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)
)
## Warning in microbenchmark::microbenchmark(dist(rbind(P, Q), method =
## "euclidean"), : less accurate nanosecond times to avoid potential integer
## overflows
## Unit: nanoseconds
## 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
## 5699 5924.5 7294.72 6191 6396 101803 100
## 9307 9676.0 16451.25 9922 10168 637222 100
## 820 902.0 1090.60 984 1066 11439 100
## 1148 1271.0 2227.53 1394 1476 82738 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
## 123.615 135.3615 151.16782 147.7025 160.720 245.180 100
## 8769.736 9171.9050 10335.37061 9706.3195 11543.468 14245.655 100
## 9.430 9.7990 11.55667 10.4550 11.808 43.993 100
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) 943.902 969.937
## dist_many_many(M1, M2, method = "euclidean", testNA = FALSE) 14.063 14.350
## mean median uq max neval
## 1084.07116 984.984 1010.138 3920.051 100
## 15.17943 14.555 14.842 35.875 100
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.