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Inconsistency coefficient

`Y = inconsistent(Z)Y = inconsistent(Z,d)`

`Y = inconsistent(Z)` computes
the inconsistency coefficient for each link of the hierarchical cluster
tree `Z`, where `Z` is
an (*m-*1)-by-3 matrix generated by the `linkage` function. The inconsistency
coefficient characterizes each link in a cluster tree by comparing
its height with the average height of other links at the same level
of the hierarchy. The higher the value of this coefficient, the less
similar the objects connected by the link.

`Y = inconsistent(Z,d)` computes
the inconsistency coefficient for each link in the hierarchical cluster
tree `Z` to depth `d`, where `d` is
an integer denoting the number of levels of the cluster tree that
are included in the calculation. By default, `d=2`.

The output, `Y`, is an (*m-*1)-by-4
matrix formatted as follows.

Column | Description |
---|---|

1 | Mean of the heights of all the links included in the calculation. |

2 | Standard deviation of the heights of all the links included in the calculation. |

3 | Number of links included in the calculation. |

4 | Inconsistency coefficient. |

For each link, *k*, the inconsistency
coefficient is calculated as:

For leaf nodes, nodes that have no further nodes under them, the inconsistency coefficient is set to 0.

[1] Jain, A., and R. Dubes. *Algorithms
for Clustering Data*. Upper Saddle River, NJ: Prentice-Hall,
1988.

[2] Zahn, C. T. "Graph-theoretical
methods for detecting and describing Gestalt clusters." *IEEE
Transactions on Computers*. Vol. C-20, Issue 1, 1971, pp.
68–86.

`cluster` | `clusterdata` | `cophenet` | `dendrogram` | `linkage` | `pdist` | `squareform`

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