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What is the semantic distance between Batman and the Bible? Wikispeedia is a fun game where you are given (or can choose) apparently unrelated source and a target Wikipedia pages, and you are asked to reach target page by only clicking links you find along the pages you visit. These click paths provide valuable information regarding human behaviour and the semantic connection between different topics, for example search engines might use such information to better understand user queries. You will analyze a dataset of such paths.

Data source:

  • Robert West and Jure Leskovec: Human Wayfinding in Information Networks. 21st International World Wide Web Conference (WWW), 2012.

  • Robert West, Joelle Pineau, and Doina Precup: Wikispeedia: An Online Game for Inferring Semantic Distances between Concepts. 21st International Joint Conference on Artificial Intelligence (IJCAI), 2009.


REQUIREMENTS: Having read Relational data tutorial , which contains also instructions for installing required libraries.

What to do

  1. Unzip exercises zip in a folder, you should obtain something like this:


WARNING: to correctly visualize the notebook, it MUST be in an unzipped folder !

  1. open Jupyter Notebook from that folder. Two things should open, first a console and then a browser. The browser should show a file list: navigate the list and open the notebook wikispeedia.ipynb

  2. Go on reading the notebook, and write in the appropriate cells when asked

Shortcut keys:

  • to execute Python code inside a Jupyter cell, press Control + Enter

  • to execute Python code inside a Jupyter cell AND select next cell, press Shift + Enter

  • to execute Python code inside a Jupyter cell AND a create a new cell aftwerwards, press Alt + Enter

  • If the notebooks look stuck, try to select Kernel -> Restart

The dataset

Each row of the dataset paths_finished.tsv is a user session, where user navigates from start page to end page. Columns are hashedIpAddress, timestamp, durationInSec, path and rating.

We define a session group as all sessions which have same start page and same end page, for example all these paths start with Linguistics and end in Rome:

import pandas as pd
import numpy as np
pd.options.display.max_colwidth = None
df = pd.read_csv('paths_finished.tsv', encoding='UTF-8', skiprows=16, header=None, sep='\t')
0 1 2 3 4
5890 2f8c281d5e0b0e93 1248913182 106 Linguistics;Philosophy;Aristotle;Ancient_Greece;Italy;Rome 3.0
5891 389b67fa365b727a 1249604227 89 Linguistics;Language;English_language;Latin;Rome 2.0
5892 0299542414c3f20a 1257970576 94 Linguistics;Philosophy;Plato;Latin;Rome NaN
5893 2b6e83d366a7514d 1260188882 113 Linguistics;Philosophy;Thomas_Aquinas;Italy;Rome 2.0
5894 0d57c8c57d75e2f5 1282028286 153 Linguistics;Language;Spanish_language;Vulgar_Latin;Roman_Empire;Rome NaN
5895 0d57c8c57d75e2f5 1295244051 62 Linguistics;Philosophy;Socrates;Ancient_Greece;Ancient_Rome;Rome 1.0
5896 772843f73d9cf93d 1307880434 177 Linguistics;Language;German_language;Latin_alphabet;<;Italy;Rome NaN
5897 654430d34a08a0f5 1339755238 81 Linguistics;Philosophy;Augustine_of_Hippo;Italy;Rome 2.0
5898 12470aee3d5ad152 1344167616 40 Linguistics;Philosophy;Plato;Italy;Rome NaN
5899 6365b049395c53ce 1345421532 67 Linguistics;Culture;Ancient_Rome;Rome 1.0
5900 05786cb24102850d 1347671980 65 Linguistics;Language;English_language;Latin;Rome 2.0
5901 369a3f7e77700217 1349302559 56 Linguistics;Language;English_language;Latin;Rome NaN

In this other session group, all sessions start with Pikachu and end with Sun:

