from sklearn.metrics.pairwise import pairwise_distances,cosine_similarity
import numpy as np
from numpy.linalg import norm
from scipy.stats.stats import pearsonr
from math import sqrt,exp
def l1(x):
return norm(x,ord=1)
def l2(x):
return norm(x)
def common(x1,x2):
# find common ratings
common = (x1<>0)&(x2<>0)
new_x1 = x1[common]
new_x2 = x2[common]
return new_x1,new_x2
def cosine_sp(x1,x2):
'x1,x2 are dicts,this version is for sparse representation'
total = 0
denom1 = 0
denom2 =0
for k in x1:
if x2.has_key(k):
total+=x1[k]*x2[k]
denom1+=x1[k]**2
denom2+=x2[k]**2
try:
return (total + 0.0) / (sqrt(denom1) * sqrt(denom2))
except ZeroDivisionError:
return 0
def cosine(x1,x2):
#find common ratings
new_x1, new_x2 = common(x1,x2)
#compute the cosine similarity between two vectors
sum = new_x1.dot(new_x2)
denom = sqrt(new_x1.dot(new_x1)*new_x2.dot(new_x2))
try:
return float(sum)/denom
except ZeroDivisionError:
return 0
#return cosine_similarity(x1,x2)[0][0]
def pearson_sp(x1,x2):
total = 0
denom1 = 0
denom2 = 0
overlapped=False
try:
mean1 = sum(x1.values())/(len(x1)+0.0)
mean2 = sum(x2.values()) / (len(x2) + 0.0)
for k in x1:
if x2.has_key(k):
total += (x1[k]-mean1) * (x2[k]-mean2)
denom1 += (x1[k]-mean1) ** 2
denom2 += (x2[k]-mean2) ** 2
overlapped=True
return (total + 0.0) / (sqrt(denom1) * sqrt(denom2))
except ZeroDivisionError:
if overlapped:
return 1
else:
return 0
def euclidean(x1,x2):
#find common ratings
new_x1, new_x2 = common(x1, x2)
#compute the euclidean between two vectors
diff = new_x1-new_x2
denom = sqrt((diff.dot(diff)))
try:
return 1/denom
except ZeroDivisionError:
return 0
def pearson(x1,x2):
#find common ratings
new_x1, new_x2 = common(x1, x2)
#compute the pearson similarity between two vectors
ind1 = new_x1 > 0
ind2 = new_x2 > 0
try:
mean_x1 = float(new_x1.sum())/ind1.sum()
mean_x2 = float(new_x2.sum())/ind2.sum()
new_x1 = new_x1 - mean_x1
new_x2 = new_x2 - mean_x2
sum = new_x1.dot(new_x2)
denom = sqrt((new_x1.dot(new_x1))*(new_x2.dot(new_x2)))
return float(sum) / denom
except ZeroDivisionError:
return 0
def similarity(x1,x2,sim):
if sim == 'pcc':
return pearson_sp(x1,x2)
if sim == 'euclidean':
return euclidean(x1,x2)
else:
return cosine_sp(x1, x2)
def normalize(vec,maxVal,minVal):
'get the normalized value using min-max normalization'
if maxVal > minVal:
return float(vec-minVal)/(maxVal-minVal)+0.01
elif maxVal==minVal:
return vec/maxVal
else:
print 'error... maximum value is less than minimum value.'
raise ArithmeticError
def sigmoid(val):
return 1/(1+exp(-val))
def denormalize(vec,maxVal,minVal):
return minVal+(vec-0.01)*(maxVal-minVal)
