def __init__(self, filename=None, Sk=10):
# Call parent constructor
super(SVDNeighbourhoodSocial, self).__init__(filename)
# Number of similar elements
self._Sk = Sk #Length of Sk(i;u)
self._ASVector = Vector()
self._SocialMatrix = Matrix()
def __init__(self, filename=None, Sk=10):
# Call parent constructor
super(SVDNeighbourhoodKoren, self).__init__(filename, Sk)
# µ denotes the overall average rating
self._Mu = None
# Mean of all rows
self._mean_rows = None
# Mean of all cols
self._mean_cols = None
# Mean of each row / col
self._mean_row = dict()
self._mean_col = dict()
self._ASVector = Vector()
self._SocialMatrix = Matrix()
class SVDNeighbourhoodKorenSocial(SVDNeighbourhood):
"""
Inherits from SVDNeighbourhood class.
Neighbourhood model, using Singular Value Decomposition.
Based on 'Factorization Meets the Neighborhood: a Multifaceted
Collaborative Filtering Model' (Yehuda Koren)
http://public.research.att.com/~volinsky/netflix/kdd08koren.pdf
:param filename: Path to a Zip file, containing an already computed SVD (U, Sigma, and V) for a matrix *M*
:type filename: string
:param Sk: number of similar elements (items or users) to be used in *predict(i,j)*
:type Sk: int
"""
def __init__(self, filename=None, Sk=10):
# Call parent constructor
super(SVDNeighbourhoodKoren, self).__init__(filename, Sk)
# µ denotes the overall average rating
self._Mu = None
# Mean of all rows
self._mean_rows = None
# Mean of all cols
self._mean_cols = None
# Mean of each row / col
self._mean_row = dict()
self._mean_col = dict()
self._ASVector = Vector()
self._SocialMatrix = Matrix()
def set_mu(self, mu):
"""
Sets the :math:`\mu`. The overall average rating
:param mu: overall average rating
:type mu: float
"""
self._Mu = mu
def _set_mean_all(self, avg=None, is_row=True):
m = self._mean_row.values()
if not is_row:
m = self._mean_col.values()
return mean(m)
def set_mean_rows(self, avg=None):
"""
Sets the average value of all rows
:param avg: the average value (if None, it computes *average(i)*)
:type avg: float
"""
self._mean_rows = self._set_mean_all(avg, is_row=True)
def set_mean_cols(self, avg=None):
"""
Sets the average value of all cols
:param avg: the average value (if None, it computes *average(i)*)
:type avg: float
"""
self._mean_cols = self._set_mean_all(avg, is_row=False)
def set_mean(self, i, avg=None, is_row=True):
"""
Sets the average value of a row (or column).
:param i: a row (or column)
:type i: user or item id
:param avg: the average value (if None, it computes *average(i)*)
:type avg: float
:param is_row: is param *i* a row (or a col)?
:type is_row: Boolean
"""
d = self._mean_row
if not is_row:
d = self._mean_col
if avg is None: #Compute average
m = self._matrix.get().row_named
if not is_row:
m = self._matrix.get().col_named
avg = mean(m(i))
d[i] = avg
def loadSocialData(self, filename):
if not os.path.isfile(filename):
sys.stderr.write("Error filename!\n")
sys.exit(1)
fobj = open(filename, 'r')
for line in fobj.readlines():
sp = line.strip().split('\t')
user_s = sp[0]
user_m = sp[1]
self._ASVector.addToVec(user_s, 1.0)
self._SocialMatrix.addToMat(user_s, user_m, 1.0)
def predict(self, i, j, Sk=None, MIN_VALUE=None, MAX_VALUE=None):
"""
Predicts the value of *M(i,j)*
It is based on 'Factorization Meets the Neighborhood: a Multifaceted
Collaborative Filtering Model' (Yehuda Koren).
Equation 3 (section 2.2):
:math:`\hat{r}_{ui} = b_{ui} + \\frac{\sum_{j \in S^k(i;u)} s_{ij} (r_{uj} - b_{uj})}{\sum_{j \in S^k(i;u)} s_{ij}}`, where
:math:`b_{ui} = \mu + b_u + b_i`
http://public.research.att.com/~volinsky/netflix/kdd08koren.pdf
:param i: row in M, M(i)
:type i: user or item id
:param j: col in M, M(j)
:type j: user or item id
:param Sk: number of k elements to be used in :math:`S^k(i; u)`
:type Sk: int
:param MIN_VALUE: min. value in M (e.g. in ratings[1..5] => 1)
:type MIN_VALUE: float
:param MAX_VALUE: max. value in M (e.g. in ratings[1..5] => 5)
:type MAX_VALUE: float
"""
# http://public.research.att.com/~volinsky/netflix/kdd08koren.pdf
# bui = µ + bu + bi
# The parameters bu and bi indicate the observed deviations of user
# u and item i, respectively, from the average
#
# S^k(i; u):
# Using the similarity measure, we identify the k items rated
# by u, which are most similar to i.
#
# sij: similarity between i and j
#
# r^ui = bui + Sumj∈S^k(i;u) sij (ruj − buj) / Sumj∈S^k(i;u) sij
if not Sk:
Sk = self._Sk
similars = self.similar_neighbours(i, j, Sk)
#Now, similars == S^k(i; u)
#bu = self._mean_col.get(j, self.set_mean(j, is_row=False)) - self._mean_cols
#bi = self._mean_row.get(i, self.set_mean(i, is_row=True)) - self._mean_rows
bu = self._mean_col[j] - self._mean_cols
bi = self._mean_row[i] - self._mean_rows
bui = bu + bi
#if self._Mu: #TODO uncomment?
