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Update the name of the decorrelation function
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‎README.md‎

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# Heuristic Multidimensional Correlation Analysis: Goal-Driven Spatial Transformation Matrices
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# Iterative Decorrelation Analysis (IDeA) and the Unit of Measurement Preserving Spatial Transformation Matrices (UPSTM)
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![](images/paste-706F2F78.png)
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Fig. 1. The weights ($w_j^i$) of the GDSTM matrix (**W**) are estimated by the HMCA algorithm.
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Fig. 1. The weights ($w_j^i$) of the UPSTM matrix (**W**) are estimated by the IDeA algorithm.
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\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
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Many multidimensional/multimodality data sets contain continuous features that are co-linear, correlated or have some association between them. The goal of spatial transformations is to find a set of [latent variables](https://en.wikipedia.org/wiki/Latent_and_observable_variables) with minimum data correlation; hence downstream data analysis be simplified. Common data transformation matrices include statistically driven approaches such as [principal component analysis](https://en.wikipedia.org/wiki/Principal_component_analysis) (PCA), [explanatory factor analysis](https://en.wikipedia.org/wiki/Exploratory_factor_analysis) (EFA), and [canonical-correlation analysis](https://en.wikipedia.org/wiki/Canonical_correlation) (CCA). An heuristic alternative for these two statistical approaches is the heuristic-multidimensional correlation analysis (HMCA). The main advantage of the heuristic approach is that it is driven by specific requirements for the output generated. The specific requirements are:
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Many multidimensional/multimodality data sets contain continuous features that are co-linear, correlated or have some association between them. The goal of spatial transformations is to find a set of [latent variables](https://en.wikipedia.org/wiki/Latent_and_observable_variables) with minimum data correlation; hence downstream data analysis be simplified. Common data transformation matrices include statistically driven approaches such as [principal component analysis](https://en.wikipedia.org/wiki/Principal_component_analysis) (PCA), [explanatory factor analysis](https://en.wikipedia.org/wiki/Exploratory_factor_analysis) (EFA), and [canonical-correlation analysis](https://en.wikipedia.org/wiki/Canonical_correlation) (CCA). An algoritm alternative for these two statistical approaches is the Iterative Decorrelation Analysis (HMCA). The main advantage of the iterative approach is that it is driven by specific output requirements. The specific requirements are:
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1. All output variables $Q=(q_1,...q_n)$ have a parent input variable $X=(x_1,...x_n)$ (See Fig 1.)
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@@ -48,7 +48,7 @@ library("FRESA.CAD")
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data('iris')
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## HMCA Decorrelation at 0.25 threshold, pearson and fast estimation
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irisDecor <- GDSTMDecorrelation(iris,thr=0.25)
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irisDecor <- IDeA(iris,thr=0.25)
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### Print the latent variables
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print(getLatentCoefficients(irisDecor))
@@ -77,9 +77,9 @@ This repository show some examples of the **FRESA.CAD::GDSTMDecorrelation(), FRE
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- **irisexample.R** showcase the effect of the HMCA algorithm on the iris data set.
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- Here an example of the output
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- ![](images/paste-8B4C5746.png)
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- ![](images/paste-AB4FBF9C.png)
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- ![](images/paste-AF234B49.png)
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- ![](images/paste-913BE963.png)
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- **ParkisonAnalysis_TrainTest.Rmd** is a demo shows the use of GDSTM and BSWiMS to gain insight of the features associated with a relevant outcome. Highlight process and functions that will aid authors to discern and statistically describe the relevant features associated with an specific outcome.
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‎RMD/COVID_19_TrainTest.Rmd‎

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```
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# Effect of GDSTM-Based Decorrelation on Feature Discovery
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# Effect of UPSTM-Based Decorrelation on Feature Discovery
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Here I showcase of to use BSWiMS feature selection/modeling function coupled with Goal Driven Sparse Transformation Matrix (GDSTM) as a pre-processing step to decorrelate highly correlated features. The aim(s) are:
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Here I showcase of to use BSWiMS feature selection/modeling function coupled with Goal Driven Sparse Transformation Matrix (UPSTM) as a pre-processing step to decorrelate highly correlated features. The aim(s) are:
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1. To improve model performance by uncovering the hidden information between correlated features.
