Add zero replacement

DESCRIPTION

@@ -60,6 +60,7 @@ Collate:
     'pca.R'
     'plot.R'
     'reexport.R'
+    'replace.R'
     'show.R'
     'simplex.R'
     'statistics.R'

NAMESPACE

@@ -52,6 +52,7 @@ exportMethods(pca)
 exportMethods(perturbation)
 exportMethods(plot)
 exportMethods(powering)
+exportMethods(replace_zero)
 exportMethods(scalar)
 exportMethods(transform_alr)
 exportMethods(transform_clr)

R/AllGenerics.R

@@ -932,6 +932,34 @@ setGeneric(
 #' @rdname pca
 NULL
 
+# Missign Values ===============================================================
+#' Zero-Replacement
+#'
+#' Multiplicative replacement of zeros in compositional data.
+#' @param x An \eqn{m \times p}{m x p} [`CompositionMatrix-class`] object.
+#' @param value A length-\eqn{p} [`numeric`] vector giving the detection limits
+#'  of each part (in \eqn{(0,1)}).
+#' @param delta A [`numeric`] vector specifying the fraction of the detection
+#'  limit to be used in replacement.
+#' @return
+#'  An \eqn{m \times p}{m x p} [`CompositionMatrix-class`] object, where all
+#'  zero values have been replaced.
+#' @references
+#'  Aitchison, J. (1986). *The Statistical Analysis of Compositional Data*.
+#'  London: Chapman and Hall. \doi{10.1007/978-94-009-4109-0}.
+#'
+#'  Martín-Fernández, J. A., Barceló-Vidal, C. & Pawlowsky-Glahn, V. (2003).
+#'  Dealing with Zeros and Missing Values in Compositional Data Sets Using
+#'  Nonparametric Imputation. *Mathematical Geology*, 35(3): 253-278.
+#'  \doi{10.1023/A:1023866030544}.
+#' @example inst/examples/ex-zero.R
+#' @author N. Frerebeau
+#' @docType methods
+#' @family imputation methods
+#' @name zero
+#' @rdname zero
+NULL
+
 # Outliers =====================================================================
 #' Outlier Detection
 #'

R/replace.R

@@ -0,0 +1,46 @@
+# REPLACE ZEROS
+#' @include AllGenerics.R
+NULL
+
+#' @export
+#' @rdname zero
+#' @aliases replace_zero,CompositionMatrix-method
+setMethod(
+  f = "replace_zero",
+  signature = c(x = "CompositionMatrix"),
+  definition = function(x, value = NULL, delta = 2/3) {
+    ## Validation
+    D <- ncol(x)
+    if (is.null(value)) return(x)
+    if (length(value) == 1) rep(value, D)
+    if (length(value) > 1) arkhe::assert_length(value, D)
+    if (length(delta) > 1) arkhe::assert_length(delta, D)
+
+    sigma <- value * delta
+    repl <- apply(X = x, MARGIN = 1, FUN = zero_multiplicative, sigma = sigma)
+
+    methods::initialize(x, t(repl))
+  }
+)
+
+zero_additive <- function(x, sigma) {
+  D <- length(x)
+
+  is_zero <- x == 0
+  Z <- sum(is_zero)
+
+  x[is_zero] <- (sigma * (Z + 1) * (D - Z)) / D^2
+  x[!is_zero] <- x[!is_zero] - (sigma * (Z + 1) * Z) / D^2
+
+  x
+}
+zero_multiplicative <- function(x, sigma) {
+  D <- length(x)
+
+  is_zero <- x == 0
+
+  x[is_zero] <- sigma[is_zero]
+  x[!is_zero] <- x[!is_zero] * (1 - (sum(sigma[is_zero])) / 1)
+
+  x
+}

inst/examples/ex-zero.R

@@ -0,0 +1,13 @@
+## Create a data.frame
+X <- data.frame(
+  Ca = c(7.72, 0, 3.11, 7.19, 7.41, 5, 0, 1, 4.51),
+  Fe = c(6.12, 5.88, 5.12, 0, 6.02, 0, 0, 5.28, 5.72),
+  Na = c(0.97, 1.59, 0, 0.86, 0.76, 0.51, 0.75, 0.52, 0.56)
+)
+
+## Coerce to a compositional matrix
+Y <- as_composition(X)
+
+## Replace zeros
+Z <- replace_zero(Y, value = c(0.02, 0.1, 0.01), delta = 2/3)
+Z

