Dendrogram using pandas and scipy

Question

I wish to generate a dendrogram based on correlation using pandas and scipy. I use a dataset (as a DataFrame) consisting of returns, which is of size n x m, where n is the number of dates and m the number of companies. Then I simply run the script

import pandas as pd
import matplotlib.pyplot as plt
from scipy.cluster import hierarchy as hc
import numpy as np

m = 5
dates = pd.date_range('2013-01-01', periods=365)
random_matrix = np.random.normal(0, 0.01, size=(len(dates), m))
dataframe = pd.DataFrame(data=random_matrix, index=dates)

z = hc.linkage(dataframe.values.T, method='average', metric='correlation')
dendrogram = hc.dendrogram(z, labels=dataframe.columns)
plt.show()

and I get a nice dendrogram. Now, the thing is that I'd also like to use other correlation measures apart from just ordinary Pearson correlation, which is a feature that's incorporated in pandas by simply invoking DataFrame.corr(method='<method>'). So, I thought at first that it was to simply run the following code

import pandas as pd
import matplotlib.pyplot as plt
from scipy.cluster import hierarchy as hc
import numpy as np

m = 5
dates = pd.date_range('2013-01-01', periods=365)
random_returns = np.random.normal(0, 0.01, size=(len(dates), m))

dataframe = pd.DataFrame(data=random_returns, index=dates)
corr = dataframe.corr() 

z = hc.linkage(corr.values, method='average')
dendrogram = hc.dendrogram(z, labels=corr.columns)
plt.show()

However, if I do this I get strange values on the y-axis as the maximum value > 1.4. Whereas if I run the first script it's about 1. What am I doing wrong? Am I using the wrong metric in hc.linkage?

EDIT I might add that the shape of the dendrogram is exactly the same. Do I have to normalize the third column of the resulting z with the maximum value?

Answer 1

Found the solution. If you have already calculated a distance matrix (be it correlation or whatever), you simply have to condense the matrix using distance.squareform. That is,

dataframe = pd.DataFrame(data=random_returns, index=dates)
corr = 1 - dataframe.corr() 

corr_condensed = hc.distance.squareform(corr) # convert to condensed
z = hc.linkage(corr_condensed, method='average')
dendrogram = hc.dendrogram(z, labels=corr.columns)
plt.show()