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# Hierarchical clustering (`scipy.cluster.hierarchy`)

These functions cut hierarchical clusterings into flat clusterings or find the roots of the forest formed by a cut by providing the flat cluster ids of each observation.

`fcluster`(Z, t[, criterion, depth, R, monocrit]) | Forms flat clusters from the hierarchical clustering defined by
`fclusterdata`(X, t[, criterion, metric, ...]) | Cluster observation data using a given metric.
`leaders`(Z, T) | Returns the root nodes in a hierarchical clustering.

These are routines for agglomerative clustering.

`linkage`(y[, method, metric]) | Performs hierarchical/agglomerative clustering on the condensed distance matrix y.
`single`(y) | Performs single/min/nearest linkage on the condensed distance matrix `y`
`complete`(y) | Performs complete/max/farthest point linkage on a condensed distance matrix
`average`(y) | Performs average/UPGMA linkage on a condensed distance matrix
`weighted`(y) | Performs weighted/WPGMA linkage on the condensed distance matrix.
`centroid`(y) | Performs centroid/UPGMC linkage.
`median`(y) | Performs median/WPGMC linkage.
`ward`(y) | Performs Ward’s linkage on a condensed or redundant distance matrix.

These routines compute statistics on hierarchies.

`cophenet`(Z[, Y]) | Calculates the cophenetic distances between each observation in
`from_mlab_linkage`(Z) | Converts a linkage matrix generated by MATLAB(TM) to a new
`inconsistent`(Z[, d]) | Calculates inconsistency statistics on a linkage.
`maxinconsts`(Z, R) | Returns the maximum inconsistency coefficient for each non-singleton cluster and its descendents.
`maxdists`(Z) | Returns the maximum distance between any non-singleton cluster.
`maxRstat`(Z, R, i) | Returns the maximum statistic for each non-singleton cluster and its descendents.
`to_mlab_linkage`(Z) | Converts a linkage matrix to a MATLAB(TM) compatible one.

Routines for visualizing flat clusters.

`dendrogram`(Z[, p, truncate_mode, ...]) | Plots the hierarchical clustering as a dendrogram.

These are data structures and routines for representing hierarchies as tree objects.

`ClusterNode`(id[, left, right, dist, count]) | A tree node class for representing a cluster.
`leaves_list`(Z) | Returns a list of leaf node ids
`to_tree`(Z[, rd]) | Converts a hierarchical clustering encoded in the matrix `Z` (by

These are predicates for checking the validity of linkage and inconsistency matrices as well as for checking isomorphism of two flat cluster assignments.

`is_valid_im`(R[, warning, throw, name]) | Returns True if the inconsistency matrix passed is valid.
`is_valid_linkage`(Z[, warning, throw, name]) | Checks the validity of a linkage matrix.
`is_isomorphic`(T1, T2) | Determines if two different cluster assignments are equivalent.
`is_monotonic`(Z) | Returns `True` if the linkage passed is monotonic.
`correspond`(Z, Y) | Checks for correspondence between linkage and condensed distance matrices
`num_obs_linkage`(Z) | Returns the number of original observations of the linkage matrix passed.

Utility routines for plotting:

`set_link_color_palette`(palette) | Set list of matplotlib color codes for dendrogram color_threshold.

## References

[R1] | “Statistics toolbox.” API Reference Documentation. The MathWorks. http://www.mathworks.com/access/helpdesk/help/toolbox/stats/. Accessed October 1, 2007.

[R2] | “Hierarchical clustering.” API Reference Documentation. The Wolfram Research, Inc. http://reference.wolfram.com/mathematica/HierarchicalClustering/tutorial/ HierarchicalClustering.html. Accessed October 1, 2007.

[R3] | Gower, JC and Ross, GJS. “Minimum Spanning Trees and Single Linkage Cluster Analysis.” Applied Statistics. 18(1): pp. 54–64. 1969.

[R4] | Ward Jr, JH. “Hierarchical grouping to optimize an objective function.” Journal of the American Statistical Association. 58(301): pp. 236–44. 1963.

[R5] | Johnson, SC. “Hierarchical clustering schemes.” Psychometrika. 32(2): pp. 241–54. 1966.

[R6] | Sneath, PH and Sokal, RR. “Numerical taxonomy.” Nature. 193: pp. 855–60. 1962.

[R7] | Batagelj, V. “Comparing resemblance measures.” Journal of Classification. 12: pp. 73–90. 1995.

[R8] | Sokal, RR and Michener, CD. “A statistical method for evaluating systematic relationships.” Scientific Bulletins. 38(22): pp. 1409–38. 1958.

[R9] | Edelbrock, C. “Mixture model tests of hierarchical clustering algorithms: the problem of classifying everybody.” Multivariate Behavioral Research. 14: pp. 367–84. 1979.

[10] | Jain, A., and Dubes, R., “Algorithms for Clustering Data.” Prentice-Hall. Englewood Cliffs, NJ. 1988.

[11] | Fisher, RA “The use of multiple measurements in taxonomic problems.” Annals of Eugenics, 7(2): 179-188. 1936

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