features {features}

Estimate features of a discretely-sampled functional data.

Description

Discretely-sampled function is first smoothed. Features of the smoothed function are then extracted. Some of the key features include mean value, first and second derivatives, critical points (i.e. local maxima and minima), curvature of function at critical points, wiggliness of the function, noise in data, and outliers in data.

Usage

features(x, y, smoother=c("glkerns", "smooth.spline"), fits.return=TRUE, 
	control = list(), ...)

Arguments

x

a vector of independent variable (e.g. time) at which the function is sampled.

y

a vector of response values to be smoothed

smoother

a character string specifying the name of the smoothing algorithm; currently only 2 smoothers are implemented: smoothing spline and a kernel smoother with a global plug-in bandwidth

fits.return

a logical variable specifying whether or not to return the smoothed function and its first 2 derivatives. Default is TRUE. It must be TRUE for plotting the results.

control

A list of control parameters. See *Details* for more information.

...

Additional arguments to be passed to the smoothers. An important optional parameter is the bandwidth that controls the smoothness of the fit. See the help for ‘glkerns’ for mode details.

Details

Argument control is a list specifing any changes to default values of control parameters. Note that the names of these must be specified completely. Partial matching will not work.

Default values of control are: ctrl <- list(npts=100, c.outlier=3, decim.out=2)

npts: an integer. Number of points to use in estimating smoothed function and for computing features

c.outlier: a constant denoting number of standard deviations away from smooth fit for determining whether a point is an outlier. Default is 3.

decim.out: number of decimals to display in the features output.

Value

A list with a number of extracted features of the underlying smooth function:

f

: a numeric vector containing 10 basic features of the function: mean, min, max, std.dev, noise, signa-to-noise ratio, minimum and maximum of first derivative, wiggliness, and number of critical points

cpts

: Locations of the critical points (e.g. points where the first derivative is zero)

curvature

: Value of second derivative at the critical points

outliers

: Locations of outlying data points

fits

an attribute of the object returned by features when fits.return=TRUE. A list with 4 vectors: abscissae, smoothed function, first derivative, and second derivative

See Also

fget, plot.features, plot, glkerns, smooth.spline

Examples

# Estimating the smooth and the derivatives of a noisy and discretely sampled function. 
n <- 200
x <- sort(runif(n))
y <- exp(-0.2 * sin(2*pi*x)) + rnorm(n, sd=0.05)

ans <- features(x, y)

fget(ans)