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pagerank_lab.py
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pagerank_lab.py
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# version code 53ead35ddb8a+
# Please fill out this stencil and submit using the provided submission script.
from vec import Vec
from mat import Mat
from math import sqrt
import pagerank
## 1: (Task 12.12.1) Find Number of Links
def find_num_links(L):
'''
Input:
- L: a square matrix representing link structure
Output:
- A vector mapping each column label of L to
the number of non-zero entries in the corresponding
column of L
Example:
>>> from matutil import listlist2mat
>>> find_num_links(listlist2mat([[1,1,1],[1,1,0],[1,0,0]]))
Vec({0, 1, 2},{0: 3, 1: 2, 2: 1})
'''
def find_num_links(L):
return Vec(L.D[1],{c: sum([L[r,c]]) for c in L.D[1] for r in L.D[0]})
## 2: (Task 12.12.2) Make Markov
def make_Markov(L):
'''
Input:
- L: a square matrix representing link structure
Output:
- None: changes L so that it plays the role of A_1
Example:
>>> from matutil import listlist2mat
>>> M = listlist2mat([[1,1,1],[1,0,0],[1,0,1]])
>>> make_Markov(M)
>>> M
Mat(({0, 1, 2}, {0, 1, 2}), {(0, 1): 1.0, (2, 0): 0.3333333333333333, (0, 0): 0.3333333333333333, (2, 2): 0.5, (1, 0): 0.3333333333333333, (0, 2): 0.5})
'''
num_links = find_num_links(L)
for c in L.D[1]:
for r in L.D[0]:
L[r,c] *= 1/num_links[c]
return L
## 3: (Task 12.12.3) Power Method
def power_method(A, i):
'''
Input:
- A1: a matrix
- i: number of iterations to perform
Output:
- An approximation to the stationary distribution
Example:
>>> from matutil import listlist2mat
>>> power_method(listlist2mat([[0.6,0.5],[0.4,0.5]]), 10)
Vec({0, 1},{0: 0.5464480874307794, 1: 0.45355191256922034})
'''
v = Vec(A.D[1],{c:1 for c in A.D[1]})
for i in range(k):
w = A*v
v = w/sqrt(w*w)
return v
## 4: (Task 12.12.4) Jordan
number_of_docs_with_jordan = len(pagerank.find_word('jordan'))
## 5: (Task 12.12.5) Wikigoogle
def wikigoogle(w, k, p):
'''
Input:
- w: a word
- k: number of results
- p: pagerank eigenvector
Output:
- the list of the names of the kth heighest-pagerank Wikipedia
articles containing the word w
'''
list_w = pagerank.find_word(w)
list_w.sort(key=lambda x: p[x], reverse = True)
return list_w[:k]
## 6: (Task 12.12.6) Using Power Method
A1 = make_Markov(pagerank.read_data())
A2 = Mat(A1.D[0], {r:1 for r in A1.D[0]})*Vec(A1.D[1],{c:1/len(A1.D[0]) for c in A1.D[1]})
A = 0.85*A1 + 0.15*A2
p = power_method(A,5)
results_for_jordan = wikigoogle('jordan',5,p)
results_for_obama = wikigoogle('obama',5,p)
results_for_tiger = wikigoogle('tiger',5,p)
results_for_matrix = wikigoogle('matrix',5,p)
## 7: (Task 12.12.7) Power Method Biased
def power_method_biased(A1, i, r):
'''
Input:
- A1: a matrix, as in power_method
- i: number of iterations
- r: bias label
Output:
- Approximate eigenvector of .55A_1 + 0.15A_2 + 0.3A_r
'''
list_r = pagerank.find_word(r)
list_links2r = [c for r in list_r for c in A1.D[0] if A1[r,c] > 0]
A_r = make_Markov(Mat(A1.D,{(r,c): 1 for r in list_r for c in list_links2r}))
A = 0.55*A1 + 0.15A2 + 0.3*A_r
return power_method(A,i)
p_sport = power_method_biased(A1,5,'sport')
sporty_results_for_jordan = wikigoogle('jordan',5,p_sport)
sporty_results_for_obama = wikigoogle('obama',5,p_sport)
sporty_results_for_tiger = wikigoogle('tiger',5,p_sport)
sporty_results_for_matrix = wikigoogle('matrix',5,p_sport)