0 1 2 3 4
45121 0d57c8c57d75e2f5 1278403914 17 Pikachu;North_America;Earth;Planet;Sun 1.0
45122 0d57c8c57d75e2f5 1278403938 42 Pikachu;Tree;Sunlight;Sun NaN
45123 0d57c8c57d75e2f5 1278403972 17 Pikachu;Tree;Plant;<;Sunlight;Sun 1.0
45124 0d57c8c57d75e2f5 1278403991 8 Pikachu;Tree;Sunlight;Sun NaN
45125 0d57c8c57d75e2f5 1278404007 9 Pikachu;Tree;Sunlight;Sun 1.0
45126 0d57c8c57d75e2f5 1278404048 8 Pikachu;Tree;Sunlight;Sun NaN
45127 0d57c8c57d75e2f5 1278404061 16 Pikachu;Tree;Sunlight;Sun NaN
45128 0d57c8c57d75e2f5 1278404065 8 Pikachu;Tree;Sunlight;Sun NaN
45129 0d57c8c57d75e2f5 1278404070 8 Pikachu;Tree;Sunlight;Sun NaN
45130 0d57c8c57d75e2f5 1278404089 8 Pikachu;Tree;Sunlight;Sun NaN
45131 0d57c8c57d75e2f5 1278404095 7 Pikachu;Tree;Sunlight;Sun NaN
45132 0d57c8c57d75e2f5 1278404101 9 Pikachu;Tree;Sunlight;Sun NaN
45133 0d57c8c57d75e2f5 1278404117 6 Pikachu;Tree;Sunlight;Sun NaN
45134 0d57c8c57d75e2f5 1278404124 10 Pikachu;Tree;Sunlight;Sun NaN
45135 0d57c8c57d75e2f5 1278404129 9 Pikachu;Tree;Sunlight;Sun NaN
45136 0d57c8c57d75e2f5 1278404142 7 Pikachu;Tree;Sunlight;Sun NaN
45137 0d57c8c57d75e2f5 1278404145 6 Pikachu;Tree;Sunlight;Sun NaN

1. filter_back

Whenever a user clicks the Back button, she navigates back one page. This fact is tracked in the data by the presence of a '<' symbol. Write a function which RETURN a NEW path without pages which were navigated back.

NOTE: you can have duplicates even without presence of <, because a user might end up to a previous page just by following circular links.

DO NOT misuse search methods, I’m watching you }:-[

Show solution
def filter_back(path):
    raise Exception('TODO IMPLEMENT ME !')

assert filter_back([]) == []
assert filter_back(['alfa']) == ['alfa']
assert filter_back(['beta','alfa','charlie']) == ['beta','alfa','charlie']

assert filter_back(['charlie', 'tango','<']) == ['charlie']
inp = ['charlie', 'tango','<']
assert filter_back(inp) == ['charlie']  # new
assert inp == ['charlie', 'tango','<']
assert filter_back(['alfa', 'beta', 'charlie','<','<','delta']) == ['alfa','delta']
assert filter_back(['alfa', 'beta', 'charlie','delta','eagle','<','<','golf','<','<','hotel']) \
       == ['alfa','beta','hotel']

# circular paths
assert filter_back(['alfa','beta','alfa','alfa','beta']) ==  ['alfa','beta','alfa','alfa','beta']
assert filter_back(['alfa','beta','alfa','<','charlie','charlie','delta','charlie','<','charlie','delta']) \
       == ['alfa','beta','charlie','charlie','delta','charlie','delta']

2. load_db

Load the tab-separated file paths_finished.tsv with a CSV Reader. The file has some rows to skip and no column names: parse it and RETURN a list of dictionaries, with hashedIpAddress, timestamp, durationInSec, path and rating as fields:

  • path: convert it with filter_back function

  • timestamp and durationInSec: convert to integer

  • rating: convert to integer, if NULL, set it to None


>>> sessions_db = load_db('paths_finished.tsv')

Parsed 51318 sessions

>>> sessions_db[:2]

[{'hashedIpAddress': '6a3701d319fc3754',
  'timestamp': 1297740409,
  'durationInSec': 166,
  'path': ['14th_century',
  'rating': None},
 {'hashedIpAddress': '3824310e536af032',
  'timestamp': 1344753412,
  'durationInSec': 88,
  'path': ['14th_century',
  'rating': 3}]
Show solution

import csv def load_db(filename): raise Exception('TODO IMPLEMENT ME !') sessions_db = load_db('paths_finished.tsv') sessions_db[:2]
from pprint import pprint
from expected_db import expected_db
for i in range(len(expected_db)):
    if expected_db[i] != sessions_db[i]:
        print('\nERROR at index', i, ':')
        print('  ACTUAL:')
        print('  EXPECTED:')
if len(sessions_db) != len(expected_db):
    print("ERROR: different lengths! sessions_db:", len(sessions_db), "expected_db", len(expected_db))

3. calc_stats

Write a function which takes the sessions db and RETURN a NEW dictionary which maps sessions groups expressed as tuples (start, end) to a dictionary of statistics about them

  • dictionary key: tuple with start,end page

  • sessions: the number of sessions in that group

  • avg_len: the average length (as number of edges) of all paths in the group

  • pages: the total number of DISTINCT pages found among all sessions in that group

