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Last data update: 2014.03.03

R: Functional DDalpha-classifier

ddalphaf.train

R Documentation

Functional DDalpha-classifier

Description

Trains the functional DDalpha-classifier

Usage

ddalphaf.train(dataf, labels,  
                adc.args = list(instance = "avr", 
                               numFcn = -1, 
                               numDer = -1), 
                classifier.type = c("ddalpha", "maxdepth", "knnaff", "lda", "qda"), 
                cv.complete = FALSE, 
                seed = 0,
                ...)

Arguments

`dataf`	list containing lists (functions) of two vectors of equal length, named "args" and "vals": arguments sorted in ascending order and corresponding them values respectively
`labels`	list of output labels of the functinal observations
`adc.args`	Represents a function sample as a multidimensional (dimension=`"numFcn"+"numDer"`) one averaging (`instance = "avr"`) or evaluating (`instance = "val"`) for that each function and it derivative on `"numFcn"` (resp. `"numDer"`) equal nonoverlapping covering intervals First two named `"args"` and `"vals"` are arguments sorted in ascending order and having same bounds for all functions and corresponding them values respectively instance type of discretizing the functions: "avr" - by avaraging over intervals of the same length "val" - by taking values on equally-spaced grid numFcn number of function intervals numDer number of first-derivative intervals Set `numFcn` and `numDer` to -1 to apply cross-validation.
`classifier.type`	the classifier which is used on the transformed space. The default value is 'ddalpha'.
`cv.complete`	T: apply complete cross-validation F: restrict cross-validation by Vapnik-Chervonenkis bound
`seed`	the random seed. The dafault value `seed=0` makes no changes.
`...`	additional parameters, passed to the classifier, selected with parameter `classifier.type`.

Details

The functional DDalpha-classifier is fast nonparametric procedure for classifying functional data. It consists of a two-step transformation of the original data plus a classifier operating on a low-dimensional hypercube. The functional data are first mapped into a finite-dimensional location-slope space and then transformed by a multivariate depth function into the DD-plot, which is a subset of the unit hypercube. This transformation yields a new notion of depth for functional data. Three alternative depth functions are employed for this, as well as two rules for the final classification. The resulting classifier is cross-validated over a small range of parameters only, which is restricted by a Vapnik-Cervonenkis bound. The entire methodology does not involve smoothing techniques, is completely nonparametric and allows to achieve Bayes optimality under standard distributional settings. It is robust and efficiently computable.

Value

Trained functional DDalpha-classifier

References

Mozharovskyi, P. (2015), Contributions to Depth-based Classification and Computation of the Tukey Depth, Verlag Dr. Kovac (Hamburg).

Mosler, K., & Mozharovskyi, P. (2014). Fast DD-classification of functional data. arXiv preprint arXiv:1403.1158.

Examples


## Not run: 
## load the Growth dataset
dataf = dataf.growth()

learn = c(head(dataf$dataf, 49), tail(dataf$dataf, 34))
labels= c(head(dataf$labels, 49), tail(dataf$labels, 34)) 
test  = tail(head(dataf$dataf, 59), 10)    # elements 50:59. 5 girls, 5 boys

c = ddalphaf.train (learn, labels, classifier.type = "ddalpha")

classified = ddalphaf.classify(test, c)

print(unlist(classified))


## End(Not run)