Various distance and similarity measures in python. Updated version will include implementation of metrics in 'Comprehensive Survey on Distance/Similarity Measures between Probability Density Functions' by Sung-Hyuk Cha
import numpy as np
class Distance(object):
def braycurtis(self, a, b):
return np.sum(np.fabs(a - b)) / np.sum(np.fabs(a + b))
def canberra(self, a, b):
return np.sum(np.fabs(a - b) / (np.fabs(a) + np.fabs(b)))
def chebyshev(self, a, b):
return np.amax(a - b)
def cityblock(self, a, b):
return self.manhattan(a, b)
def correlation(self, a, b):
a = a - np.mean(a)
b = b - np.mean(b)
return 1.0 - np.mean(a * b) / np.sqrt(np.mean(np.square(a)) * np.mean(np.square(b)))
def cosine(self, a, b):
return 1 - np.dot(a, b) / (np.sqrt(np.dot(a, a)) * np.sqrt(np.dot(b, b)))
def dice(self, a, b):
nft = ((1 - a) * b).sum()
ntf = (a * (1 - b)).sum()
ntt = (a * b).sum()
return float((ntf + nft) / np.array(2.0 * ntt + ntf + nft))
def euclidean(self, a, b):
return np.sqrt(np.sum(np.dot((a - b), (a - b))))
def hamming(self, a, b, w = None):
if w is None:
w = np.ones(a.shape[0])
return np.average(a != b, weights = w)
def jaccard(self, u, v):
return np.double(np.bitwise_and((u != v), np.bitwise_or(u != 0, v != 0)).sum()) / np.double(np.bitwise_or(u != 0, v != 0).sum())
def kulsinski(self, a, b):
nft = ((1 - a) * b).sum()
ntf = (a * (1 - b)).sum()
ntt = (a * b).sum()
return (ntf + nft - ntt + len(a)) / (ntf + nft + len(a))
def mahalanobis(self, a, b, vi):
return np.sqrt(np.dot(np.dot((a - b), vi),(a - b).T))
def manhattan(self, a, b):
return np.sum(np.fabs(a - b))
def matching(self, a, b):
return self.hamming(a, b)
def minkowski(self, a, b, p):
return np.power(np.sum(np.power(np.fabs(a - b), p)), 1 / p)
def rogerstanimoto(self, a, b):
nff = ((1 - a) * (1 - b)).sum()
nft = ((1 - a) * b).sum()
ntf = (a * (1 - b)).sum()
ntt = (a * b).sum()
return float(2.0 * (ntf + nft)) / float(ntt + nff + (2.0 * (ntf + nft)))
def russellrao(self, a, b):
return float(len(a) - (a * b).sum()) / len(a)
def seuclidean(self, a, b, V):
return np.sqrt(np.sum((a - b) ** 2 / V))
def sokalmichener(self, a, b):
nff = ((1 - a) * (1 - b)).sum()
nft = ((1 - a) * b).sum()
ntf = (a * (1 - b)).sum()
ntt = (a * b).sum()
return float(2.0 * (ntf + nft)) / float(ntt + nff + 2.0 * (ntf + nft))
def sokalsneath(self, a, b):
nft = ((1 - a) * b).sum()
ntf = (a * (1 - b)).sum()
ntt = (a * b).sum()
return float(2.0 * (ntf + nft)) / np.array(ntt + 2.0 * (ntf + nft))
def sqeuclidean(self, a, b):
return np.sum(np.dot((a - b), (a - b)))
def wminkowski(self, a, b, p, w):
return np.power(np.sum(np.power(np.fabs(w * (a - b)), p)), 1 / p)
def yule(self, a, b):
nff = ((1 - a) * (1 - b)).sum()
nft = ((1 - a) * b).sum()
ntf = (a * (1 - b)).sum()
ntt = (a * b).sum()
return float(2.0 * ntf * nft / np.array(ntt * nff + ntf * nft))
def main():
from scipy.spatial import distance
a = np.array([1, 2, 43])
b = np.array([3, 2, 1])
d = Distance()
print('-----------------------------------------------------------------')
print('My braycurtis: {}'.format(d.braycurtis(a, b)))
print('SciPy braycurtis: {}'.format(distance.braycurtis(a, b)))
print('-----------------------------------------------------------------')
print('My canberra: {}'.format(d.canberra(a, b)))
print('SciPy canberra: {}'.format(distance.canberra(a, b)))
print('-----------------------------------------------------------------')
print('My chebyshev: {}'.format(d.chebyshev(a, b)))
print('SciPy chebyshev: {}'.format(distance.chebyshev(a, b)))
print('-----------------------------------------------------------------')
print('My cityblock: {}'.format(d.cityblock(a, b)))
print('SciPy cityblock: {}'.format(distance.cityblock(a, b)))
print('-----------------------------------------------------------------')
print('My correlation: {}'.format(d.correlation(a, b)))
print('SciPy correlation: {}'.format(distance.correlation(a, b)))
print('-----------------------------------------------------------------')
print('My euclidean: {}'.format(d.euclidean(a, b)))
print('SciPy euclidean: {}'.format(distance.euclidean(a, b)))
print('-----------------------------------------------------------------')
print('My hamming: {}'.format(d.hamming(a, b)))
print('SciPy hamming: {}'.format(distance.hamming(a, b)))
print('-----------------------------------------------------------------')
print('My jaccard: {}'.format(d.jaccard(a, b)))
print('SciPy jaccard: {}'.format(distance.jaccard(a, b)))
print('-----------------------------------------------------------------')
print('My manhattan: {}'.format(d.cityblock(a, b)))
print('SciPy manhattan: {}'.format(distance.cityblock(a, b)))
print('-----------------------------------------------------------------')
print('My cosine: {}'.format(d.cosine(a, b)))
print('SciPy cosine: {}'.format(distance.cosine(a, b)))
print('-----------------------------------------------------------------')
print('My dice: {}'.format(d.dice(a, b)))
print('SciPy dice: {}'.format(distance.dice(a, b)))
print('-----------------------------------------------------------------')
print('My kulsinski: {}'.format(d.kulsinski(a, b)))
print('SciPy kulsinski: {}'.format(distance.kulsinski(a, b)))
