| Title: | Distance and Similarity Measures |
|---|---|
| Description: | Provides an extensible framework for the efficient calculation of auto- and cross-proximities, along with implementations of the most popular ones. |
| Authors: | David Meyer [aut, cre], Christian Buchta [aut] |
| Maintainer: | David Meyer <[email protected]> |
| License: | GPL-2 |
| Version: | 0.4-27 |
| Built: | 2024-10-09 06:35:14 UTC |
| Source: | CRAN |
These functions compute and return the auto-distance/similarity matrix between either rows or columns of a matrix/data frame, or a list, as well as the cross-distance matrix between two matrices/data frames/lists.
dist(x, y = NULL, method = NULL, ..., diag = FALSE, upper = FALSE, pairwise = FALSE, by_rows = TRUE, convert_similarities = TRUE, auto_convert_data_frames = TRUE) simil(x, y = NULL, method = NULL, ..., diag = FALSE, upper = FALSE, pairwise = FALSE, by_rows = TRUE, convert_distances = TRUE, auto_convert_data_frames = TRUE) pr_dist2simil(x) pr_simil2dist(x) as.dist(x, FUN = NULL) as.simil(x, FUN = NULL) ## S3 method for class 'dist' as.matrix(x, diag = 0, ...) ## S3 method for class 'simil' as.matrix(x, diag = NA, ...)dist(x, y = NULL, method = NULL, ..., diag = FALSE, upper = FALSE, pairwise = FALSE, by_rows = TRUE, convert_similarities = TRUE, auto_convert_data_frames = TRUE) simil(x, y = NULL, method = NULL, ..., diag = FALSE, upper = FALSE, pairwise = FALSE, by_rows = TRUE, convert_distances = TRUE, auto_convert_data_frames = TRUE) pr_dist2simil(x) pr_simil2dist(x) as.dist(x, FUN = NULL) as.simil(x, FUN = NULL) ## S3 method for class 'dist' as.matrix(x, diag = 0, ...) ## S3 method for class 'simil' as.matrix(x, diag = NA, ...)
x |
For |
y |
|
method |
a function, a registry entry, or a mnemonic string referencing the
proximity measure. A list of all available measures can be obtained
using |
diag |
logical value indicating whether the diagonal of the
distance/similarity matrix should be printed by
In the context of |
upper |
logical value indicating whether the upper triangle of the
distance/similarity matrix should be printed by
|
pairwise |
logical value indicating whether distances should be
computed for the pairs of |
by_rows |
logical indicating whether proximities between rows, or columns should be computed. |
convert_similarities, convert_distances
|
logical indicating whether distances should be automatically converted into similarities (and the other way round) if needed. |
auto_convert_data_frames |
logical indicating whether data frames should be converted to matrices if all variables are numeric, or all are logical, or all are complex. |
FUN |
optional function to be used by |
... |
further arguments passed to the proximity function. |
The interface is fashioned after dist, but can
also compute cross-distances, and allows user extensions by means of
registry of all proximity measures (see pr_DB).
Missing values are allowed but are excluded from all computations
involving the rows within which they occur. If some columns are
excluded in calculating a Euclidean, Manhattan, Canberra or
Minkowski distance, the sum is scaled up proportionally to the
number of columns used (compare dist in
package stats).
Data frames are silently coerced to matrix if all columns are of
(same) mode numeric or logical.
Distance measures can be used with simil, and similarity
measures with dist. In these cases, the result is transformed
accordingly using the specified coercion functions (default:
and ).
Objects of class simil and dist can be converted one in
another using as.dist and as.simil, respectively.
Distance and similarity objects can conveniently be subset (see examples). Note that duplicate indexes are silently ignored.
Auto distances/similarities are returned as an object of class dist/simil and
cross-distances/similarities as an object of class crossdist/crosssimil.
David Meyer [email protected] and Christian Buchta [email protected]
Anderberg, M.R. (1973), Cluster analysis for applications, 359 pp., Academic Press, New York, NY, USA.
Cox, M.F. and Cox, M.A.A. (2001), Multidimensional Scaling, Chapman and Hall.
