Sequentially the secondary suppression candidates (columns in x) are used to reduce the x-matrix by Gaussian elimination. Candidates who completely eliminate one or more primary suppressed cells (columns in x) are omitted and made secondary suppressed. This ensures that the primary suppressed cells do not depend linearly on the non-suppressed cells. How to order the input candidates is an important choice. The singleton problem and the related problem of zeros are also handled.
Usage
GaussSuppression(
x,
candidates = 1:ncol(x),
primary = NULL,
forced = NULL,
hidden = NULL,
singleton = rep(FALSE, nrow(x)),
singletonMethod = "anySum",
printInc = TRUE,
tolGauss = (.Machine$double.eps)^(1/2),
whenEmptySuppressed = warning,
whenEmptyUnsuppressed = message,
whenPrimaryForced = warning,
removeDuplicated = TRUE,
iFunction = GaussIterationFunction,
iWait = Inf,
xExtraPrimary = NULL,
unsafeAsNegative = FALSE,
printXdim = FALSE,
...
)Arguments
- x
Matrix that relates cells to be published or suppressed to inner cells. yPublish = crossprod(x,yInner)
- candidates
Indices of candidates for secondary suppression
- primary
Indices of primary suppressed cells
- forced
Indices forced to be not suppressed.
forcedhas precedence overprimary. SeewhenPrimaryForcedbelow.Indices to be removed from the above
candidatesinput (see details)- singleton
Logical or integer vector of length
nrow(x)specifying inner cells for singleton handling. Normally, for frequency tables, this means cells with 1s when 0s are non-suppressed and cells with 0s when 0s are suppressed. For some singleton methods, integer values representing the unique magnitude table contributors are needed. For all other singleton methods, only the values after conversion withas.logicalmatter.- singletonMethod
Method for handling the problem of singletons and zeros:
"anySum"(default),"anySum0","anySumNOTprimary","subSum","subSpace","sub2Sum","none"or aNumSingletonmethod (see details).- printInc
Printing "..." to console when TRUE
- tolGauss
A tolerance parameter for sparse Gaussian elimination and linear dependency. This parameter is used only in cases where integer calculation cannot be used.
- whenEmptySuppressed
Function to be called when empty input to primary suppressed cells is problematic. Supply NULL to do nothing.
- whenEmptyUnsuppressed
Function to be called when empty input to candidate cells may be problematic. Supply NULL to do nothing.
- whenPrimaryForced
Function to be called if any forced cells are primary suppressed (suppression will be ignored). Supply NULL to do nothing. The same function will also be called when there are forced cells marked as singletons (will be ignored).
- removeDuplicated
Specifies whether to remove duplicated columns and rows in
xbefore running the main algorithm. Removing duplicates results in a faster algorithm while generally maintaining the same results. In some cases, singleton handling for magnitude tables may be affected. In such cases, singleton handling will generally be improved. Singletons are considered when removing duplicate rows, so not all duplicates are removed. The available options forremoveDuplicatedare as follows:TRUE(default): Removes both duplicate columns and rows.FALSE: No removal of duplicates."cols": Removes only duplicate columns."rows": Removes only duplicate rows."rows2": Removes only duplicate non-singleton rows in a way that preserves singleton handling.Combined possibilities: Variants can be combined with "_". For example,
"cols_rows"is equivalent toTRUE, and"cols_rows2"represents an alternative variant. Combining"rows"and"rows2"is possible, but superfluous calculations are then performed."test": A special variant for testing purposes. The four configurationsTRUE,FALSE,"cols_rows2", and"rows"are executed.
- iFunction
A function to be called during the iterations. See the default function,
GaussIterationFunction, for description of parameters.- iWait
The minimum number of seconds between each call to
iFunction. WheneveriWait<Inf,iFunctionwill also be called after last iteration.- xExtraPrimary
Extra x-matrix that defines extra primary suppressed cells in addition to those defined by other inputs.
- unsafeAsNegative
When
TRUE, unsafe primary cells due to forced cells are included in the output vector as negative indices.- printXdim
When set to
TRUE, theprintIncparameter is also automatically set toTRUE. Additionally, the dimensions of thexmatrix are printed twice: first, the dimensions of the inputx, potentially extended withxExtraPrimary; second, the dimensions after applyingsingletonMethodandremoveDuplicated.- ...
Extra unused parameters
Details
It is possible to specify too many (all) indices as candidates.
Indices specified as primary or hidded will be removed.
Hidden indices (not candidates or primary) refer to cells that will not be published, but do not need protection.