# bui += self._Mu
sim_ratings = []
sum_similarity = 0.0
for similar, sij in similars[1:]:
sim_rating = self.get_matrix().value(similar, j)
if sim_rating is None:
continue
ruj = sim_rating
fix_sij = sij + self.social_intensity(similar, j)
sum_similarity += fix_sij
bj = self._mean_row[similar]- self._mean_rows
buj = bu + bj
sim_ratings.append(fix_sij * (ruj - buj))
if not sum_similarity or not sim_ratings:
return nan
Sumj_Sk = sum(sim_ratings)/sum_similarity
rui = bui + Sumj_Sk
predicted_value = rui
if MIN_VALUE:
predicted_value = max(predicted_value, MIN_VALUE)
if MAX_VALUE:
predicted_value = min(predicted_value, MAX_VALUE)
return float(predicted_value)
def social_intensity(self, user_m, user_s):
res = 0.0
try:
res += self._SocialMatrix.getItem(user_s,user_m) / self._ASVector[user_s]
except:
res += 0.0
try:
res += 0.5 * self._SocialMatrix.getItem(user_m, user_s) / self._ASVector[user_m]
except:
res += 0.0
return res
class SVDNeighbourhoodSocial(SVD):
"""
Classic Neighbourhood plus Singular Value Decomposition. Inherits from SVD class
Predicts the value of :math:`M_{i,j}`, using simple avg. (weighted) of
all the ratings by the most similar users (or items). This similarity, *sim(i,j)* is derived from the SVD
:param filename: Path to a Zip file, containing an already computed SVD (U, Sigma, and V) for a matrix *M*
:type filename: string
:param Sk: number of similar elements (items or users) to be used in *predict(i,j)*
:type Sk: int
"""
def __init__(self, filename=None, Sk=10):
# Call parent constructor
super(SVDNeighbourhoodSocial, self).__init__(filename)
# Number of similar elements
self._Sk = Sk #Length of Sk(i;u)
self._ASVector = Vector()
self._SocialMatrix = Matrix()
def similar_neighbours(self, i, j, Sk=10):
similars = self.similar(i, Sk*10) #Get 10 times Sk
# Get only those items that user j has already rated
current = 0
_Sk = Sk
for similar, weight in similars[1:]:
if self.get_matrix().value(similars[current][0], j) == 0.0:
similars.pop(current)
current -= 1
_Sk += 1
current += 1
_Sk -= 1
if _Sk == 0:
break # We have enough elements to use
return similars[:Sk]
def loadSocialData(self, filename):
if not os.path.isfile(filename):
sys.stderr.write("Error filename!\n")
sys.exit(1)
fobj = open(filename, 'r')
for line in fobj.readlines():
sp = line.strip().split('\t')
user_s = sp[0]
user_m = sp[1]
self._ASVector.addToVec(user_s, 1.0)
self._SocialMatrix.addToMat(user_s, user_m, 1.0)
def predict(self, i, j, Sk=10, weighted=True, MIN_VALUE=None, MAX_VALUE=None):
"""
Predicts the value of :math:`M_{i,j}`, using simple avg. (weighted) of
all the ratings by the most similar users (or items)
if *weighted*:
:math:`\hat{r}_{ui} = \\frac{\sum_{j \in S^{k}(i;u)} sim(i, j) r_{uj}}{\sum_{j \in S^{k}(i;u)} sim(i, j)}`
else:
:math:`\hat{r}_{ui} = mean(\sum_{j \in S^{k}(i;u)} r_{uj})`
:param i: row in M, :math:`M_{i \cdot}`
:type i: user or item id
:param j: col in M, :math:`M_{\cdot j}`
:type j: item or user id
:param Sk: number of k elements to be used in :math:`S^k(i; u)`
:type Sk: int
:param weighted: compute avg. weighted of all the ratings?
:type weighted: Boolean
:param MIN_VALUE: min. value in M (e.g. in ratings[1..5] => 1)
:type MIN_VALUE: float
:param MAX_VALUE: max. value in M (e.g. in ratings[1..5] => 5)
:type MAX_VALUE: float
"""
if not Sk:
Sk = self._Sk
similars = self.similar_neighbours(i, j, Sk)
#Now, similars == S^k(i; u)
sim_ratings = []
sum_similarity = 0.0
for similar, weight in similars:
sim_rating = self.get_matrix().value(similar, j)
if sim_rating is None: #== 0.0:
continue
fix_weight = weight + self.social_intensity(similar, j)
sum_similarity += fix_weight
if weighted:
sim_ratings.append(fix_weight * sim_rating)
else:
sim_ratings.append(sim_rating)
if not sum_similarity or not sim_ratings:
return nan
if weighted:
predicted_value = sum(sim_ratings)/sum_similarity
else:
predicted_value = mean(sim_ratings)
if MIN_VALUE:
predicted_value = max(predicted_value, MIN_VALUE)
if MAX_VALUE:
predicted_value = min(predicted_value, MAX_VALUE)
return float(predicted_value)
def social_intensity(self, user_m, user_s):
res = 0.0
try:
res += self._SocialMatrix.getItem(user_s,user_m) / self._ASVector[user_s]
except:
res += 0.0
try:
res += 0.5 * self._SocialMatrix.getItem(user_m, user_s) / self._ASVector[user_m]
except:
res += 0.0
return res