# msc.lm: Morse Smale Complex Linear Regression In msr: Morse-Smale Approximation, Regression and Visualization

## Description

Piecewise linear regression on the decomposition of the domain based on the partion induced by the Morse-Smale complex. For `msc.elnet` an elastic net is fitted insetad of a simple lienar regression.

For prediction the linear model are either avergaed based on weighting the contributions from each partition for a predicting point or predicted based on the linear model corresponding to the highest partition probability. The weights for each partition are computed depending on the underlying Morse-Smale complex type (see `msc.nn`). The functions can be called with `msc.nn` without predictive capacities, then prediction of unseen data is not supported.

## Usage

 ```1 2``` ```msc.lm(ms, nfold = 10, modelSelect=FALSE, blend=FALSE, verbose=FALSE) msc.elnet(ms, nfold = 10, blend=FALSE) ```

## Arguments

 `ms` A Morse-Smale complex object, see `msc.nn`

.

 `nfold` Number of folds for crossvlaidation, used for selecting an appropriate persitence level if the underlying Morse-Smale complex objects has multiple levels. `modelSelect` Do a forward stepwise model selection for each linear model (for each parttion ther eis on linear model) `blend` Use blending for model preidtcion. FALSE results in pecewise linear model. `verbose` Print model fitting information

## Value

An object of class `c("msc.lm")` or `c("msc.elnet")`, that can be used for prediction with `predict`.

The object `c("msc.lm")` has the following components:

 `ms` The Morse-Smale complex, see `msc.nn` `lms` The linear models and crossvalidation results for each level in ms. `blend` Use blending for model prediction.

The object `c("msc.elnet")` has the following components:

 `ms` The Morse-Smale complex, see `msc.nn` `elnet` The elastic net models and crossvalidation results for each level in ms.

Samuel Gerber

## References

[1] Samuel Gerber and Kristin Potter The Morse-Smale Complex for Data Analysis, Journal of Statistical Software, 2012, vol. 50, no. 2, pp 1-22

[2] Samuel Gerber, Oliver Ruebel Peer-Timo Bremer, Valerio Pascucci, Ross Whitaker, Morse-Smale Regression, Journal of Computational and Graphical Statistics, 2012

[3] Samuel Gerber, Peer-Timo Bremer, Valerio Pascucci, Ross Whitaker, Visual Exploration of High Dimensional Scalar Functions, IEEE Transactions on Visualization and Computer Graphics, vol. 16, no. 6, pp 1271-1280, Nov.-Dec. 2010.

`msc.nn`, `predict.msc.lm`, `glmnet`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```#create Morse-Smale complex regression of fourpeaks2d data set data(fourpeaks) d <- fourpeaks() #build Morse-Smale complex ms <- msc.nn.svm(y=d[,1], x=d[, 2:3], pLevel=0.1, knn = 10) msr <- msc.lm(ms) #show slected persitence level by cross validtaion msr\$ms\$predictLevel #print mean squared crossvalidated error msr\$lms[[msr\$ms\$predictLevel]]\$cv #predict fp <- predict(msr, d[, 2:3]) #fit an elastic model insteaed msr <- msc.elnet(ms) #prediction for ealstic model fp <- predict(msr, d[, 2:3]) ```