naginterfaces.library.mv.cluster_​hier_​indicator

naginterfaces.library.mv.cluster_hier_indicator(cd, iord, dord, k, dlevel)

cluster_hier_indicator computes a cluster indicator variable from the results of cluster_hier().

For full information please refer to the NAG Library document for g03ej

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g03/g03ejf.html

Parameters

cdfloat, array-like, shape $(n-1)$

The clustering distances in increasing order as returned by cluster_hier().

iordint, array-like, shape $\left(n\right)$

The objects in dendrogram order as returned by cluster_hier().

dordfloat, array-like, shape $\left(n\right)$

The clustering distances corresponding to the order in $iord$.

kint

Indicates if a specified number of clusters is required.

If $k>0$ then cluster_hier_indicator will attempt to find $k$ clusters.

If $k\le 0$ then cluster_hier_indicator will find the clusters based on the distance given in $dlevel$.

dlevelfloat

If $k\le 0$, $dlevel$ must contain the distance at which clusters are produced. Otherwise $dlevel$ need not be set.

Returns

kint

The number of clusters produced, $k$.

dlevelfloat

If $k>0$ on entry, $dlevel$ contains the distance at which the required number of clusters are found. Otherwise $dlevel$ remains unchanged.

icint, ndarray, shape $\left(n\right)$

$ic[\text{i}-1]$ indicates to which of $k$ clusters the $\text{i}$th object belongs, for $\text{i}=1,2,\dots ,n$.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 2$.

(errno $1$)

On entry, $k<0$ and $dlevel\le 0.0$.

(errno $1$)

On entry, $k=⟨value⟩$ and $n=⟨value⟩$.

Constraint: $k\le n$.

(errno $2$)

On entry the values of $dord$ and $cd$ are not compatible.

(errno $2$)

On entry the values of $cd$ are not in increasing order.

Warns

NagAlgorithmicWarning

(errno $3$)

No clustering is performed when $k=n$.

(errno $3$)

All data is merged when $k=1$.

(errno $3$)

All data merged into one cluster at $dlevel$, $dlevel=⟨value⟩$.

(errno $3$)

No clustering takes place below $dlevel$, $dlevel=⟨value⟩$.

(errno $4$)

The precise number of clusters requested is not possible because of tied clustering distances.

Notes

In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.

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 cluster_hier()), 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. cluster_hier_indicator takes the information from the tree and produces the clusters that exist at a given distance. This is equivalent to taking the dendrogram (see cluster_hier_dendrogram()) 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 cluster_hier_indicator 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 $1$.

References

Everitt, B S, 1974, Cluster Analysis, Heinemann

Krzanowski, W J, 1990, Principles of Multivariate Analysis, Oxford University Press