Fuzzy Correspondence Analysis and Fuzzy Principal Components Analysis

Theses functions analyse a table of fuzzy variables.

A fuzzy variable takes values of type \(a=(a_1,\dots,a_k)\) giving the importance of k categories.

A missing data is denoted (0,...,0).
Only the profile a/sum(a) is used, and missing data are replaced by the mean profile of the others in the function prep.fuzzy.var. See ref. for details.

Usage

prep.fuzzy.var (df, col.blocks, row.w = rep(1, nrow(df)))
dudi.fca(df, scannf = TRUE, nf = 2)
dudi.fpca(df, scannf = TRUE, nf = 2)

Arguments

df

a data frame containing positive or null values

col.blocks

a vector containing the number of categories for each fuzzy variable

row.w

a vector of row weights

scannf

a logical value indicating whether the eigenvalues bar plot should be displayed

nf

if scannf FALSE, an integer indicating the number of kept axes

Value

The function prep.fuzzy.var returns a data frame with the attribute col.blocks. The function dudi.fca returns a list of class fca and dudi (see dudi) containing also

cr

a data frame which rows are the blocs, columns are the kept axes, and values are the correlation ratios.

The function dudi.fpca returns a list of class pca and dudi (see dudi) containing also

1. cent

2. norm

3. blo

4. indica

5. FST

6. inertia

References

Chevenet, F., Dolédec, S. and Chessel, D. (1994) A fuzzy coding approach for the analysis of long-term ecological data. Freshwater Biology, 31, 295–309.

Author

Daniel Chessel
Anne-Béatrice Dufour anne-beatrice.dufour@univ-lyon1.fr

Examples

w1 <- matrix(c(1,0,0,2,1,1,0,2,2,0,1,0,1,1,1,0,1,3,1,0), 4, 5)
w1 <- data.frame(w1) 
w2 <- prep.fuzzy.var(w1, c(2, 3))
#> 1 missing data found in block 1 
#> 1 missing data found in block 2 
w1
#>   X1 X2 X3 X4 X5
#> 1  1  1  2  1  1
#> 2  0  1  0  1  3
#> 3  0  0  1  1  1
#> 4  2  2  0  0  0
w2 
#>          X1        X2        X3        X4        X5
#> 1 0.5000000 0.5000000 0.5000000 0.2500000 0.2500000
#> 2 0.0000000 1.0000000 0.0000000 0.2500000 0.7500000
#> 3 0.3333333 0.6666667 0.3333333 0.3333333 0.3333333
#> 4 0.5000000 0.5000000 0.2777778 0.2777778 0.4444444
attributes(w2)
#> $names
#> [1] "X1" "X2" "X3" "X4" "X5"
#> 
#> $row.names
#> [1] 1 2 3 4
#> 
#> $class
#> [1] "data.frame"
#> 
#> $col.blocks
#> FV1 FV2 
#>   2   3 
#> 
#> $row.w
#> [1] 0.25 0.25 0.25 0.25
#> 
#> $col.freq
#> [1] 0.3333333 0.6666667 0.2777778 0.2777778 0.4444444
#> 
#> $col.num
#> [1] 1 1 2 2 2
#> Levels: 1 2
#> 

data(bsetal97)
w <- prep.fuzzy.var(bsetal97$biol, bsetal97$biol.blo)
#> 17 missing data found in block 1 
#> 14 missing data found in block 2 
#> 28 missing data found in block 3 
#> 8 missing data found in block 4 
#> 5 missing data found in block 5 
#> 19 missing data found in block 6 
#> 10 missing data found in block 7 
#> 5 missing data found in block 8 
#> 2 missing data found in block 9 
#> 12 missing data found in block 10 

if(adegraphicsLoaded()) {
  g1 <- plot(dudi.fca(w, scann = FALSE, nf = 3), plabels.cex = 1.5)
} else {
  scatter(dudi.fca(w, scann = FALSE, nf = 3), csub = 3, clab.moda = 1.5)
  scatter(dudi.fpca(w, scann = FALSE, nf = 3), csub = 3, clab.moda = 1.5)
}

#> Error in s.label(dfxy = dudi.fpca(w, scann = FALSE, nf = 3)$li, xax = 1,     yax = 2, plot = FALSE, storeData = TRUE, pos = -3, plabels = list(        cex = 0.75), csub = 3, clab = list(moda = 1.5)): non convenient selection for dfxy (can not be converted to dataframe)

if (FALSE) { # \dontrun{
w1 <- prep.fuzzy.var(bsetal97$biol, bsetal97$biol.blo)
w2 <- prep.fuzzy.var(bsetal97$ecol, bsetal97$ecol.blo)
d1 <- dudi.fca(w1, scannf = FALSE, nf = 3)
d2 <- dudi.fca(w2, scannf = FALSE, nf = 3)
plot(coinertia(d1, d2, scannf = FALSE))
} # }