【机器学习基础】机器学习距离与相似度计算

from math import *def euclidean_distance(x, y):        return sqrt(sum(pow(a - b, 2) for a, b in zip(x, y)))print(euclidean_distance([0, 3, 4, 5], [7, 6, 3, -1]))

def normalized_euclidean(a, b):    sumnum = 0    for i in range(len(a)):        avg = (a[i] - b[i]) / 2        si = ((a[i] - avg) ** 2 + (b[i] - avg) ** 2) ** 0.5        sumnum += ((a[i] - b[i]) / si) ** 2    return sumnum ** 0.5

from math import *
def manhattan_distance(x,y):    return sum(abs(a-b) for a,b in zip(x,y))print(manhattan_distance([10,20,10],[10,20,20]))

def hamming_distance(s1, s2):    """Return the Hamming distance between equal-length sequences"""    if len(s1) != len(s2):        raise ValueError("Undefined for sequences of unequal length")    return sum(el1 != el2 for el1, el2 in zip(s1, s2))

def chebyshev_distance(p, q):    assert len(p) == len(q)    return max([abs(x - y) for x, y in zip(p, q)])def chebyshev_distance_procedural(p, q):    assert len(p) == len(q)    d = 0    for x, y in zip(p, q):        d = max(d, abs(x - y))    return d

import pandas as pdimport scipy as spfrom scipy.spatial.distance import mahalanobisdatadict = {'country': ['Argentina', 'Bolivia', 'Brazil', 'Chile', 'Ecuador', 'Colombia', 'Paraguay', 'Peru', 'Venezuela'],'d1': [0.34, -0.19, 0.37, 1.17, -0.31, -0.3, -0.48, -0.15, -0.61],'d2': [-0.57, -0.69, -0.28, 0.68, -2.19, -0.83, -0.53, -1, -1.39],'d3': [-0.02, -0.55, 0.07, 1.2, -0.14, -0.85, -0.9, -0.47, -1.02],'d4': [-0.69, -0.18, 0.05, 1.43, -0.02, -0.7, -0.72, 0.23, -1.08],'d5': [-0.83, -0.69, -0.39, 1.31, -0.7, -0.75, -1.04, -0.52, -1.22],'d6': [-0.45, -0.77, 0.05, 1.37, -0.1, -0.67, -1.4, -0.35, -0.89]}pairsdict = {'country1': ['Argentina', 'Chile', 'Ecuador', 'Peru'],'country2': ['Bolivia', 'Venezuela', 'Colombia', 'Peru']}#DataFrame that contains the data for each countrydf = pd.DataFrame(datadict)#DataFrame that contains the pairs for which we calculate the Mahalanobis distancepairs = pd.DataFrame(pairsdict)#Add data to the country pairspairs = pairs.merge(df, how='left', left_on=['country1'], right_on=['country'])pairs = pairs.merge(df, how='left', left_on=['country2'], right_on=['country'])#Convert data columns to list in a single cellpairs['vector1'] = pairs[['d1_x','d2_x','d3_x','d4_x','d5_x','d6_x']].values.tolist()pairs['vector2'] = pairs[['d1_y','d2_y','d3_y','d4_y','d5_y','d6_y']].values.tolist()mahala = pairs[['country1', 'country2', 'vector1', 'vector2']]#Calculate covariance matrixcovmx = df.cov()invcovmx = sp.linalg.inv(covmx)#Calculate Mahalanobis distancemahala['mahala_dist'] = mahala.apply(lambda x: (mahalanobis(x['vector1'], x['vector2'], invcovmx)), axis=1)mahala = mahala[['country1', 'country2', 'mahala_dist']]

def canberra_distance(p, q):    n = len(p)    distance = 0    for i in n:        if p[i] == 0 and q[i] == 0:            distance += 0        else:            distance += abs(p[i] - q[i]) / (abs(p[i]) + abs(q[i]))    return distance

def minkowski_distance(p, q, n):    assert len(p) == len(q)    return sum([abs(x - y) ^ n for x, y in zip(p, q)]) ^ 1 / ndef minkowski_distance_procedural(p, q, n):    assert len(p) == len(q)    s = 0    for x, y in zip(p, q):        s += abs(x - y) ^ n    return s ^ (1 / n)

import Levenshteintexta = 'Coggle'textb = 'Google'print Levenshtein.distance(texta,textb)

dw = 0.944 + (3 * 0.1(1 − 0.944)) = 0.961

from math import *
def square_rooted(x):    return round(sqrt(sum([a*a for a in x])),3)
def cosine_similarity(x,y):    numerator = sum(a*b for a,b in zip(x,y))   denominator = square_rooted(x)*square_rooted(y)   return round(numerator/float(denominator),3)
print(cosine_similarity([3, 45, 7, 2], [2, 54, 13, 15]))

def jaccard_sim(a, b):    unions = len(set(a).union(set(b)))    intersections = len(set(a).intersection(set(b)))    return intersections / unionsa = ['x', 'y']b = ['x', 'z', 'v']print(jaccard_sim(a, b))

def jaccard_similarity(x,y):    intersection_cardinality = len(set.intersection(*[set(x), set(y)]))    union_cardinality = len(set.union(*[set(x), set(y)]))    return intersection_cardinality/float(union_cardinality)
print(jaccard_similarity([0,1,2,5,6],[0,2,3,5,7,9]))

def dice_coefficient(a, b):    """dice coefficient 2nt/na + nb."""    a_bigrams = set(a)    b_bigrams = set(b)    overlap = len(a_bigrams & b_bigrams)    return overlap * 2.0/(len(a_bigrams) + len(b_bigrams))