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2. To simplify the interpretation of the machine learning models.
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This demo will use:
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- *FRESA.CAD::GDSTMDecorrelation()*. For Decorrelation of Multidimensional data sets
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- *FRESA.CAD::IDeA()*. For Decorrelation of Multidimensional data sets
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- *FRESA.CAD::getDerivedCoefficients()*. For the extraction of the model of the newly discovered of decorrelated features.
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#### Decorrelation: Training and Testing Sets Creation
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I compute a decorrelated version of the training and testing sets using the *GDSTMDecorrelation()* function of FRESA.CAD. The first decorrelation will be driven by features associated with the outcome. The second decorrelation will find the GDSTM without the outcome restriction.
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I compute a decorrelated version of the training and testing sets using the *IDeA()* function of FRESA.CAD. The first decorrelation will be driven by features associated with the outcome. The second decorrelation will find the UPSTM without the outcome restriction.
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```{r results = "asis", warning = FALSE, dpi=600, fig.height= 6.0, fig.width= 8.0}
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## The GDSTM transformation driven by the Outcome
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deTrain <- GDSTMDecorrelation(trainSet,Outcome="PCR_result",thr=0.8,verbose = TRUE)
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## The UPSTM transformation driven by the Outcome
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deTrain <- IDeA(trainSet,Outcome="PCR_result",thr=0.8,verbose = TRUE)
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deTest <- predictDecorrelate(deTrain,testSet)
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## The GDSTM transformation without outcome
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deTrainU <- GDSTMDecorrelation(trainSet,thr=0.8,verbose = TRUE)
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## The UPSTM transformation without outcome
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deTrainU <- IDeA(trainSet,thr=0.8,verbose = TRUE)
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deTestU <- predictDecorrelate(deTrainU,testSet)
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```
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scale = "none",
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mar = c(10,10),
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col=rev(heat.colors(5)),
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main = "Test Set Correlation after GDSTM",
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main = "Test Set Correlation after UPSTM",
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cexRow = 0.35,
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cexCol = 0.35,
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key.title=NA,
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DECOR.control=list(Outcome="PCR_result",thr=0.8)
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)
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bpDecor <- predictionStats_binary(cvBSWiMSDeCor$medianTest,"BSWiMS Outcome-Driven GDSTM",cex=0.60)
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bpDecor <- predictionStats_binary(cvBSWiMSDeCor$medianTest,"BSWiMS Outcome-Driven UPSTM",cex=0.60)
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pander::pander(bpDecor$CM.analysis$tab)
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pander::pander(bpDecor$accc)
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pander::pander(bpDecor$aucs)
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DECOR.control=list(thr=0.8)
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)
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bpDecorU <- predictionStats_binary(cvBSWiMSDeCorU$medianTest,"BSWiMS Data Driven GDSTM",cex=0.60)
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bpDecorU <- predictionStats_binary(cvBSWiMSDeCorU$medianTest,"BSWiMS Data Driven UPSTM",cex=0.60)
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pander::pander(bpDecorU$CM.analysis$tab)
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pander::pander(bpDecorU$accc)
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pander::pander(bpDecorU$aucs)

‎RMD/FDeA_ML_testing_ARCENE.Rmd‎

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---
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title: 'Filtered Fit: FDeA and the GDSTM'
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title: 'Filtered Fit: FDeA and the UPSTM'
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output:
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html_document:
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df_print: paged
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---
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## Filtered ML fit and the GDSTM with FRESA.CAD
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## Filtered ML fit and the UPSTM with FRESA.CAD
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Here we make use of the **FRESA.CAD::filteredfit()** function to train ML models with and without GDSTM on the ARCENE data set.
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Here we make use of the **FRESA.CAD::filteredfit()** function to train ML models with and without UPSTM on the ARCENE data set.
