strong {softclassval}

And (conjunction) operators

Description

And operators for the soft performance calculation. The predefined operators are:

Name	Definition	dev?	postproc?	hard?	Explanation
gdl	pmin (r, p)	FALSE		FALSE	the Gödel-operator (weak conjunction)
luk	pmax (r + p - 1, 0)	FALSE		FALSE	Łukasiewicz-operator (strong conjunction)
prd	r * p	FALSE		FALSE	product operator
and	r * p	FALSE		TRUE	Boolean conjunction: accepts only 0 or 1, otherwise yields NA
wMAE	r * abs (r - p)	TRUE		FALSE	for weighted mean absolute error
wRMAE	r * abs (r - p)	TRUE	sqrt	FALSE	for weighted root mean absolute error (bound for RMSE)
##' wMSE	r * (r - p)^2	TRUE		FALSE	for weighted mean squared error
wRMSE	r * (r - p)^2	TRUE	sqrt	FALSE	for root weighted mean squared error

Usage

strong(r, p)

luk(r, p)

weak(r, p)

gdl(r, p)

prd(r, p)

and(r, p)

wMAE(r, p)

wRMAE(r, p)

wMSE(r, p)

wRMSE(r, p)

Arguments

r

reference vector, matrix, or array with numeric values in [0, 1], for and in {0, 1}

p

prediction vector, matrix, or array with numeric values in [0, 1], for and in {0, 1}

Value

numeric of the same size as p

Author(s)

Claudia Beleites

References

see the literature in citation ("softclassval")

See Also

Performance measures: sens

Examples

ops <- c ("luk", "gdl", "prd", "and", "wMAE", "wRMAE", "wMSE", "wRMSE")

## make a nice table


lastline <- function (f){
  body <- body (get (f))    ## function body
  body <- deparse (body)
  body [length (body) - 1]  ## last line is closing brace
}

data.frame (source = sapply (ops, lastline),
            dev = sapply (ops, function (f) dev (get (f))),
            hard = sapply (ops, function (f) hard (get (f))),
            postproc = I (lapply (ops, function (f) postproc (get (f))))
            )

x <- softclassval:::v
x

luk (0.7, 0.8)

## The behaviour of the operators
## op (x, 1)
cbind (x, sapply (c ("luk", "gdl", "prd", "wMAE", "wRMAE", "wMSE", "wRMSE"),
                  function (op, x) get (op) (x, 1), x))

## op (x, 0)
cbind (x, sapply (c ("luk", "gdl", "prd", "wMAE", "wRMAE", "wMSE", "wRMSE"),
                  function (op, x) get (op) (x, 0), x))

## op (x, x)
cbind (x, sapply (c ("luk", "gdl", "prd", "wMAE", "wRMAE", "wMSE", "wRMSE"),
                  function (op, x) get (op) (x, x), x))


## Note that the deviation operators are not commutative
## (due to the weighting by reference)
zapsmall (
cbind (sapply (c ("luk", "gdl", "prd", "wMAE", "wRMAE", "wMSE", "wRMSE"),
                  function (op, x) get (op) (1, x), x)) -
cbind (sapply (c ("luk", "gdl", "prd", "wMAE", "wRMAE", "wMSE", "wRMSE"),
                  function (op, x) get (op) (x, 1), x))
)