`cLinear()` is the compositional-linear kernel, which is useful for compositional data (relative frequencies or proportions). `Aitchison()` is akin to the RBF kernel for this type of data. Thus, the expected input for both kernels is a matrix or data.frame containing strictly non-negative or (even better) positive numbers. This input has dimension NxD, with N>1 samples and D>1 compositional features.
Usage
cLinear(X, cos.norm = FALSE, feat_space = FALSE, zeros = "none")
Aitchison(X, g = NULL, zeros = "none")Arguments
- X
Matrix or data.frame that contains the compositional data.
- cos.norm
Should the resulting kernel matrix be cosine normalized? (Defaults: FALSE).
- feat_space
If FALSE, only the kernel matrix is returned. Otherwise, the feature space is also returned. (Defaults: FALSE).
- zeros
"none" to warrant that there are no zeroes in X, "pseudo" to replace zeroes by a pseudocount. (Defaults="none").
- g
Gamma hyperparameter. If g=0 or NULL, the matrix of squared Aitchison distances is returned instead of the Aitchison kernel matrix. (Defaults=NULL).
Details
In compositional data, samples (rows) sum to an arbitrary or irrelevant number. This is most clear when working with relative frequencies, as all samples add to 1 (or 100, or other uninformative value). Zeroes are a typical challenge when using compositional approaches. They introduce ambiguity because they can have multiple causes; a zero may signal a true absence, or a value so small that it is below the detection threshold of an instrument. A simple approach to deal with zeroes is replacing them by a pseudocount. More sophisticated approaches are reviewed elsewhere; see for instance the R package `zCompositions`.
References
Ramon, E., Belanche-Muñoz, L. et al (2021). kernInt: A kernel framework for integrating supervised and unsupervised analyses in spatio-temporal metagenomic datasets. Frontiers in microbiology 12 (2021): 609048. doi: 10.3389/fmicb.2021.609048
Examples
data <- soil$abund
## This data is sparse and contains a lot of zeroes. We can replace them by pseudocounts:
Kclin <- cLinear(data,zeros="pseudo")
Kclin[1:5,1:5]
#> X103.CA2 X103.CO3 X103.SR3 X103.IE2 X103.BP1
#> X103.CA2 10275.8219 1904.924 2674.1133 416.1493 2110.8775
#> X103.CO3 1904.9238 10322.174 2081.3274 1388.0667 2174.0920
#> X103.SR3 2674.1133 2081.327 11933.4557 688.7321 1751.3419
#> X103.IE2 416.1493 1388.067 688.7321 13005.5436 805.6387
#> X103.BP1 2110.8775 2174.092 1751.3419 805.6387 10272.4113
## With the feature space:
Kclin <- cLinear(data,zeros="pseudo",feat_space=TRUE)
## With cosine normalization:
Kcos <- cLinear(data,zeros="pseudo",cos.norm=TRUE)
Kcos[1:5,1:5]
#> X103.CA2 X103.CO3 X103.SR3 X103.IE2 X103.BP1
#> X103.CA2 1.00000000 0.1849625 0.24148402 0.03599786 0.20545587
#> X103.CO3 0.18496253 1.0000000 0.18753041 0.11980101 0.21113301
#> X103.SR3 0.24148402 0.1875304 1.00000000 0.05528444 0.15818002
#> X103.IE2 0.03599786 0.1198010 0.05528444 1.00000000 0.06970113
#> X103.BP1 0.20545587 0.2111330 0.15818002 0.06970113 1.00000000
## Aitchison kernel:
Kait <- Aitchison(data,g=0.0001,zeros="pseudo")
Kait[1:5,1:5]
#> X103.CA2 X103.CO3 X103.SR3 X103.IE2 X103.BP1
#> X103.CA2 1.0000000 0.1865950 0.18523961 0.10593743 0.1954115
#> X103.CO3 0.1865950 1.0000000 0.16376915 0.12807255 0.1969826
#> X103.SR3 0.1852396 0.1637692 1.00000000 0.09478411 0.1540746
#> X103.IE2 0.1059374 0.1280725 0.09478411 1.00000000 0.1145587
#> X103.BP1 0.1954115 0.1969826 0.15407461 0.11455872 1.0000000