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> Isabelle Guyon, Steve R. Gunn, Asa Ben-Hur, Gideon Dror, 2004. Result analysis of the NIPS 2003 feature selection challenge. In: NIPS. [$$Web Link$$](http://books.nips.cc/papers/files/nips17/NIPS2004_0194.pdf). *from: <https://archive.ics.uci.edu/ml/datasets/Arcene>*
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>
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psDecor <- predictionStats_binary(cbind(datasetframe_test$Labels,
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predict(mLASSODecor,datasetframe_test)),
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"LASSO after GDSTM",cex=0.75)
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"LASSO after UPSTM",cex=0.75)
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pander::pander(psDecor$aucs)
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‎RMD/FDeA_ML_testing_DARWIN.Rmd‎

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---
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title: "FDeA and the GDSTM: DARWIN Data Set"
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title: "FDeA and the UPSTM: DARWIN Data Set"
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output:
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html_document:
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df_print: paged
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```
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# Effect of GDSTM-Based Decorrelation on Feature Discovery: The DARWIN Evaluation
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# Effect of UPSTM-Based Decorrelation on Feature Discovery: The DARWIN Evaluation
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Here I showcase of to use BSWiMS feature selection/modeling function coupled with Goal Driven Sparse Transformation Matrix (GDSTM) as a pre-processing step to decorrelate highly correlated features. The aim(s) are:
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Here I showcase of to use BSWiMS feature selection/modeling function coupled with Goal Driven Sparse Transformation Matrix (UPSTM) as a pre-processing step to decorrelate highly correlated features. The aim(s) are:
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1. To improve model performance by uncovering the hidden information between correlated features.
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2. To simplify the interpretation of the machine learning models.
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This demo will use:
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- FRESA.CAD::GDSTMDecorrelation(). For Decorrelation of Multidimensional data sets
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- FRESA.CAD::IDeA(). For Decorrelation of Multidimensional data sets
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- FRESA.CAD::getDerivedCoefficients(). For the extraction of the model of the newly discovered of decorrelated features.
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#### Decorrelation: Training and Testing Sets Creation
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I compute a decorrelated version of the training and testing sets using the *GDSTMDecorrelation()* function of FRESA.CAD. The first decorrelation will be driven by features associated with the outcome. The second decorrelation will find the GDSTM without the outcome restriction.
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I compute a decorrelated version of the training and testing sets using the *IDeA()* function of FRESA.CAD. The first decorrelation will be driven by features associated with the outcome. The second decorrelation will find the UPSTM without the outcome restriction.
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```{r results = "asis", warning = FALSE, dpi=600, fig.height= 6.0, fig.width= 8.0}
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## The GDSTM transformation driven by the Outcome
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deTrain <- GDSTMDecorrelation(trainSet,Outcome="class",thr=0.8,verbose = TRUE,skipRelaxed=FALSE)
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## The UPSTM transformation driven by the Outcome
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deTrain <- IDeA(trainSet,Outcome="class",thr=0.8,verbose = TRUE,skipRelaxed=FALSE)
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deTest <- predictDecorrelate(deTrain,testSet)
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## The GDSTM transformation without outcome
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deTrainU <- GDSTMDecorrelation(trainSet,thr=0.8,verbose = TRUE,skipRelaxed=FALSE)
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## The UPSTM transformation without outcome
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deTrainU <- IDeA(trainSet,thr=0.8,verbose = TRUE,skipRelaxed=FALSE)
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deTestU <- predictDecorrelate(deTrainU,testSet)
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```
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scale = "none",
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mar = c(10,10),
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col=rev(heat.colors(5)),
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main = "Test Set Correlation after GDSTM",
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main = "Test Set Correlation after UPSTM",
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cexRow = 0.45,
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cexCol = 0.45,
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key.title=NA,
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DECOR.control=list(Outcome="class",thr=0.8,skipRelaxed=FALSE)
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)
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bpDecor <- predictionStats_binary(cvBSWiMSDeCor$medianTest,"Outcome-Driven GDSTM",cex=0.60)
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bpDecor <- predictionStats_binary(cvBSWiMSDeCor$medianTest,"Outcome-Driven UPSTM",cex=0.60)
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pander::pander(bpDecor$CM.analysis$tab)
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pander::pander(bpDecor$accc)
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pander::pander(bpDecor$aucs)

‎RMD/FDeA_ML_testing_sonar.Rmd‎

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---
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title: "FDeA and the GDSTM: Sonar Tests"
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title: "FDeA and the UPSTM: Sonar Tests"
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output:
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html_document:
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df_print: paged
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editor_options:
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chunk_output_type: console
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---
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## Filtered ML fit and the GDSTM with FRESA.CAD
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## Filtered ML fit and the UPSTM with FRESA.CAD
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Here we make use of the **FRESA.CAD::filteredfit()** function to train ML models with and without GDSTM.
