UtilLesionWeightsMatrix: Determine lesion weights distribution 2D matrix

In RJafroc: Artificial Intelligence Systems and Observer Performance

Determine lesion weights distribution 2D matrix

Description

Determine the lesion weights distribution 2D matrix of a dataset or manually specify the lesion weights distribution 2D matrix.

Usage

UtilLesionWeightsMatrixDataset(dataset, relWeights = 0)

UtilLesionWeightsMatrixLesDistr(lesDistr, relWeights = 0)

Arguments

dataset	A dataset object.
relWeights	The relative weights of the lesions: a unit sum vector of length equal to the maximum number of lesions per dis. case. For example, c(0.2, 0.4, 0.1, 0.3) means that on cases with one lesion the weight of the lesion is unity, on cases with two lesions the ratio of the weight of the first lesion to that of the second lesion is 0.2:0.4, i.e., lesion 2 is twice as important as lesion 1. On cases with 4 lesions the weights are in the ratio 0.2:0.4:0.1:0.3. The default is zero, in which case equal lesion weights are assumed.
lesDistr	A unit sum vector of length equal to the maximum number of lesions per diseased case, specifying the relative frequency of lesions per dis. case in the dataset. For example, c(0.8, 0.15, 0.05) specifies a dataset in which 80 percent of the dis. cases have one lesion per dis. case, 15 percent have two lesions per dis. case and 5 percent have three lesions per dis. case. As another example, c(0.8, 0.15, 0, 0.05) specifies a dataset in which 80 percent of the dis. cases have one lesion per dis. case, 15 percent have two lesions per dis. case, there are no cases with three lesions per dis. case and 5 percent have four lesions per dis. case.

Details

Two characteristics of an FROC dataset, apart from the ratings, affect the FOM: the distribution of lesion per case and the distribution of lesion weights. This function addresses the weights. The distribution of lesions is addressed in UtilLesionDistrVector. See PlotRsmOperatingCharacteristics for a function that depends on lesWghtDistr. The underlying assumption is that lesion 1 is the same type across all diseased cases, lesion 2 is the same type across all diseased cases, ..., etc. This allows assignment of weights independent of the case index.

Value

lesWghtDistr The 2D lesion weights distribution matrix. The first column enumerates the number of lesions per case, while the remaining columns contain the weights. Missing values are filled with -Inf. Not to be confused with the lesionWeight list member in an FROC dataset, which enumerates the weights of lesions on individual cases.

Examples

UtilLesionWeightsMatrixDataset (dataset01) # FROC data

##      [,1] [,2] [,3]
##[1,]    1  1.0 -Inf
##[2,]    2  0.5  0.5

UtilLesionWeightsMatrixDataset (dataset02) # ROC data

##      [,1] [,2]
##[1,]    1  1

## Example 1: dataset with 1 to 4 lesions per case, with frequency as per first argument
UtilLesionWeightsMatrixLesDistr (c(0.6, 0.2, 0.1, 0.1), c(0.2, 0.4, 0.1, 0.3))

##       [,1]  [,2]      [,3]      [,4]   [,5]
##[1,]    1 1.0000000      -Inf      -Inf -Inf 
##[2,]    2 0.3333333 0.6666667      -Inf -Inf
##[3,]    3 0.2857143 0.5714286 0.1428571 -Inf
##[4,]    4 0.2000000 0.4000000 0.1000000  0.3

## Explanation 
##> c(0.2)/sum(c(0.2))
##[1] 1 ## (weights for cases with 1 lesion)
##> c(0.2, 0.4)/sum(c(0.2, 0.4))
##[1] 0.3333333 0.6666667 ## (weights for cases with 2 lesions)
##> c(0.2, 0.4, 0.1)/sum(c(0.2, 0.4, 0.1))
##[1] 0.2857143 0.5714286 0.1428571 ## (weights for cases with 3 lesions)
##> c(0.2, 0.4, 0.1, 0.3)/sum(c(0.2, 0.4, 0.1, 0.3))
##[1] 0.2000000 0.4000000 0.1000000  0.3 ## (weights for cases with 4 lesions)


## Example2 : dataset with *no* cases with 3 lesions per case
UtilLesionWeightsMatrixLesDistr (c(0.1, 0.7, 0.0, 0.2), c(0.4, 0.3, 0.2, 0.1))

##       [,1]  [,2]      [,3]    [,4]
##[1,]    1 1.0000000      -Inf  -Inf
##[2,]    2 0.5714286 0.4285714  -Inf
##[3,]    4 0.5000000 0.3750000 0.125

## Explanation: note that row with 3 lesions per case does not occur 
##> c(0.4)/sum(c(0.4))
##[1] 1 ## (weights for cases with 1 lesion)
##> c(0.4, 0.3)/sum(c(0.4, 0.3))
##[1] 0.5714286 0.4285714 ## (weights for cases with 2 lesions)
##> c(0.4, 0.3, 0.1)/sum(c(0.4, 0.3, 0.1))
##[1] 0.500 0.375 0.125 ## (weights for cases with 4 lesions)

RJafroc documentation built on Nov. 10, 2022, 5:45 p.m.