inst/tinytest/test_zero.R

@@ -0,0 +1,11 @@
+# Replace zeros ================================================================
+X <- data.frame(
+  Ca = c(7.72, 0, 3.11, 7.19, 7.41, 5, 0, 1, 4.51),
+  Fe = c(6.12, 5.88, 5.12, 0, 6.02, 0, 0, 5.28, 5.72),
+  Na = c(0.97, 1.59, 0, 0.86, 0.76, 0.51, 0.75, 0.52, 0.56)
+)
+Y <- as_composition(X)
+
+## Multiplicative replacement
+Z <- replace_zero(Y, value = c(0.02, 0.1, 0.01), delta = 2/3)
+expect_equal_to_reference(Z, file = "_snaps/zero_multiplicative.rds")

pkgdown/_pkgdown.yml

@@ -19,6 +19,9 @@ reference:
 - title: Visualization
   contents:
   - has_concept("plot methods")
+- title: Missing Values
+  contents:
+  - has_concept("imputation methods")
 - title: Multivariate Analysis
   contents:
   - has_concept("multivariate analysis")

vignettes/bibliography.bib

@@ -75,8 +75,6 @@ @article{filzmoser2005
   pages = {579--587},
   issn = {00983004},
   doi = {10.1016/j.cageo.2004.11.013},
-  url = {http://linkinghub.elsevier.com/retrieve/pii/S0098300404002304},
-  urldate = {2018-07-01},
   langid = {english}
 }
 
@@ -90,8 +88,6 @@ @article{filzmoser2008
   pages = {233--248},
   issn = {1874-8961, 1874-8953},
   doi = {10.1007/s11004-007-9141-5},
-  url = {http://link.springer.com/10.1007/s11004-007-9141-5},
-  urldate = {2017-11-22},
   abstract = {Outlier detection based on the Mahalanobis distance (MD) requires an appropriate transformation in case of compositional data. For the family of logratio transformations (additive, centered and isometric logratio transformation) it is shown that the MDs based on classical estimates are invariant to these transformations, and that the MDs based on affine equivariant estimators of location and covariance are the same for additive and isometric logratio transformation. Moreover, for 3-dimensional compositions the data structure can be visualized by contour lines. In higher dimension the MDs of closed and opened data give an impression of the multivariate data behavior.},
   langid = {english}
 }
@@ -119,8 +115,6 @@ @article{filzmoser2012
   pages = {77--85},
   issn = {00983004},
   doi = {10.1016/j.cageo.2011.06.014},
-  url = {http://linkinghub.elsevier.com/retrieve/pii/S0098300411002056},
-  urldate = {2017-11-26},
   abstract = {Compositional data—and most data in geochemistry are of this type—carry relative rather than absolute information. For multivariate outlier detection methods this implies that not the given data but appropriately transformed data need to be used. We use the isometric logratio (ilr) transformation, which seems to be generally the most proper one for theoretical and practical reasons. In this space it is difficult to interpret the outliers, because the reason for outlyingness can be complex. Therefore we introduce tools that support the interpretation of outliers by representing multivariate information in biplots, maps, and univariate scatterplots.},
   langid = {english}
 }
@@ -134,8 +128,6 @@ @book{filzmoser2018
   publisher = {{Springer-Verlag}},
   location = {{Berlin Heidelberg}},
   doi = {10.1007/978-3-319-96422-5},
-  url = {http://link.springer.com/10.1007/978-3-319-96422-5},
-  urldate = {2020-06-03},
   isbn = {978-3-319-96420-1 978-3-319-96422-5},
   langid = {english}
 }
@@ -150,8 +142,6 @@ @article{fiserova2011
   pages = {455--468},
   issn = {1874-8961, 1874-8953},
   doi = {10.1007/s11004-011-9333-x},
-  url = {http://link.springer.com/10.1007/s11004-011-9333-x},
-  urldate = {2020-06-03},
   langid = {english}
 }
 