Sokol, R.S. and Sneath P.H.A (1963), Principles of Numerical Taxonomy, W. H. Freeman and Co., San Francisco.
dist for compatibility information, and
pr_DB for the proximity data base.
### show available proximities summary(pr_DB) ### get more information about a particular one pr_DB$get_entry("Jaccard") ### binary data x <- matrix(sample(c(FALSE, TRUE), 8, rep = TRUE), ncol = 2) dist(x, method = "Jaccard") ### for real-valued data dist(x, method = "eJaccard") ### for positive real-valued data dist(x, method = "fJaccard") ### cross distances dist(x, x, method = "Jaccard") ### pairwise (diagonal) dist(x, x, method = "Jaccard", pairwise = TRUE) ### this is the same but less efficient as.matrix(stats::dist(x, method = "binary")) ### numeric data x <- matrix(rnorm(16), ncol = 4) ## test inheritance of names rownames(x) <- LETTERS[1:4] colnames(x) <- letters[1:4] dist(x) dist(x, x) ## custom distance function f <- function(x, y) sum(x * y) dist(x, f) ## working with lists z <- unlist(apply(x, 1, list), recursive = FALSE) (d <- dist(z)) dist(z, z) ## subsetting d[[1:2]] subset(d, c(1,3,4)) d[[c(1,2,2)]] # duplicate index gets ignored ## transformations and self-proximities as.matrix(as.simil(d, function(x) exp(-x)), diag = 1) ## row and column indexes row.dist(d) col.dist(d)### show available proximities summary(pr_DB) ### get more information about a particular one pr_DB$get_entry("Jaccard") ### binary data x <- matrix(sample(c(FALSE, TRUE), 8, rep = TRUE), ncol = 2) dist(x, method = "Jaccard") ### for real-valued data dist(x, method = "eJaccard") ### for positive real-valued data dist(x, method = "fJaccard") ### cross distances dist(x, x, method = "Jaccard") ### pairwise (diagonal) dist(x, x, method = "Jaccard", pairwise = TRUE) ### this is the same but less efficient as.matrix(stats::dist(x, method = "binary")) ### numeric data x <- matrix(rnorm(16), ncol = 4) ## test inheritance of names rownames(x) <- LETTERS[1:4] colnames(x) <- letters[1:4] dist(x) dist(x, x) ## custom distance function f <- function(x, y) sum(x * y) dist(x, f) ## working with lists z <- unlist(apply(x, 1, list), recursive = FALSE) (d <- dist(z)) dist(z, z) ## subsetting d[[1:2]] subset(d, c(1,3,4)) d[[c(1,2,2)]] # duplicate index gets ignored ## transformations and self-proximities as.matrix(as.simil(d, function(x) exp(-x)), diag = 1) ## row and column indexes row.dist(d) col.dist(d)
Registry containing similarities and distances.
pr_DB pr_DB$get_field(name) pr_DB$get_fields() pr_DB$get_field_names() pr_DB$set_field(name, default = NA, type = NA, is_mandatory = FALSE, is_modifiable = TRUE, validity_FUN = NULL) pr_DB$entry_exists(name) pr_DB$get_entry(name) pr_DB$get_entries(name = NULL, pattern = NULL) pr_DB$get_entry_names(name) pr_DB$set_entry(...) pr_DB$modify_entry(...) pr_DB$delete_entry(name) ## S3 method for class 'pr_DB' summary(object, verbosity = c("short", "long"), ...)pr_DB pr_DB$get_field(name) pr_DB$get_fields() pr_DB$get_field_names() pr_DB$set_field(name, default = NA, type = NA, is_mandatory = FALSE, is_modifiable = TRUE, validity_FUN = NULL) pr_DB$entry_exists(name) pr_DB$get_entry(name) pr_DB$get_entries(name = NULL, pattern = NULL) pr_DB$get_entry_names(name) pr_DB$set_entry(...) pr_DB$modify_entry(...) pr_DB$delete_entry(name) ## S3 method for class 'pr_DB' summary(object, verbosity = c("short", "long"), ...)
