Gower distance calculations may be incorrect

[Nowosad]

Dear @HajkD -- I think that the Gower distance is not correctly implemented in the package. As far as I understand it -- for categorical features it should either return 0 (if identical) or 1 (if different). Moreover, this distance should be bounded between 0 and 1. However, the current version of the code has no understanding of categorical variables and returns values larger than 1.

reference <- data.frame(cat = factor(c("A","B", "A", "C"), levels = c("A","B", "C")))

# Compute Gower distance with cluster::daisy
gower_dist <- cluster::daisy(reference, metric = "gower")
as.matrix(gower_dist)
#>   1 2 3 4
#> 1 0 1 0 1
#> 2 1 0 1 1
#> 3 0 1 0 1
#> 4 1 1 1 0

# Compute Gower distance with philentropy::distance
reference2 <- reference
reference2$cat <- as.integer(reference2$cat)
gower_dist2 <- philentropy::distance(reference2, method = "gower")
#> Metric: 'gower' with unit: 'log'; comparing: 4 vectors
gower_dist2
#>    v1 v2 v3 v4
#> v1  0  1  0  2
#> v2  1  0  1  1
#> v3  0  1  0  2
#> v4  2  1  2  0

[brownag]

I think this is "expected" in that the implementation in the package is correct for probability distribution functions.

It is following Cha (2007) which indicates an upper bound not of 1 but 2/N (for actual PDFs), it would not necessarily be bounded in the integer factor label case.

It may be a good idea to indicate this difference in the docs, and possibly even throw a warning? It is not the general metric for mixed data types (Gower, 1971) which includes normalization based on the range of the input variable.

[HajkD]

Hi @brownag and @Nowosad

I fully agree with @brownag. The implementation is correct according to Cha (2007). However, I do agree that this should be clearer in the documentation.

The question is, would it make sense to add the 'cluster::daisy()' version to philentropy and if yes how would this be most practical?

Many thanks for this excellent and important disucssion!
Hajk

[Nowosad]

Hi all,

1. I completely agree about underlining in the documentation that the "gower" method calculates distances between probability distributions only (so it is not working on mixed data types).
2. I would assume that most users trying the "gower" method are actually looking for the one working on mixed data types -- that makes this method rather unique.
3. I think it would be great to have the mixed data types version in philentropy, but at the moment I cannot think of how to make it with minimal changes to the code.

CC: @goergen95

[brownag]

I tinkered with this a little bit, will need to look back at my notes.

We'd perhaps need to be a little careful as I don't think just changing to Gower 1971 would be backward compatible... But indeed as @Nowosad says, most folks probably figure it is the former, and may not have noticed it wasn't behaving the way that is expected for that more general version.

if we could come up with some heuristics to check for mixed / factor data types etc perhaps we could have a separate internal implementation that kicks in when detected and an optional flag to force it one way or another. It would add a bit more machinery to the internals but I think it would be possible to do..

[Nowosad]

I also think that this is a good approach -- to keep the current approach, but also allow for the "mixed data" type (maybe as "gower_mix", "gower2", etc.)...