NAG Library Function Document

nag_mv_cluster_indicator (g03ejc)

void	nag_mv_cluster_indicator (Integer n, const double cd[], const Integer iord[], const double dord[], Integer k, double dlevel, Integer ic[], NagError *fail)

3 Description

Given a distance or dissimilarity matrix for

n

objects, cluster analysis aims to group the

n

objects into a number of more or less homogeneous groups or clusters. With agglomerative clustering methods (see nag_mv_hierar_cluster_analysis (g03ecc)), a hierarchical tree is produced by starting with

n

clusters each with a single object and then at each of

n - 1

stages, merging two clusters to form a larger cluster until all objects are in a single cluster. nag_mv_cluster_indicator (g03ejc) takes the information from the tree and produces the clusters that exist at a given distance. This is equivalent to taking the dendrogram (see nag_mv_dendrogram (g03ehc)) and drawing a line across at a given distance to produce clusters.

As an alternative to giving the distance at which clusters are required, you can specify the number of clusters required and nag_mv_cluster_indicator (g03ejc) will compute the corresponding distance. However, it may not be possible to compute the number of clusters required due to ties in the distance matrix.

If there are

k

clusters then the indicator variable will assign a value between 1 and

k

to each object to indicate to which cluster it belongs. Object 1 always belongs to cluster 1.

4 References

Everitt B S (1974) Cluster Analysis Heinemann

Krzanowski W J (1990) Principles of Multivariate Analysis Oxford University Press

5 Arguments

1: n – IntegerInput

On entry: the number of objects,

n

Constraint:

n \geq 2

2: cd[ $n - 1$ ] – const doubleInput

On entry: the clustering distances in increasing order as returned by nag_mv_hierar_cluster_analysis (g03ecc).

Constraint:

cd [i] \geq cd [i - 1]

, for

i = 1, 2, \dots, n - 2

3: iord[n] – const IntegerInput

On entry: the objects in the dendrogram order as returned by nag_mv_hierar_cluster_analysis (g03ecc).

4: dord[n] – const doubleInput

On entry: the clustering distances corresponding to the order in iord.

5: k – Integer *Input/Output

On entry: indicates if a specified number of clusters is required.

$k > 0$: nag_mv_cluster_indicator (g03ejc) will attempt to find k clusters.
$k \leq 0$: nag_mv_cluster_indicator (g03ejc) will find the clusters based on the distance given in dlevel.

Constraint:

k \leq n

On exit: the number of clusters produced,

k

6: dlevel – double *Input/Output

On entry: if

k \leq 0

, then dlevel must contain the distance at which clusters are produced. Otherwise dlevel need not be set.

Constraint: if

k \leq 0

dlevel > 0.0

On exit: if

k > 0

on entry, then dlevel contains the distance at which the required number of clusters are found. Otherwise dlevel remains unchanged.

7: ic[n] – IntegerOutput

On exit:

ic [i - 1]

indicates to which of

k

clusters the

i

th object belongs, for

i = 1, 2, \dots, n

8: fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_2_INT_ARG_GT: On entry, $k = ⟨value⟩$ while $n = ⟨value⟩$ . These arguments must satisfy $k \leq n$ .
NE_CLUSTER: The precise number of clusters requested is not possible because of
tied clustering distances. The actual number of clusters produced is $⟨value⟩$ .
NE_INCOMP_ARRAYS: Arrays cd and dord are not compatible.
NE_INT_ARG_LT: On entry, $n = ⟨value⟩$ .
Constraint: $n \geq 2$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_NOT_INCREASING: The sequence cd is not increasing:
$cd [⟨value⟩] = ⟨value⟩$ , $cd [⟨value⟩] = ⟨value⟩$ .
NE_REAL_INT: On entry, $dlevel = ⟨value⟩$ , $k = ⟨value⟩$ .
Constraint: $k \leq 0$ and $dlevel > 0.0$ .
NW_2_INT: On exit, $k = ⟨value⟩$ , $n = ⟨value⟩$ .
Trivial solution returned.
NW_INT: On exit, $k = 1$ .
Trivial solution returned.
NW_REAL_REALARR: On entry, $dlevel = ⟨value⟩$ , $cd [⟨value⟩] = ⟨value⟩$ .
Trivial solution returned.

7 Accuracy

The accuracy will depend upon the accuracy of the distances in cd and dord (see nag_mv_hierar_cluster_analysis (g03ecc)).

8 Parallelism and Performance

Not applicable.

9 Further Comments

A fixed number of clusters can be found using the non-hierarchical method used in nag_mv_kmeans_cluster_analysis (g03efc).

10 Example

Data consisting of three variables on five objects are input. Euclidean squared distances are computed using nag_mv_distance_mat (g03eac) and median clustering performed using nag_mv_hierar_cluster_analysis (g03ecc). A dendrogram is produced by nag_mv_dendrogram (g03ehc) and printed. nag_mv_cluster_indicator (g03ejc) finds two clusters and the results are printed.

NAG Library Function Documentnag_mv_cluster_indicator (g03ejc)

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG Library Function Document

nag_mv_cluster_indicator (g03ejc)