name |
character string representing the name of an entry (case-insensitive). |
pattern |
regular expression to be matched to all fields of class
|
default |
optional default value for the field. |
type |
optional character string specifying the class to be
required for this field. If |
is_mandatory |
logical specifying whether new entries are required to have a value for this field. |
is_modifiable |
logical specifying whether entries can be changed with respect to that field. |
validity_FUN |
optional function or character string with the name of a function that checks the validity of a field entry. Such a function gets the value to be investigated as argument, and should stop with an error message if the value is not correct. |
object |
a registry object. |
verbosity |
controlling the verbosity of the output of the
summary method for the registry. |
... |
for |
pr_DB represents the registry of all proximity measures
available. For each
measure, it comprises meta-information that can be queried and
extended. Also, new measures can be added. This is done using
the following accessor functions of the pr_DB object:
get_field_names() returns a character
vector with all field names. get_field() returns the information
for a specific field as a list with components named as described
above. get_fields() returns a list with all field
entries. set_field() is used to create new fields in the
repository (the default value will be set in all
entries).
get_entry_names() returns a character vector with (the first
alias of) all entries. entry_exists() is a predicate checking
if an entry with the specified alias exists in the
registry. get_entry() returns the specified entry if it exists (and, by
default, gives an error if it does not). get_entries() is used to
query more than one entry: either those matching name exactly, or
those where the regular expression in pattern matches any
character field in an entry. By default, all values are
returned. delete_entry removes an existing entry from the
registry (note that only user-provided entries can be deleted).
set_entry and modify_entry require a named list
of arguments used as field entries.
At least the names index field is required. set_entry
will check for all other mandatory fields. If specified in the field
meta data, each field entry and the entry as a whole is checked for
validity. Note that only user-specified fields and/or entries can be
modified, the data shipped with the package are read-only.
The registry fields currently available are as follows:
Function to register (see below).
Character vector with an alias(es) for the measure.
Optional function (or function name) for preprocessing code (see below).
Optional function (or function name) for postprocessing code (see below).
logical indicating whether this measure is a distance (TRUE)
or similarity (FALSE).
Optional Function or function name for converting between similarities and distances when needed.
Optional, the scale the measure applies to
("metric", "ordinal", "nominal",
"binary", or "other"). If
NULL, it is assumed to apply to some other unknown scale.
logical indicating whether FUN is just a measure,
and therefore, if dist shall do the loop over all pairs of
observations/variables, or if FUN does the loop on its own.
C_FUNlogical indicating whether FUN is a C function.
logical; if TRUE and binary data (or data to be
interpreted as such) are supplied, the number of concordant and
discordant pairs is precomputed for every two binary data vectors and
supplied to the measure function.
Optional character string with the symbolic representation of the formula.
Optional reference (character).
Optional description (character). Ideally, describes the context in which the measure can be applied.
A function specified as FUN parameter has mandatory arguments
x and y (if abcd is FALSE), and a,
b, c, d, n otherwise. Additionally, it gets
all optional parameters specified by the user in the ...
argument of the dist and simil functions, possibly
changed and/or complemented by the corresponding (optional)
PREFUN function. It must return the
(diss-)similarity value computed from the arguments.
x and y are two vectors from the
data matrix (matrices) supplied. If abcd is FALSE, it is
assumed that binary measures will be used, and the number of all
n concordant and discordant pairs (x_k, y_k)
precomputed and supplied instead of x and
y. a, b, c, and d are the counts of
all (TRUE, TRUE), (TRUE, FALSE), (FALSE, TRUE), and (FALSE, FALSE)
pairs, respectively.
A function specified as PREFUN parameter has mandatory arguments
x, y, p, and reg_entry, with y and
p possibly being NULL depending on the task at
hand. x and y are the data objects, p is a
(possibly empty) list with all specified proximity parameters, and
reg_entry is the registry entry (a named list containing all
information specified in reg_add).
The preprocessing function is allowed to change all these
information, and if so, is required to return *all* arguments
as a named list in the same order.
