# Source code for geomstats.learning.agglomerative_hierarchical_clustering

```
"""The Agglomerative Hierarchical Clustering (AHC) on manifolds.
Lead author: Yann Cabanes.
"""
from sklearn.cluster import AgglomerativeClustering
import geomstats.backend as gs
[docs]class AgglomerativeHierarchicalClustering(AgglomerativeClustering):
"""The Agglomerative Hierarchical Clustering on manifolds.
Recursively merges the pair of clusters that minimally increases
a given linkage distance.
Parameters
----------
n_clusters : int or None, default=2
The number of clusters to find. It must be ``None`` if
``distance_threshold`` is not ``None``.
distance : str or callable, default='euclidean'
Distance used to compute the linkage. Can be 'euclidean', 'l1', 'l2',
'manhattan', 'cosine', or 'precomputed'.
If linkage is 'ward', only 'euclidean' is accepted.
If 'precomputed', a distance matrix (instead of a similarity matrix)
is needed as input for the fit method.
memory : str or object, default=None
Used to cache the output of the computation of the tree.
By default, no caching is done. If a string is given, it is the
path to the caching directory.
connectivity : array-like or callable, default=None
Connectivity matrix. Defines for each sample the neighboring
samples following a given structure of the data.
This can be a connectivity matrix itself or a callable that transforms
the data into a connectivity matrix. Default is None, i.e, the
hierarchical clustering algorithm is unstructured.
compute_full_tree : 'auto' or bool, default='auto'
Stop early the construction of the tree at n_clusters. This is useful
to decrease computation time if the number of clusters is not small
compared to the number of samples. This option is useful only when
specifying a connectivity matrix. Note also that when varying the
number of clusters and using caching, it may be advantageous to compute
the full tree. It must be ``True`` if ``distance_threshold`` is not
``None``. By default `compute_full_tree` is 'auto', which is equivalent
to `True` when `distance_threshold` is not `None` or that `n_clusters`
is inferior to the maximum between 100 or `0.02 * n_samples`.
Otherwise, 'auto' is equivalent to `False`.
linkage : {'ward', 'complete', 'average', 'single'}, default='average'
Which linkage criterion to use. The linkage criterion determines which
distance to use between sets of observation. The algorithm will merge
the pairs of cluster that minimize this criterion.
- average uses the average of the distances of each observation of
the two sets.
- complete or maximum linkage uses the maximum distances between
all observations of the two sets.
- single uses the minimum of the distances between all observations
of the two sets.
- ward minimizes the variance of the clusters being merged.
It works for the 'euclidean' distance only.
distance_threshold : float, default=None
The linkage distance threshold above which, clusters will not be
merged. If not ``None``, ``n_clusters`` must be ``None`` and
``compute_full_tree`` must be ``True``.
Attributes
----------
n_clusters_ : int
The number of clusters found by the algorithm. If
``distance_threshold=None``, it will be equal to the given
``n_clusters``.
labels_ : ndarray, shape=[...,]
Cluster labels for each point.
n_leaves_ : int
Number of leaves in the hierarchical tree.
n_connected_components_ : int
The estimated number of connected components in the graph.
children_ : array-like, shape=[n_samples-1, 2]
The children of each non-leaf node. Values less than `n_samples`
correspond to leaves of the tree which are the original samples.
A node `i` greater than or equal to `n_samples` is a non-leaf
node and has children `children_[i - n_samples]`. Alternatively
at the i-th iteration, children[i][0] and children[i][1]
are merged to form node `n_samples + i`.
References
----------
This algorithm uses the scikit-learn library:
https://github.com/scikit-learn/scikit-learn/blob/95d4f0841/sklearn/
cluster/_agglomerative.py#L656
"""
def __init__(
self,
n_clusters=2,
distance="euclidean",
memory=None,
connectivity=None,
compute_full_tree="auto",
linkage="average",
distance_threshold=None,
):
if isinstance(distance, str):
affinity = distance
else:
def affinity(data):
n_samples = data.shape[0]
affinity_matrix = gs.zeros([n_samples, n_samples])
for i_sample in range(1, n_samples):
affinity_matrix[i_sample, :i_sample] = distance(
data[i_sample, ...], data[:i_sample, ...]
).reshape(i_sample)
affinity_matrix += affinity_matrix.T
return affinity_matrix
super().__init__(
n_clusters=n_clusters,
affinity=affinity,
memory=memory,
connectivity=connectivity,
compute_full_tree=compute_full_tree,
linkage=linkage,
distance_threshold=distance_threshold,
)
```