Modeling Function Overview and Peaksigmoid: Difference between pages

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'''High-Level Modeling Functions'''
===Purpose===
The following output a model structure (or similar) and are generally considered "high-level" modeling functions designed for relatively simple use by less-experienced users as well as expert users.
Outputs a sigmoid function.
:[[analysis]] - Graphical user interface for data analysis.
:[[caltransfer]] - Create or apply calibration and instrument transfer models.
:[[cluster]] - KNN and K-means cluster analysis with dendrograms.
:[[cls]] - Classical Least Squares regression for multivariate Y.
:[[corrspec]] - Resolves correlation spectroscopy maps.
:[[frpcr]] - Full-ratio PCR calibration and prediction.
:[[knn]] - K-nearest neighbor classifier.
:[[mcr]] - Multivariate curve resolution with constraints.
:[[mlr]] - Multiple Linear Regression for multivariate Y.
:[[modelselector]] - Create or apply a model selector model.
:[[mpca]] - Multi-way (unfold) principal components analysis.
:[[npls]] - Multilinear-PLS (N-PLS) for true multi-way regression.
:[[parafac]] - Parallel factor analysis for n-way arrays.
:[[parafac2]] - Parallel factor analysis for unevenly sized n-way arrays.
:[[pca]] - Principal components analysis.
:[[pcr]] - Principal components regression for multivariate Y.
:[[pls]] - Partial least squares regression for multivariate Y.
:[[plsda]] - Partial least squares discriminant analysis.
:[[purity]] - Self-modeling mixture analysis method based on purity of variables or spectra.
:[[simca]] - Soft Independent Method of Class Analogy.
:[[tld]] - Trilinear decomposition.
:[[tucker]] - Analysis for n-way arrays.


'''Medium-Level Modeling Functions'''
 
The following provide functionality not generally available through another higher-level function and may be of use for certain analysis methods but also require more knowledge of Matlab and the methods involved.
===Synopsis===
   
 
:[[gram]] - Generalized rank annihilation method.
:[y,y1,y2] = peaksigmoid(x,ax)
:[[mlpca]] - Maximum likelihood principal components analysis.
 
:[[coda_dw]] - Calculates values for the Durbin_Watson criterion of columns of data set.
 
:[[comparelcms_sim_interactive]] - Interactive interface for COMPARELCMS.
===Inputs===
:[[cr]] - Continuum Regression for multivariate y.
 
:[[evolvfa]] - Evolving factor analysis (forward and reverse).
* '''x''' = 3 element vector where
:[[ewfa]] - Evolving window factor analysis.
:* x(1) = coefficient
:[[glsw]] - Generalized least-squares weighting/preprocessing.
:* x(2) = offset
:[[gram]] - Generalized rank annihilation method.
:* x(3) = decay constant
:[[lwrpred]] - Predictions based on locally weighted regression models.
 
:[[mlpca]] - Maximum likelihood principal components analysis.
===Outputs===
:[[polypls]] - PLS regression with polynomial inner-relation.
 
:[[ridge]] - Ridge regression by Hoerl-Kennard-Baldwin.
 
:[[wtfa]] - Window target factor analysis.
 
   
 
(Sub topic of [[Categorical_Index|Categorical_Index]])
<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>

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



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) =
  • y(3) =