def Sokal_Michener(original, test):
"""
Sokal and Michener Distance is distance measure for nominal or ordinal
data.
Given 2 lists (original and test), calculates the Sokal and Michener
Distance based on the formula,
1 - [(number of regions where both species are present or absent)/
(number of regions where both species are absent different)]
@see: Sokal RR, Michener CD (1958) A statistical method for evaluating
systematic relationships. Univ Kansas Sci Bull 38:1409-1438
@param original: list of original data
@param test: list of data to test against original
"""
if len(original) <> len(test):
raise DistanceInputSizeError("Size (length) of inputs must be \
equal for Sokal & Michener's distance")
in_original = 0.0
# in_test = 0.0
in_both = 0.0
for index in range(len(original)):
if original[index] == test[index]: in_both = in_both + 1
if original[index] != test[index]: in_original = in_original + 1
# if original[index] < test[index]: in_test = in_test + 1
# print in_original
return 1 - (in_both / (in_both + in_original))
def Bray_Curtis(original, test):
"""
Bray-Curtis Distance is distance measure for interval or ratio data.
@see: Bray JR and Curtis JT. 1957. An ordination of the upland forest
communities of S. Winconsin. Ecological Monographs 27: 325-349.
@param original: list of original data
@param test: list of data to test against original"""
if len(original) != len(test):
raise DistanceInputSizeError("Size (length) of inputs must be \
equal for Bray-Curtis distance")
return Manhattan(original, test) / (summation(original) + summation(test))
def Canberra(original, test):
"""
Canberra Distance is distance measure for interval or ratio data.
@see: Lance GN and Williams WT. 1966. Computer programs for hierarchical
polythetic classification. Computer Journal 9: 60-64.
@param original: list of original data
@param test: list of data to test against original"""
if len(original) != len(test):
raise DistanceInputSizeError("Size (length) of inputs must be \
equal for Canberra distance")
sum = 0
for i in range(len(original)):
sum = sum + (abs(original[i] - test[i]) / abs(original[i] + test[i]))
return sum
def Manhattan(original, test):
"""
Manhattan Distance is distance measure for interval or ratio data.
Manhattan Distance is also known as City Block Distance. It is essentially
summation of the absolute difference between each element.
@see: Krause, Eugene F. 1987. Taxicab Geometry. Dover. ISBN 0-486-25202-7.
@param original: list of original data
@param test: list of data to test against original"""
if len(original) != len(test):
raise DistanceInputSizeError("Size (length) of inputs must be \
equal for Manhattan distance")
sum = 0
for i in range(len(original)):
sum = sum + abs(original[i] - test[i])
return sum
def Minkowski(original, test, power=3):
"""
Minkowski Distance is distance measure for interval or ratio data.
Minkowski Distance is a generalized absolute form of Euclidean Distance.
Minkowski Distance = Euclidean Distance when power = 2
@param original: list of original data
@param test: list of data to test against original
@param power: expontential variable
@type power: integer"""
if len(original) != len(test):
raise DistanceInputSizeError("Size (length) of inputs must be \
equal for Minkowski distance")
sum = 0
for i in range(len(original)):
sum = sum + abs(original[i] - test[i])**power
return sum**(1 / float(power))
def Hamming(original, test):
"""
Hamming Distance is distance measure for ordinal data - only for ordered
data.
Given 2 lists (original and test), calculates the Hamming Distance by
counting the number of ordered differences between the 2 lists.
@param original: list of original data
@param test: list of data to test against original
"""
if len(original) <> len(test):
raise DistanceInputSizeError("Size (length) of inputs must be \
equal for Hamming's distance")
mismatch = 0
for index in range(len(original)):
if original[index] <> test[index]: mismatch = mismatch + 1
return mismatch
def Euclidean(original, test):
"""
Euclidean Distance is distance measure for interval or ratio data.
euclidean(original, test) -> euclidean distance between original and test
Adapted from BioPython
@param original: list of original data
@param test: list of data to test against original"""
# lightly modified from implementation by Thomas Sicheritz-Ponten.
# This works faster than the Numeric implementation on shorter
# vectors.
if len(original) != len(tst):
raise DistanceInputSizeError("Size (length) of inputs must be \
equal for Euclidean distance")
sum = 0
for i in range(len(original)):
sum = sum + (original[i] - test[i])**2
return math.sqrt(sum)