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Here we make use of the **FRESA.CAD::filteredfit()** function to train ML models with and without UPSTM.
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Naive-Bayes (NB) and LASSO models are used in this demo.
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AllRocAUC <- rbind(AllRocAUC,psPCA$aucs)
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psDecor <- predictionStats_binary(cbind(classoutcomes,prDecor),
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"NB GDSTM",cex=0.75)
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"NB UPSTM",cex=0.75)
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pander::pander(psDecor$aucs)
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AllRocAUC <- rbind(AllRocAUC,psDecor$aucs);
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psDecor2 <- predictionStats_binary(cbind(classoutcomes,prDecor2),
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"NB GDSTM Spearman",cex=0.75)
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"NB UPSTM Spearman",cex=0.75)
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pander::pander(psDecor2$aucs)
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AllRocAUC <- rbind(AllRocAUC,psDecor2$aucs);
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psDecor <- predictionStats_binary(cbind(classoutcomes,
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predict(mLASSODecor,datasetframe_test)),
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"LASSO GDSTM",cex=0.75)
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"LASSO UPSTM",cex=0.75)
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pander::pander(psDecor$aucs)
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AllRocAUC <- rbind(AllRocAUC,psDecor$aucs);
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psDecor2 <- predictionStats_binary(cbind(classoutcomes,
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predict(mLASSODecor2,datasetframe_test)),
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"LASSO GDSTM Spearman",cex=0.75)
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"LASSO UPSTM Spearman",cex=0.75)
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pander::pander(psDecor2$aucs)
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AllRocAUC <- rbind(AllRocAUC,psDecor2$aucs);
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```{r results = "asis", warning = FALSE, dpi=600, fig.height= 6.0, fig.width= 8.0}
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rownames(AllRocAUC) <- c("NB:Raw","NB:PCA","NB:GDSTM_P","NB:GDSTM_S",
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"LASSO:Raw","LASSO:PCA","LASSO:GDSTM_P","LASSO:GDSTM_S")
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rownames(AllRocAUC) <- c("NB:Raw","NB:PCA","NB:UPSTM_P","NB:UPSTM_S",
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"LASSO:Raw","LASSO:PCA","LASSO:UPSTM_P","LASSO:UPSTM_S")
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pander::pander(AllRocAUC)
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bpROCAUC <- barPlotCiError(as.matrix(AllRocAUC),
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metricname = "ROCAUC",
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```
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## Visualization of GDSTM
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## Visualization of UPSTM
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The GDSTM is stored in the filteredFit() object. Hence, we can analyze and display the matrix.
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The UPSTM is stored in the filteredFit() object. Hence, we can analyze and display the matrix.
