def _hierarchical_clustering_herc(self,
linkage="ward",
max_k=10,
leaf_order=True):
# hierarchcial clustering
dist = np.sqrt((1 - self.corr).round(8) / 2)
dist = pd.DataFrame(dist,
columns=self.corr.columns,
index=self.corr.index)
p_dist = squareform(dist, checks=False)
clustering = hr.linkage(p_dist,
method=linkage,
optimal_ordering=leaf_order)
# optimal number of clusters
k = af.two_diff_gap_stat(self.corr, dist, clustering, max_k)
return clustering, k
def assets_clusters(returns,
correlation="pearson",
linkage="ward",
k=None,
max_k=10,
leaf_order=True):
r"""
Create asset classes based on hierarchical clustering.
Parameters
----------
returns : DataFrame
Assets returns.
correlation : str can be {'pearson', 'spearman' or 'distance'}.
The correlation matrix used for create the clusters.
The default is 'pearson'. Posible values are:
- 'pearson': pearson correlation matrix.
- 'spearman': spearman correlation matrix.
- 'abs_pearson': absolute value pearson correlation matrix.
- 'abs_spearman': absolute value spearman correlation matrix.
- 'distance': distance correlation matrix.
linkage : string, optional
Linkage method of hierarchical clustering, see `linkage <https://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.linkage.html?highlight=linkage#scipy.cluster.hierarchy.linkage>`_ for more details.
The default is 'single'. Posible values are:
- 'single'.
- 'complete'.
- 'average'.
- 'weighted'.
- 'centroid'.
- 'median'.
- 'ward'.
k : int, optional
Number of clusters. This value is took instead of the optimal number
of clusters calculated with the two difference gap statistic.
The default is None.
max_k : int, optional
Max number of clusters used by the two difference gap statistic
to find the optimal number of clusters. The default is 10.
leaf_order : bool, optional
Indicates if the cluster are ordered so that the distance between
successive leaves is minimal. The default is True.
Returns
-------
clusters : DataFrame
A dataframe with asset classes based on hierarchical clustering.
Raises
------
ValueError when the value cannot be calculated.
Examples
--------
::
clusters = cf.assets_clusters(returns, correlation='pearson', linkage='ward', k=None, max_k=10, leaf_order=True)
The clusters dataframe looks like this:
.. image:: images/clusters_df.png
"""
if not isinstance(returns, pd.DataFrame):
raise ValueError("returns must be a DataFrame")
# Correlation matrix from covariance matrix
if correlation in {"pearson", "spearman"}:
corr = returns.corr(method=correlation)
if correlation in {"abs_pearson", "abs_spearman"}:
corr = np.abs(returns.corr(method=correlation[4:]))
elif correlation == "distance":
corr = af.dcorr_matrix(returns)
# hierarchcial clustering
dist = np.sqrt((1 - corr).round(8) / 2)
dist = pd.DataFrame(dist, columns=corr.columns, index=corr.index)
p_dist = squareform(dist, checks=False)
clustering = hr.linkage(p_dist,
method=linkage,
optimal_ordering=leaf_order)
if k is None:
# optimal number of clusters
k = af.two_diff_gap_stat(corr, dist, clustering, max_k)
clusters_inds = hr.fcluster(clustering, k, criterion="maxclust")
clusters = {"Assets": [], "Clusters": []}
for i, v in enumerate(clusters_inds):
clusters["Assets"].append(corr.columns.tolist()[i])
clusters["Clusters"].append("Cluster " + str(v))
clusters = pd.DataFrame(clusters)
clusters = clusters.sort_values(by=["Assets"])
return clusters