Morse Smale Complex Linear Regression

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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

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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.

Author(s)

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.

See Also

msc.nn, predict.msc.lm, glmnet

Examples

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#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])