Variable Selection and Peaksigmoid: Difference between pages

Revision as of 11:37, 4 August 2016

Purpose

Outputs a sigmoid function.

Synopsis

[y,y1,y2] = peaksigmoid(x,ax)

Inputs

x = 3 element vector where

x(1) = coefficient
x(2) = offset
x(3) = decay constant

Outputs

${\sqrt {1-e^{2}}}$

$f\left({{a}_{i}},\mathbf {x} \right)={{x}_{1}}\left[{{x}_{4}}{{\operatorname {e} }^{\frac {-4\ln \left(2\right){{\left({{a}_{i}}-{{x}_{2}}\right)}^{2}}}{x_{3}^{2}}}}+\left(1-{{x}_{4}}\right)\left[{\frac {x_{3}^{2}}{{{\left({{a}_{i}}-{{x}_{2}}\right)}^{2}}+x_{3}^{2}}}\right]\right]$

$f\left({{a}_{i}},\mathbf {x} \right)={{x}_{1}}\left[{{x}_{4}}{{\operatorname {e} }^{\frac {-4\ln \left(2\right){{\left({{a}_{i}}-{{x}_{2}}\right)}^{2}}}{x_{3}^{2}}}}+\left(1-{{x}_{4}}\right)\left[{\frac {1-x_{3}^{2}}{{{\left({1}+{{x}_{2}}\right)}^{2}}+x_{3}^{2}}}\right]\right]$

Failed to parse (syntax error): {\displaystyle f\left( {{a}_{i}},\mathbf{x} \right)={{x}_{1}}\left[ {}+\left( 1-{{x}_{4}} \right)\left[ \frac{1-x_{3}^{2}}{{{\left( \right)}+x_{3}^{2}} \right] \right]}

y(1) =

y(2) = ${\operatorname {d} \!y \over \operatorname {d} \!{x}_{i}}$

y(3) = ${\operatorname {d^{2}} \!y \over \operatorname {d} \!{{x}_{i}}^{2}}$

@@ Line 1: / Line 1: @@
-:[[calibsel]] - Statistical procedure for variable selection.
+===Purpose===
-:[[fullsearch]] - Exhaustive Search Algorithm for small problems.
+Outputs a sigmoid function.
-:[[gaselctr]] - Genetic algorithm for variable selection with PLS.
-:[[genalg]] - Genetic Algorithm for Variable Selection. See also [[Genetic Algorithms for Variable Selection]].
-:[[genalgplot]] - Plot GA results using selected variable plot, color-coded by RMSECV.
-:[[ipls]] - Interval PLS variable selection. [[Interval PLS (IPLS) for Variable Selection]].
-:[[rpls]] - Recursive PLS (and PCR) variable selection.
-:[[sratio]] - Calculates selectivity ratio for a given regression model.
-:[[selectvars]] - Selects variables that are predictive.
-:[[vip]] - Calculate Variable Importance in Projection from regression model.
-(Sub topic of [[Categorical_Index|Categorical_Index]])
+===Synopsis===
+:[y,y1,y2] = peaksigmoid(x,ax)
+===Inputs===
+* '''x''' =  3 element vector where
+:* x(1) = coefficient
+:* x(2) = offset
+:* x(3) = decay constant
+===Outputs===
+<math>\sqrt{1-e^2}</math>
+<math>f\left( {{a}_{i}},\mathbf{x} \right)={{x}_{1}}\left[ {{x}_{4}}{{\operatorname{e}}^{\frac{-4\ln \left( 2 \right){{\left( {{a}_{i}}-{{x}_{2}} \right)}^{2}}}{x_{3}^{2}}}}+\left( 1-{{x}_{4}} \right)\left[ \frac{x_{3}^{2}}{{{\left( {{a}_{i}}-{{x}_{2}} \right)}^{2}}+x_{3}^{2}} \right] \right]</math>
+<math>f\left( {{a}_{i}},\mathbf{x} \right)={{x}_{1}}\left[ {{x}_{4}}{{\operatorname{e}}^{\frac{-4\ln \left( 2 \right){{\left( {{a}_{i}}-{{x}_{2}} \right)}^{2}}}{x_{3}^{2}}}}+\left( 1-{{x}_{4}} \right)\left[ \frac{1-x_{3}^{2}}{{{\left( {1}+{{x}_{2}} \right)}^{2}}+x_{3}^{2}} \right] \right]</math>
+<math>f\left( {{a}_{i}},\mathbf{x} \right)={{x}_{1}}\left[ {}+\left( 1-{{x}_{4}} \right)\left[ \frac{1-x_{3}^{2}}{{{\left( \right)}+x_{3}^{2}} \right] \right]</math>
+* '''y(1) ''' =
+* '''y(2)  '''  = <math>{\operatorname{d}\!y\over\operatorname{d}\!{x}_{i}}</math>
+* ''' y(3)  '''  = <math>{\operatorname{d^2}\!y\over\operatorname{d}\!{{x}_{i}}^{2}}</math>