◽  
Optimal Parameters ◽  
Number Of Components ◽  
Kernel Partial Least Squares ◽  
Dependent Variables

Kernel partial least squares regression (KPLS) is a non-linear method for predicting one or more dependent variables from a set of predictors, which transforms the original datasets into a feature space where it is possible to generate a linear model and extract orthogonal factors also called components. A difficulty in implementing KPLS regression is determining the number of components and the kernel function parameters that maximize its performance. In this work, a method is proposed to improve the predictive ability of the KPLS regression by means of memetic algorithms. A metaheuristic tuning procedure is carried out to select the number of components and the kernel function parameters that maximize the cumulative predictive squared correlation coefficient, an overall indicator of the predictive ability of KPLS. The proposed methodology led to estimate optimal parameters of the KPLS regression for the improvement of its predictive ability.

Functionals of random mappings: exact and asymptotic results

1991 ◽  
Vol 23 (3) ◽  
pp. 437-455 ◽  
Author(s):  
P. J. Donnelly ◽  
W. J. Ewens ◽  
S. Padmadisastra
Keyword(s):  
Frequency Spectrum ◽  
Exact Results ◽  
Asymptotic Results ◽  
Number Of Components ◽  
Random Mapping ◽  
Random Mappings ◽  
Simulation Results ◽  
Central Tool

A random mapping partitions the set {1, 2, ···, m} into components, where i and j are in the same component if some functional iterate of i equals some functional iterate of j. We consider various functionals of these partitions and of samples from it, including the number of components of ‘small' size and of size O(m) as m → ∞the size of the largest component, the number of components, and various symmetric functionals of the normalized component sizes. In many cases exact results, while available, are uniformative, and we consider various approximations. Numerical and simulation results are also presented. A central tool for many calculations is the ‘frequency spectrum', both exact and asymptotic.

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