Most efficient way to construct similarity matrix

Question

I'm using the following links to create a "Euclidean Similarity Matrix" (that I convert to a DataFrame). https://stats.stackexchange.com/questions/53068/euclidean-distance-score-and-similarity http://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.spatial.distance.euclidean.html

The way I'm doing it is an iterative approach which works but it takes a while when the datasets are big. The pandas pd.DataFrame.corr() is really fast and useful for pearson correlations.

How can I perform a Euclidean Similarity measure w/o exhaustive iteration?

My naive code below:

#Euclidean Similarity

#Create DataFrame
DF_var = pd.DataFrame.from_dict({"s1":[1.2,3.4,10.2],"s2":[1.4,3.1,10.7],"s3":[2.1,3.7,11.3],"s4":[1.5,3.2,10.9]}).T
DF_var.columns = ["g1","g2","g3"]
#      g1   g2    g3
# s1  1.2  3.4  10.2
# s2  1.4  3.1  10.7
# s3  2.1  3.7  11.3
# s4  1.5  3.2  10.9

#Create empty matrix to fill
M_euclid = np.zeros((DF_var.shape[1],DF_var.shape[1]))

#Iterate through DataFrame columns to measure euclidean distance
for i in range(DF_var.shape[1]):
    u = DF_var[DF_var.columns[i]]
    for j in range(DF_var.shape[1]):
        v = DF_var[DF_var.columns[j]]
        #Euclidean distance -> Euclidean similarity
        M_euclid[i,j] = (1/(1+sp.spatial.distance.euclidean(u,v)))
DF_euclid = pd.DataFrame(M_euclid,columns=DF_var.columns,index=DF_var.columns)

#           g1        g2        g3
# g1  1.000000  0.215963  0.051408
# g2  0.215963  1.000000  0.063021
# g3  0.051408  0.063021  1.000000

Answer 1

There are two useful function within scipy.spatial.distance that you can use for this: pdist and squareform. Using pdist will give you the pairwise distance between observations as a one-dimensional array, and squareform will convert this to a distance matrix.

One catch is that pdist uses distance measures by default, and not similarity, so you'll need to manually specify your similarity function. Judging by the commented output in your code, your DataFrame is also not in the orientation pdist expects, so I've undone the transpose you did in your code.

import pandas as pd
from scipy.spatial.distance import euclidean, pdist, squareform


def similarity_func(u, v):
    return 1/(1+euclidean(u,v))

DF_var = pd.DataFrame.from_dict({"s1":[1.2,3.4,10.2],"s2":[1.4,3.1,10.7],"s3":[2.1,3.7,11.3],"s4":[1.5,3.2,10.9]})
DF_var.index = ["g1","g2","g3"]

dists = pdist(DF_var, similarity_func)
DF_euclid = pd.DataFrame(squareform(dists), columns=DF_var.index, index=DF_var.index)

Answer 2

You want scipy.spatial.distance.pdist or sklearn.metrics.pairwise.pairwise_distances