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```{r results = "asis", warning = FALSE, dpi=600, fig.height= 6.0, fig.width= 8.0}
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gplots::heatmap.2(mNBDecor$GDSTM,
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gplots::heatmap.2(mNBDecor$UPSTM,
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trace = "none",
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mar = c(10,10),
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col=rev(heat.colors(7)),
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main = paste("GDSTM Matrix (Pearson, LM):",studyName),
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main = paste("UPSTM Matrix (Pearson, LM):",studyName),
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cexRow = 0.7,
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cexCol = 0.7,
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key.title=NA,
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key.xlab="beta",
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xlab="GDSTM Feature", ylab="Input Feature")
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xlab="UPSTM Feature", ylab="Input Feature")
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gplots::heatmap.2(mNBDecor2$GDSTM,
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gplots::heatmap.2(mNBDecor2$UPSTM,
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trace = "none",
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mar = c(10,10),
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col=rev(heat.colors(7)),
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main = paste("GDSTM Matrix (Spearman, RLM):",studyName),
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main = paste("UPSTM Matrix (Spearman, RLM):",studyName),
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cexRow = 0.7,
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cexCol = 0.7,
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key.title=NA,
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key.xlab="beta",
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xlab="GDSTM Feature", ylab="Input Feature")
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xlab="UPSTM Feature", ylab="Input Feature")
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```
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## Repeated Holdout Cross-Validation
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par(mfrow=c(2,2))
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bpraw <- predictionStats_binary(cvNBRaw$testPredictions,"NB RAW",cex=0.70)
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bpPCA <- predictionStats_binary(cvNBPCA$testPredictions,"NB PCA",cex=0.70)
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bpdecor <- predictionStats_binary(cvNBDecor$testPredictions,"NB GDSTM",cex=0.70)
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bpdecorC <- predictionStats_binary(cvNBDecorC$testPredictions,"NB GDSTM Outcome Driven",cex=0.70)
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bpdecor <- predictionStats_binary(cvNBDecor$testPredictions,"NB UPSTM",cex=0.70)
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bpdecorC <- predictionStats_binary(cvNBDecorC$testPredictions,"NB UPSTM Outcome Driven",cex=0.70)
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pander::pander(bpraw$aucs)
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pander::pander(bpPCA$aucs)
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AllRocAUC <- rbind(AllRocAUC,psPCA$aucs)
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psDecor <- predictionStats_binary(cbind(classoutcomes,prDecor),
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"NB GDSTM",cex=0.75)
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"NB UPSTM",cex=0.75)
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pander::pander(psDecor$aucs)
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AllRocAUC <- rbind(AllRocAUC,psDecor$aucs);
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psDecor2 <- predictionStats_binary(cbind(classoutcomes,prDecor2),
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"NB GDSTM Spearman",cex=0.75)
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"NB UPSTM Spearman",cex=0.75)
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pander::pander(psDecor2$aucs)
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AllRocAUC <- rbind(AllRocAUC,psDecor2$aucs);
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psDecorD <- predictionStats_binary(cbind(classoutcomes,prDecorD),
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"NB GDSTMD Spearman",cex=0.75)
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"NB UPSTMD Spearman",cex=0.75)
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pander::pander(psDecorD$aucs)
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AllRocAUC <- rbind(AllRocAUC,psDecorD$aucs);
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psDecor <- predictionStats_binary(cbind(classoutcomes,
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predict(mLASSODecor,datasetframe_test)),
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"LASSO GDSTM",cex=0.75)
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"LASSO UPSTM",cex=0.75)
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pander::pander(psDecor$aucs)
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AllRocAUC <- rbind(AllRocAUC,psDecor$aucs);
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psDecorD <- predictionStats_binary(cbind(classoutcomes,
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predict(mLASSODecorD,datasetframe_test)),
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"LASSO GDSTMD",cex=0.75)
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"LASSO UPSTMD",cex=0.75)
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pander::pander(psDecorD$aucs)
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AllRocAUC <- rbind(AllRocAUC,psDecorD$aucs);
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psDecor2 <- predictionStats_binary(cbind(classoutcomes,
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predict(mLASSODecor2,datasetframe_test)),
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"LASSO GDSTM Spearman",cex=0.75)
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"LASSO UPSTM Spearman",cex=0.75)
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pander::pander(psDecor2$aucs)
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AllRocAUC <- rbind(AllRocAUC,psDecor2$aucs);
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@@ -642,8 +642,8 @@ AllRocAUC <- rbind(AllRocAUC,psDecor2$aucs);
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```{r results = "asis", warning = FALSE, dpi=600, fig.height= 6.0, fig.width= 8.0}
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rownames(AllRocAUC) <- c("NB:Raw","NB:PCA","NB:GDSTM_P","NB:GDSTMD_P","NB:GDSTM_S",
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"LASSO:Raw","LASSO:PCA","LASSO:GDSTM_P","LASSO:GDSTMD_P","LASSO:GDSTM_S")
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rownames(AllRocAUC) <- c("NB:Raw","NB:PCA","NB:UPSTM_P","NB:UPSTMD_P","NB:UPSTM_S",
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"LASSO:Raw","LASSO:PCA","LASSO:UPSTM_P","LASSO:UPSTMD_P","LASSO:UPSTM_S")
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pander::pander(AllRocAUC)
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bpROCAUC <- barPlotCiError(as.matrix(AllRocAUC),
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metricname = "ROCAUC",

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