R/01-metrics.R In Mercator: Clustering and Visualizing Distance Matrices

Documented in binaryDistancegoodmanKruskalDistancegoodmanKruskalSimilarityhammingDistancejaccardDistancejaccardSimilaritypearsonDistancepearsonSimilarityrussellRaoSimilaritysokalMichenerDistancesokalMichenerSimilarity

```### Definitions of various similarity or distance measures between
### binary vectors. In the main reeference (below), Choi and colleagues
### reviewed 76 different measures of simialrity or distance between
### binary vectors. They also produced a hierarchical clustering of
### these measures, based on the correlation between their distance
### values on multiple simulated data sets. For metrics that are highly
### similar, we choose a single representative.

# [1] Choi SS, Cha SH, Tappert CC, A Survey of Binary Similarity and Distance Measures.
#     Systemics, Cybernetics, and Informatics. 2010; 8(1):43-48.

### Cluster 1 contains Dice & Sorenson, Ochiai, Kulczynski, Bray & Curtis,
### Baroni-Urbani & Buser, and Jaccard
jaccardSimilarity <- function(X) {
N11 <- X %*% t(X)
N01 <- (1 - X) %*% t(X)
N10 <- X %*% t(1 - X)
den <- (N11 + N01 + N10)
den[den == 0] <- 1
N11 / den
}
jaccardDistance <- function(X) {
as.dist( 1 - jaccardSimilarity(X))
}

### Cluster 2 contains Sokal & Sneath, Gilbert & Wells, Gower & Legendre,
### Pearson & Heron, and Sokal & Michener.
sokalMichenerSimilarity <- function(X) {
N11 <- X %*% t(X)
N01 <- (1 - X) %*% t(X)
N10 <- X %*% t(1 - X)
N00 <- (1 - X) %*% t(1 - X)
(N00 + N11) / (N00 + N11 + N01 + N10)
}
sokalMichenerDistance <- function(X) {3
as.dist( 1 - sokalMichenerSimilarity(X))
}

### Also in Cluster 2 are Hamming, Manhattan, Canberra, Minkowski,
### and Euclidean. We might want to try Euclidean as well.
### Hamming
hammingDistance <- function(X) {
b <- (1 - X) %*% t(X)
c <- X %*% t(1 - X)
as.dist(b + c)
}

### Cluster 3 contains Driver & Kroeber, Forbes, Fossum, and
### Russell & Rao
russellRaoSimilarity <- function(X) {
N11 <- X %*% t(X)
N11/ ncol(X)
}
russellRaoDistance <- function(X) {
as.dist( 1 - russellRaoSimilarity(X) )
}

### Remaining metrics are more isolated, without strong clutering.
### We consider a few examples.

### Pearson correlation
pearsonSimilarity <- function(X) {
a <- X %*% t(X)
b <- (1 - X) %*% t(X)
c <- X %*% t(1 - X)
d <- (1 - X) %*% t(1 - X)
n <- a + b + c + d
(n*(a*d - b*c)^2)/((a + b)*(a + c)*(b + d)*(c + d))
}
pearsonDistance <- function(X) {
as.dist( ncol(X) - pearsonSimilarity(X) )
}

### Goodman & Kruskal
goodmanKruskalSimilarity <- function(X) {
a <- X %*% t(X)
b <- (1 - X) %*% t(X)
c <- X %*% t(1 - X)
d <- (1 - X) %*% t(1 - X)
n <- a + b + c + d
sig <- pmax(a, b) + pmax(c, d) + pmax(a, c) + pmax(b, d)
sigprime <- pmax(a + c, b + d) + pmax(a + b, c + d)
(sig - sigprime) / (2*n - sigprime)
}
goodmanKruskalDistance <- function(X) {
as.dist( 1 - goodmanKruskalSimilarity(X) )
}

binaryDistance <- function(X, metric) {
METRICS <- c(jaccard = jaccardDistance,
sokalMichener = sokalMichenerDistance,
hamming = hammingDistance,
russellRao = russellRaoDistance,
pearson = pearsonDistance,
goodmanKruskal = goodmanKruskalDistance,
manhattan = function(x) {
DD <- dist(t(X), "manhattan")
DD/max(DD)
},
canberra = function(x) dist(t(X), "canberra")/ncol(X),
binary = function(x) dist(t(X), "binary"),
euclid = function(x) {
DD <- dist(t(X), "euclid")
DD/max(DD)
}
) # why is this a list and not a vector?
fullname <- match.arg(metric, names(METRICS))
FUN <- METRICS[[fullname]]
RES <- FUN(t(X))
comment(RES) <- fullname
RES
}
```

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Mercator documentation built on Nov. 12, 2020, 3:02 a.m.