A function specified as POSTFUN parameter has two mandatory
arguments: result and p. result will contain the
computed raw data, i.e. a vector of length for
auto-distances (see dist for details on
dist objects), or a matrix for cross-distances. p contains
the specified proximity parameters. Post-processing functions need to
return the result object (even if unmodified).
A function specified as convert parameter should preserve the
type of its argument.
David Meyer [email protected]
## create a new distance measure mydist <- function(x,y) x * y ## create a new entry in the registry with two aliases pr_DB$set_entry(FUN = mydist, names = c("test", "mydist")) ## look it up (index is case insensitive): pr_DB$get_entry("TEST") ## modify the content of the description field in the new entry pr_DB$modify_entry(names = "test", description = "foo function") ## create a new field pr_DB$set_field("New") ## look up the test entry again (two ways) pr_DB$get_entry("test") pr_DB[["test"]] ## show total number of entries length(pr_DB) ## show all entries (short list) pr_DB$get_entries(pattern = "foo") ## show more details summary(pr_DB, "long") ## get all entries in a list (and extract first two ones) pr_DB$get_entries()[1:2] ## get all entries as a data frame (select first 3 fields) as.data.frame(pr_DB)[,1:3] ## delete test entry pr_DB$delete_entry("test") ## check if it is really gone pr_DB$entry_exists("test")## create a new distance measure mydist <- function(x,y) x * y ## create a new entry in the registry with two aliases pr_DB$set_entry(FUN = mydist, names = c("test", "mydist")) ## look it up (index is case insensitive): pr_DB$get_entry("TEST") ## modify the content of the description field in the new entry pr_DB$modify_entry(names = "test", description = "foo function") ## create a new field pr_DB$set_field("New") ## look up the test entry again (two ways) pr_DB$get_entry("test") pr_DB[["test"]] ## show total number of entries length(pr_DB) ## show all entries (short list) pr_DB$get_entries(pattern = "foo") ## show more details summary(pr_DB, "long") ## get all entries in a list (and extract first two ones) pr_DB$get_entries()[1:2] ## get all entries as a data frame (select first 3 fields) as.data.frame(pr_DB)[,1:3] ## delete test entry pr_DB$delete_entry("test") ## check if it is really gone pr_DB$entry_exists("test")
Compute the row (column) sums or means for a sparse symmetric (distance) matrix.
rowSums.dist(x, na.rm = FALSE) rowMeans.dist(x, na.rm = FALSE, diag = TRUE) colSums.dist(x, na.rm = FALSE) colMeans.dist(x, na.rm = FALSE, diag = TRUE)rowSums.dist(x, na.rm = FALSE) rowMeans.dist(x, na.rm = FALSE, diag = TRUE) colSums.dist(x, na.rm = FALSE) colMeans.dist(x, na.rm = FALSE, diag = TRUE)
x |
an object of class |
na.rm |
logical, should missing values (including |
diag |
logical, should the diagonal elements be included in the computation? |
These functions are more efficient than expanding an object of
class dist to matrix and using rowSums or rowMeans.
colSums and colMeans are provided for convenience.
However, note that due to symmetry the result is always the
same as for rowSums or rowMeans.
A numeric vector of row sums.
Christian Buchta
as.matrix, as.dist, and rowSums.
## x <- matrix(runif(10*2),ncol=2) d <- dist(x) rowSums(as.matrix(d)) rowSums.dist(d) # the same rowMeans(as.matrix(d)) rowMeans.dist(d) # the same rowMeans.dist(d, diag = FALSE) # not the same ## NAs d[3] <- NA rowSums.dist(d, na.rm = TRUE) rowMeans.dist(d, na.rm = TRUE)## x <- matrix(runif(10*2),ncol=2) d <- dist(x) rowSums(as.matrix(d)) rowSums.dist(d) # the same rowMeans(as.matrix(d)) rowMeans.dist(d) # the same rowMeans.dist(d, diag = FALSE) # not the same ## NAs d[3] <- NA rowSums.dist(d, na.rm = TRUE) rowMeans.dist(d, na.rm = TRUE)