vignettes/Many_Distances.Rmd
Many_Distances.Rmd
The philentropy package has several mechanisms to calculate distances between probability density functions. The main one is to use the the distance()
function, which enables to compute 46 different distances/similarities between probability density functions (see ?philentropy::distance
and a companion vignette for details). Alternatively, it is possible to call each distance/dissimilarity function directly. For example, the euclidean()
function will compute the euclidean distance, while jaccard
- the Jaccard distance. The complete list of available distance measures are available with the philentropy::getDistMethods()
function.
Both of the above approaches have their pros and cons. The distance()
function is more flexible as it allows users to use any distance measure and can return either a matrix
or a dist
object. It also has several defensive programming checks implemented, and thus, it is more appropriate for regular users. Single distance functions, such as euclidean()
or jaccard()
, can be, on the other hand, slightly faster as they directly call the underlining C++ code.
Now, we introduce three new low-level functions that are intermediaries between distance()
and single distance functions. They are fairly flexible, allowing to use of any implemented distance measure, but also usually faster than calling the distance()
functions (especially, if it is needed to use many times). These functions are:
dist_one_one()
- expects two vectors (probability density functions), returns a single valuedist_one_many()
- expects one vector (a probability density function) and one matrix (a set of probability density functions), returns a vector of valuesdist_many_many()
- expects two matrices (two sets of probability density functions), returns a matrix of valuesLet’s start testing them by attaching the philentropy package.
dist_one_one()
dist_one_one()
is a lower level equivalent to distance()
. However, instead of accepting a numeric data.frame
or matrix
, it expects two vectors representing probability density functions. In this example, we create two vectors, P
and Q
.
To calculate the euclidean distance between them we can use several approaches - (a) build-in R dist()
function, (b) philentropy::distance()
, (c) philentropy::euclidean()
, or the new dist_one_one()
.
# install.packages("microbenchmark")
microbenchmark::microbenchmark(
dist(rbind(P, Q), method = "euclidean"),
distance(rbind(P, Q), method = "euclidean", test.na = FALSE, mute.message = TRUE),
euclidean(P, Q, FALSE),
dist_one_one(P, Q, method = "euclidean", testNA = FALSE)
)
## Unit: microseconds
## expr
## dist(rbind(P, Q), method = "euclidean")
## distance(rbind(P, Q), method = "euclidean", test.na = FALSE, mute.message = TRUE)
## euclidean(P, Q, FALSE)
## dist_one_one(P, Q, method = "euclidean", testNA = FALSE)
## min lq mean median uq max neval
## 21.017 22.6785 33.91872 23.9470 26.1130 305.616 100
## 27.555 28.9300 67.36313 29.9755 33.1265 2190.872 100
## 2.548 2.9290 3.72877 3.1580 3.7405 24.948 100
## 3.645 4.2180 6.32354 4.7135 5.1485 127.471 100
All of them return the same, single value. However, as you can see in the benchmark above, some are more flexible, and others are faster.
dist_one_many()
The role of dist_one_many()
is to calculate distances between one probability density function (in a form of a vector
) and a set of probability density functions (as rows in a matrix
).
Firstly, let’s create our example data.
P
is our input vector and M
is our input matrix.
Distances between the P
vector and probability density functions in M
can be calculated using several approaches. For example, we could write a for
loop (adding a new code) or just use the existing distance()
function and extract only one row (or column) from the results. The dist_one_many()
allows for this calculation directly as it goes through each row in M
and calculates a given distance measure between P
and values in this row.
# install.packages("microbenchmark")
microbenchmark::microbenchmark(
as.matrix(dist(rbind(P, M), method = "euclidean"))[1, ][-1],
distance(rbind(P, M), method = "euclidean", test.na = FALSE, mute.message = TRUE)[1, ][-1],
dist_one_many(P, M, method = "euclidean", testNA = FALSE)
)
## Unit: microseconds
## expr
## as.matrix(dist(rbind(P, M), method = "euclidean"))[1, ][-1]
## distance(rbind(P, M), method = "euclidean", test.na = FALSE, mute.message = TRUE)[1, ][-1]
## dist_one_many(P, M, method = "euclidean", testNA = FALSE)
## min lq mean median uq max neval
## 389.581 528.141 705.30695 703.8735 799.2435 2660.721 100
## 33281.702 39837.296 47609.73996 45371.5355 52265.8085 92813.572 100
## 34.407 40.242 56.62543 49.6750 59.3605 169.750 100
The dist_one_many()
returns a vector of values. It is, in this case, much faster than distance()
, and visibly faster than dist()
while allowing for more possible distance measures to be used.
dist_many_many()
dist_many_many()
calculates distances between two sets of probability density functions (as rows in two matrix
objects).
Let’s create two new matrix
example data.
set.seed(2020-08-20)
M1 <- t(replicate(10, sample(1:10, size = 10) / 55))
M2 <- t(replicate(10, sample(1:10, size = 10) / 55))
M1
is our first input matrix and M2
is our second input matrix. I am not aware of any function build-in R that allows calculating distances between rows of two matrices, and thus, to solve this problem, we can create our own - many_dists()
…
many_dists = function(m1, m2){
r = matrix(nrow = nrow(m1), ncol = nrow(m2))
for (i in seq_len(nrow(m1))){
for (j in seq_len(nrow(m2))){
x = rbind(m1[i, ], m2[j, ])
r[i, j] = distance(x, method = "euclidean", mute.message = TRUE)
}
}
r
}
… and compare it to dist_many_many()
.
# install.packages("microbenchmark")
microbenchmark::microbenchmark(
many_dists(M1, M2),
dist_many_many(M1, M2, method = "euclidean", testNA = FALSE)
)
## Unit: microseconds
## expr min lq
## many_dists(M1, M2) 3049.288 3479.443
## dist_many_many(M1, M2, method = "euclidean", testNA = FALSE) 48.604 57.196
## mean median uq max neval
## 5008.11392 4017.414 5288.151 24289.867 100
## 77.55257 64.302 78.925 507.448 100
Both many_dists()
and dist_many_many()
return a matrix. The above benchmark concludes that dist_many_many()
is about 30 times faster than our custom many_dists()
approach.