Singleton methods for frequency tables: All singleton methods, except
"sub2Sum"and theNumSingletonmethods, have been implemented with frequency tables in mind. The singleton method"subSum"makes new virtual primary suppressed cells, which are the sum of the singletons within each group. The"subSpace"method is conservative and ignores the singleton dimensions when looking for linear dependency. The default method,"anySum", is between the other two. Instead of making virtual cells of sums within groups, the aim is to handle all possible sums, also across groups. In addition,"subSumSpace"and"subSumAny"are possible methods, primarily for testing. These methods are similar to"subSpace"and"anySum", and additional cells are created as in"subSum". It is believed that the extra cells are redundant. Note that in order to give information about unsafe cells,"anySum"is internally changed to"subSumAny"when there are forced cells. All the above methods assume that any published singletons are primary suppressed. If this is not the case, either"anySumNOTprimary"or"anySum0"must be used. Notably,"anySum0"is an enhancement of"anySumNOTprimary"for situations where zeros are singletons. Using that method avoids suppressing a zero marginal along with only one of its children.Singleton methods for magnitude tables: The singleton method
"sub2Sum"makes new virtual primary suppressed cells, which are the sum of two inner cells. This is done when a group contains exactly two primary suppressed inner cells provided that at least one of them is singleton. This was the first method implemented. Other magnitude methods follow the coding according toNumSingleton. The"sub2Sum"method is equivalent to"numFFT". Also note that"num","numFFF"and"numFTF"are equivalent to"none".Combined: For advanced use,
singletoncan be a two-element list with names"freq"and"num". ThensingletonMethodmust be a corresponding named two-element vector. For example:singletonMethod = c(freq = "anySumNOTprimary", num = "sub2Sum")
References
Langsrud, Ø. (2024): “Secondary Cell Suppression by Gaussian Elimination: An Algorithm Suitable for Handling Issues with Zeros and Singletons”. Presented at: Privacy in statistical databases, Antibes, France. September 25-27, 2024. doi:10.1007/978-3-031-69651-0_6
Examples
# Input data
df <- data.frame(values = c(1, 1, 1, 5, 5, 9, 9, 9, 9, 9, 0, 0, 0, 7, 7),
var1 = rep(1:3, each = 5),
var2 = c("A", "B", "C", "D", "E"), stringsAsFactors = FALSE)
# Make output data frame and x
fs <- FormulaSums(df, values ~ var1 * var2, crossTable = TRUE, makeModelMatrix = TRUE)
x <- fs$modelMatrix
datF <- data.frame(fs$crossTable, values = as.vector(fs$allSums))
# Add primary suppression
datF$primary <- datF$values
datF$primary[datF$values < 5 & datF$values > 0] <- NA
datF$suppressedA <- datF$primary
datF$suppressedB <- datF$primary
datF$suppressedC <- datF$primary
# zero secondary suppressed
datF$suppressedA[GaussSuppression(x, primary = is.na(datF$primary))] <- NA
#> GaussSuppression_anySum: .....................
# zero not secondary suppressed by first in ordering
datF$suppressedB[GaussSuppression(x, c(which(datF$values == 0), which(datF$values > 0)),
primary = is.na(datF$primary))] <- NA
#> GaussSuppression_anySum: .....................
# with singleton
datF$suppressedC[GaussSuppression(x, c(which(datF$values == 0), which(datF$values > 0)),
primary = is.na(datF$primary), singleton = df$values == 1)] <- NA
#> GaussSuppression_anySum: .....................
datF
#> var1 var2 values primary suppressedA suppressedB suppressedC
#> 1 Total Total 72 72 72 72 72
#> 2 1 Total 13 13 13 13 13
#> 3 2 Total 45 45 45 45 45
#> 4 3 Total 14 14 14 14 14
#> 5 Total A 10 10 10 10 10
#> 6 Total B 10 10 10 10 10
#> 7 Total C 10 10 10 10 10
#> 8 Total D 21 21 21 21 21
#> 9 Total E 21 21 21 21 21
#> 10 1 A 1 NA NA NA NA
#> 11 1 B 1 NA NA NA NA
#> 12 1 C 1 NA NA NA NA
#> 13 1 D 5 5 5 5 5
#> 14 1 E 5 5 5 5 NA
#> 15 2 A 9 9 9 NA NA
#> 16 2 B 9 9 9 NA NA
#> 17 2 C 9 9 9 NA NA
#> 18 2 D 9 9 9 9 9
#> 19 2 E 9 9 9 9 NA
#> 20 3 A 0 0 NA 0 0
#> 21 3 B 0 0 NA 0 0
#> 22 3 C 0 0 NA 0 0
#> 23 3 D 7 7 7 7 7
#> 24 3 E 7 7 7 7 7