print('-----------------------------------------------------------------')
iv = np.array([[1, 0.5, 0.5], [0.5, 1, 0.5], [0.5, 0.5, 1]])
print('My mahalanobis: {}'.format(d.mahalanobis(a, b, iv)))
print('SciPy mahalanobis: {}'.format(distance.mahalanobis(a, b, iv)))
print('-----------------------------------------------------------------')
print('My seuclidean: {}'.format(d.seuclidean(a, b, np.array([0.1, 0.1, 0.1]))))
print('SciPy seuclidean: {}'.format(distance.seuclidean(a, b, [0.1, 0.1, 0.1])))
print('-----------------------------------------------------------------')
print('My sokalmichener: {}'.format(d.sokalmichener(a, b)))
print('SciPy sokalmichener: {}'.format(distance.sokalmichener(a, b)))
print('-----------------------------------------------------------------')
print('My sokal_sneath: {}'.format(d.sokalsneath(a, b)))
print('SciPy sokal_sneath: {}'.format(distance.sokalsneath(a, b)))
print('-----------------------------------------------------------------')
print('My sqeuclidean: {}'.format(d.sqeuclidean(a, b)))
print('SciPy sqeuclidean: {}'.format(distance.sqeuclidean(a, b)))
print('-----------------------------------------------------------------')
print('My minkowski: {}'.format(d.minkowski(a, b, 2)))
print('SciPy minkowski: {}'.format(distance.minkowski(a, b, 2)))
print('-----------------------------------------------------------------')
print('My rogerstanimoto: {}'.format(d.rogerstanimoto(a, b)))
print('SciPy rogerstanimoto: {}'.format(distance.rogerstanimoto(a, b)))
print('-----------------------------------------------------------------')
print('My russellrao: {}'.format(d.russellrao(a, b)))
print('SciPy russellrao: {}'.format(distance.russellrao(a, b)))
print('-----------------------------------------------------------------')
print('My wminkowski: {}'.format(d.wminkowski(a, b, 2, np.ones(3))))
print('SciPy wminkowski: {}'.format(distance.wminkowski(a, b, 2, np.ones(3))))
print('-----------------------------------------------------------------')
print('My yule: {}'.format(d.yule(a, b)))
print('SciPy yule: {}'.format(distance.yule(a, b)))
print('-----------------------------------------------------------------')
if __name__ == '__main__':
main()-----------------------------------------------------------------
My braycurtis: 0.8461538461538461
SciPy braycurtis: 0.8461538461538461
-----------------------------------------------------------------
My canberra: 1.4545454545454546
SciPy canberra: 1.4545454545454546
-----------------------------------------------------------------
My chebyshev: 42
SciPy chebyshev: 42
-----------------------------------------------------------------
My cityblock: 44.0
SciPy cityblock: 44
-----------------------------------------------------------------
My correlation: 1.8762686682028846
SciPy correlation: 1.8762686682028846
-----------------------------------------------------------------
My euclidean: 42.04759208325728
SciPy euclidean: 42.04759208325728
-----------------------------------------------------------------
My hamming: 0.6666666666666666
SciPy hamming: 0.6666666666666666
-----------------------------------------------------------------
My jaccard: 0.6666666666666666
SciPy jaccard: 0.6666666666666666
-----------------------------------------------------------------
My manhattan: 44.0
SciPy manhattan: 44
-----------------------------------------------------------------
My cosine: 0.6896504488650589
SciPy cosine: 0.6896504488650589
-----------------------------------------------------------------
My dice: -0.9230769230769231
SciPy dice: -0.9230769230769231
-----------------------------------------------------------------
My kulsinski: 2.111111111111111
SciPy kulsinski: 2.111111111111111
-----------------------------------------------------------------
My mahalanobis: 41.036569057366385
SciPy mahalanobis: 41.036569057366385
-----------------------------------------------------------------
My seuclidean: 132.9661611087573
SciPy seuclidean: 132.9661611087573
-----------------------------------------------------------------
My sokalmichener: 2.1333333333333333
SciPy sokalmichener: 2.1333333333333333
-----------------------------------------------------------------
My sokal_sneath: 2.0869565217391304
SciPy sokal_sneath: 2.0869565217391304
-----------------------------------------------------------------
My sqeuclidean: 1768
SciPy sqeuclidean: 1768.0
-----------------------------------------------------------------
My minkowski: 42.04759208325728
SciPy minkowski: 42.04759208325728
-----------------------------------------------------------------
My rogerstanimoto: 2.1333333333333333
SciPy rogerstanimoto: 2.1333333333333333
-----------------------------------------------------------------
My russellrao: -15.666666666666666
SciPy russellrao: -15.666666666666666
-----------------------------------------------------------------
My wminkowski: 42.04759208325728
SciPy wminkowski: 42.04759208325728
-----------------------------------------------------------------
My yule: 1.5575221238938053
SciPy yule: 1.5575221238938053
-----------------------------------------------------------------