@@ -177,8 +167,6 @@ @article{greenacre2021
   pages = {271--299},
   issn = {2326-8298, 2326-831X},
   doi = {10.1146/annurev-statistics-042720-124436},
-  url = {https://www.annualreviews.org/doi/10.1146/annurev-statistics-042720-124436},
-  urldate = {2022-11-11},
   abstract = {Compositional data are nonnegative data carrying relative, rather than absolute, information—these are often data with a constant-sum constraint on the sample values, for example, proportions or percentages summing to 1\% or 100\%, respectively. Ratios between components of a composition are important since they are unaffected by the particular set of components chosen. Logarithms of ratios (logratios) are the fundamental transformation in the ratio approach to compositional data analysis—all data thus need to be strictly positive, so that zero values present a major problem. Components that group together based on domain knowledge can be amalgamated (i.e., summed) to create new components, and this can alleviate the problem of data zeros. Once compositional data are transformed to logratios, regular univariate and multivariate statistical analysis can be performed, such as dimension reduction and clustering, as well as modeling. Alternative methodologies that come close to the ideals of the logratio approach are also considered, especially those that avoid the problem of data zeros, which is particularly acute in large bioinformatic data sets.},
   langid = {english}
 }
@@ -194,8 +182,19 @@ @article{hron2017
   pages = {797--814},
   issn = {1874-8961, 1874-8953},
   doi = {10.1007/s11004-017-9684-z},
-  url = {http://link.springer.com/10.1007/s11004-017-9684-z},
-  urldate = {2021-12-17},
+  langid = {english}
+}
+
+@article{martin-fernandez2003,
+  title = {Dealing with {{Zeros}} and {{Missing Values}} in {{Compositional Data Sets Using Nonparametric Imputation}}},
+  author = {Martín-Fernández, J. A. and Barceló-Vidal, C. and Pawlowsky-Glahn, V.},
+  date = {2003},
+  journaltitle = {Mathematical Geology},
+  volume = {35},
+  number = {3},
+  pages = {253--278},
+  issn = {08828121},
+  doi = {10.1023/A:1023866030544},
   langid = {english}
 }
 
@@ -209,8 +208,6 @@ @article{mommsen1988
   pages = {47--57},
   issn = {0003-813X, 1475-4754},
   doi = {10.1111/j.1475-4754.1988.tb00434.x},
-  url = {http://doi.wiley.com/10.1111/j.1475-4754.1988.tb00434.x},
-  urldate = {2017-10-16},
   abstract = {A new similarity measure is proposed, the ‘dilution factor spread’ or, derived from it, a ‘goodness of fit’ parameter. This has the advantage that raw data without any transformation can be used, diluted samples are recognized and errors of individual concentration values can easily be included. The use of this similarity coefficient in multivariate cluster analyses to construct dendrograms is shown and compared with the use of the well-known similarity measure of Euclidian distance in attribute space and of the cos θ measure.},
   langid = {english}
 }
@@ -226,7 +223,6 @@ @article{mommsen2007
   pages = {359--371},
   issn = {0003-813X, 1475-4754},
   doi = {10.1111/j.1475-4754.2007.00306.x},
-  url = {http://doi.wiley.com/10.1111/j.1475-4754.2007.00306.x},
   abstract = {Neutron activation analysis of pottery was established at Bonn in 1983 and has since become one of the primary archaeometry-based analytical techniques at the facility. A brief history of the laboratory and a discussion of the best relative fit procedure for pottery is provided. When comparing concentration data for pottery, a best relative fit should always be considered. This mathematical procedure generally results in ‘sharper’ concentration patterns and improves the separability of chemically not very different compositional groups. This is demonstrated for a set of 30 Late Cypriot (Myc. IIIC1) pottery samples from Sinda, Cyprus, which allow formation of a good reference pattern for this site. Applying factors in the range of 0.82-1.43, a number of samples from Egypt and Palestine can be assigned with high probability to a Cypriot origin.},
   langid = {english}
 }
@@ -256,8 +252,6 @@ @article{rousseeuw1990
   pages = {633--639},
   issn = {0162-1459, 1537-274X},
   doi = {10.1080/01621459.1990.10474920},
-  url = {http://www.tandfonline.com/doi/abs/10.1080/01621459.1990.10474920},
-  urldate = {2022-06-10},
   langid = {english}
 }
 
@@ -272,16 +266,6 @@ @article{santos2020
   pages = {102423},
   issn = {2352409X},
   doi = {10.1016/j.jasrep.2020.102423},
-  url = {https://linkinghub.elsevier.com/retrieve/pii/S2352409X20302145},
-  urldate = {2023-09-13},
-  langid = {english}
-}
-
-@article{tsagris2011,
-  title = {A Data-Based Power Transformation for Compositional Data},
-  author = {Tsagris, Michail T. and Preston, Simon and Wood, Andrew T. A.},
-  date = {2011},
-  url = {https://arxiv.org/pdf/1106.1451.pdf},
   langid = {english}
 }