  • freqs: a dictionary which maps edges found in all sessions of that group to their count

  • max_freq: the highest count among all freqs

Output example (for complete output see

>>> calc_stats(sessions_db)
    ('Linguistics', 'Rome'): {'avg_len': 4.166666666666667,
                              'freqs': { ('Ancient_Greece', 'Ancient_Rome'): 1,
                                         ('Ancient_Greece', 'Italy'): 1,
                                         ('Ancient_Rome', 'Rome'): 2,
                                         ('Aristotle', 'Ancient_Greece'): 1,
                                         ('Augustine_of_Hippo', 'Italy'): 1,
                                         ('Culture', 'Ancient_Rome'): 1,
                                         ('English_language', 'Latin'): 3,
                                         ('German_language', 'Italy'): 1,
                                         ('Italy', 'Rome'): 5,
                                         ('Language', 'English_language'): 3,
                                         ('Language', 'German_language'): 1,
                                         ('Language', 'Spanish_language'): 1,
                                         ('Latin', 'Rome'): 4,
                                         ('Linguistics', 'Culture'): 1,
                                         ('Linguistics', 'Language'): 5,
                                         ('Linguistics', 'Philosophy'): 6,
                                         ('Philosophy', 'Aristotle'): 1,
                                         ('Philosophy', 'Augustine_of_Hippo'): 1,
                                         ('Philosophy', 'Plato'): 2,
                                         ('Philosophy', 'Socrates'): 1,
                                         ('Philosophy', 'Thomas_Aquinas'): 1,
                                         ('Plato', 'Italy'): 1,
                                         ('Plato', 'Latin'): 1,
                                         ('Roman_Empire', 'Rome'): 1,
                                         ('Socrates', 'Ancient_Greece'): 1,
                                         ('Spanish_language', 'Vulgar_Latin'): 1,
                                         ('Thomas_Aquinas', 'Italy'): 1,
                                         ('Vulgar_Latin', 'Roman_Empire'): 1},
                           'max_freq': 6,
                           'pages': 19,
                           'sessions': 12},
     ('Pikachu', 'Sun'):   {'avg_len': 3.0588235294117645,
                            'freqs': {('Earth', 'Planet'): 1,
                                      ('North_America', 'Earth'): 1,
                                      ('Pikachu', 'North_America'): 1,
                                      ('Pikachu', 'Tree'): 16,
                                      ('Planet', 'Sun'): 1,
                                      ('Sunlight', 'Sun'): 16,
                                      ('Tree', 'Sunlight'): 16},
                            'max_freq': 16,
                            'pages': 7,
                            'sessions': 17},
Show solution
def calc_stats(sessions):
    raise Exception('TODO IMPLEMENT ME !')

stats_db = calc_stats(sessions_db)

from pprint import pprint
from expected_stats_db import expected_stats_db
for t in expected_stats_db:
    if not t in stats_db:
        print('\nERROR: missing key for session group', t)
    elif expected_stats_db[t] != stats_db[t]:
        print('\nERROR at key for session group', t, ':')
        print('  ACTUAL:')
        print('  EXPECTED:')

diff = stats_db.keys() - expected_stats_db.keys()
if len(diff) > 0:
    print('ERROR! Found these extra keys in stats_db:', diff)

4. plot_network

Given a sessions group (start_page, target_page), we want to display the pages clicked by users for all its sessions. Since some sessions share edges, we will show their click frequency.

  • Set edges attributes 'weight', 'label' as \(freq\), 'penwidth' as \(5 \large \frac{freq}{max\_freq}\) and 'color' as '#45daed'

  • Only display edges (and pages connected by such edges) for which the click count is strictly greater than the given threshold

  • NOTE: when applying a threshold, it’s fine if some nodes don’t appear linked to either source or target

Example 1:

>>> plot_network(stats_db,'Linguistics', 'Rome')


Example 2:

>>> plot_network(stats_db, 'Batman', 'Bible', 0)  # default threshold zero, big graph


Show solution

from soft import draw_nx import networkx as nx def plot_network(stats, source_page, target_page, threshold=0): raise Exception('TODO IMPLEMENT ME !') plot_network(stats_db,'Linguistics', 'Rome')

plot_network(stats_db, 'Batman', 'Bible', 0) # default threshold zero, big graph

plot_network(stats_db, 'Batman', 'Bible', 1) # we take only edges > 1