ser_permutation_vector function

Class ser_permutation_vector -- A Single Permutation Vector for Seriation

The class ser_permutation_vector

represents a single permutation vector.

ser_permutation_vector(x, method = NULL)

## S3 method for class 'ser_permutation_vector'
c(..., recursive = FALSE)

## S3 method for class 'ser_permutation_vector'
rev(x)

get_method(x, printable = FALSE)

## S3 method for class 'ser_permutation_vector'
length(x)

## S3 method for class 'ser_permutation_vector'
print(x, ...)

## S3 method for class 'ser_permutation_vector'
summary(object, ...)

Arguments

• x, object: an object if class ser_permutation_vector. Options for the constructor are: (1) an integer permutation vector, (2) an object of class hclust , (3) a numeric vector with a MDS configuration, or (4) NA to indicate a identity permutation.
• method: a string representing the method used to obtain the permutation vector.
• ...: further arguments.
• recursive: ignored
• printable: a logical; prints "unknown" instead of NULL for non-existing methods.

Returns

The constructor ser_permutation_vector() returns an object a ser_permutation_vector

Details

A permutation vector maps a set of $n$ objects ${O_1, O_2, ..., O_n}$ onto itself.

Ordering Representation:

In seriation we represent a permutation $\pi$

as a vector which lists the objects' indices in their permuted order. This can be seen as replacing the object in position $i$ with the object in position $\pi(i)$. For example, the permutation vector $<3, 1, 2>$ indicates that in first position is the object with index 3 then the object with index 1 and finally the object with index 2. This representation is often called a (re)arrangement or ordering. The ordering can be extracted from a permutation vector object via get_order(). Such an ordering can be directly used to subset the list of original objects with "[" to apply the permutation.

Rank Representation:

An alternative way to specify a permutation is via a list of the ranks of the objects after permutation. This representation is often called a map or substitution. Ranks can be extracted from a permutation vector using get_rank().

Permutation Matrix:

Another popular representation is a permutation matrix which performs permutations using matrix multiplication. A permutation matrix can be obtained using get_permutation_matrix().

ser_permutation_vector objects are usually packed into a ser_permutation object which is a collection (a list) of $k$ permutation vectors for $k$-mode data.

The constructor ser_permutation_vector()

checks if the permutation vector is valid (i.e. if all integers occur exactly once).

Examples

o <- structure(sample(10), names = paste0("X", 1:10))
o

p <- ser_permutation_vector(o, "random")
p

## some methods
length(p)
get_method(p)
get_order(p)
get_rank(p)
get_permutation_matrix(p)

r <- rev(p)
r
get_order(r)

## create a symbolic identity permutation vector (with unknown length)
## Note: This can be used to permute an object, but methods
##       like length and get_order are not available.
ip <- ser_permutation_vector(NA)
ip

See Also

Other permutation: get_order(), permutation_vector2matrix(), permute(), ser_dist(), ser_permutation()

Author(s)

Michael Hahsler