Description
For this assignment, you will build an intelligent system that can learn to answer questions like this one. In
order to do that, the system will approximate the semantic similarity of any pair of words. The semantic
similarity between two words is the measure of the closeness of their meanings. For example, the semantic
similarity between “car” and “vehicle” is high, while that between “car” and “flower” is low.
In order to answer the TOEFL question, you will compute the semantic similarity between the word
you are given and all the possible answers, and pick the answer with the highest semantic similarity to the
given word. More precisely, given a word w and a list of potential synonyms s1, s2, s3, s4, we compute the
similarities of (w, s1), (w, s2), (w, s3), (w, s4) and choose the word whose similarity to w is the highest.
We will measure the semantic similarity of pairs of words by first computing a semantic descriptor
vector of each of the words, and then taking the similarity measure to be the cosine similarity between
the two vectors.
Given a text with n words denoted by (w1, w2, …, wn) and a word w, let descw be the semantic descriptor
vector of w computed using the text. descw is an n-dimensional vector. The i-th coordinate of descw is
the number of sentences in which both w and wi occur. For efficiency’s sake, we will store the semantic
descriptor vector as a dictionary, not storing the zeros that correspond to words which don’t co-occur with
w. For example, suppose we are given the following text (the opening of Notes from the Underground by
Fyodor Dostoyevsky, translated by Constance Garnett):
I am a sick man. I am a spiteful man. I am an unattractive man. I believe my liver is diseased.
However, I know nothing at all about my disease, and do not know for certain what ails me.
The word “man” only appears in the first three sentences. Its semantic descriptor vector would be:
{“i”: 3, “am”: 3, “a”: 2, “sick”: 1, “spiteful”: 1, “an”: 1, “unattractive”: 1}
The word “liver” only occurs in the second sentence, so its semantic descriptor vector is:
{“i”: 1, “believe”: 1, “my”: 1, “is”: 1, “diseased”: 1}
We store all words in all-lowercase, since we don’t consider, for example, “Man” and “man” to be different
words. We do, however, consider, e.g., “believe” and “believes”, or “am” and “is” to be different words.
We discard all punctuation.
The cosine similarity between two vectors u = {u1, u2, . . . , uN } and v = {v1, v2, . . . , vN } is defined as:
sim(u, v) = u · v
|u||v|
=
PN
i=1 uivi
rPN
i=1 u
2
i
PN
i=1 v
2
i
We cannot apply the formula directly to our semantic descriptors since we do not store the entries which
are equal to zero. However, we can still compute the cosine similarity between vectors by only considering
the positive entries.
For example, the cosine similarity of “man” and “liver”, given the semantic descriptors above, is
3 · 1 (for the word “i”)
p
(32 + 32 + 22 + 12 + 12 + 12 + 12)(12 + 12 + 12 + 12 + 12)
= 3/
√
130 = 0.2631 . . .
Engineering Science, University of Toronto Page 3 of 6
CSC 180 H1F Project # 3 — Semantic Similarity
Part 1.
Implement the following functions in synonyms.py. Note that the names of the functions are case-sensitive
and must not be changed. You are not allowed to change the number of input parameters, nor to add any
global variables. Doing so will cause your code to fail when run with our testing programs, so that you
will not get any marks for functionality. We provide you with a starter version of synonyms.py
Subpart (a) cosine_similarity(vec1, vec2) (10%)
This function returns the cosine similarity between the sparse vectors vec1 and vec2, stored as dictionaries.
For example,
cosine_similarity({“a”: 1, “b”: 2, “c”: 3}, {“b”: 4, “c”: 5, “d”: 6})
should return approximately 0.70 (as a float).
Subpart (b) build_semantic_descriptors(sentences) (35%)
This function takes in a list sentences which contains lists of strings (words) representing sentences, and
returns a dictionary d such that for every word w that appears in at least one of the sentences, d[w] is itself
a dictionary which represents the semantic descriptor of w (note: the variable names here are arbitrary).
For example, if sentences represents the opening of Notes from the Underground above:
[[“i”, “am”, “a”, “sick”, “man”],
[“i”, “am”, “a”, “spiteful”, “man”],
[“i”, “am”, “an”, “unattractive”, “man”],
[“i”, “believe”, “my”, “liver”, “is”, “diseased”],
[“however”, “i”, “know”, “nothing”, “at”, “all”, “about”, “my”,
“disease”, “and”, “do”, “not”, “know”, “for”, “certain”, “what”, “ails”, “me”]],
part of the dictionary returned would be:
{ “man”: {“i”: 3, “am”: 3, “a”: 2, “sick”: 1, “spiteful”: 1, “an”: 1,
“unattractive”: 1},
“liver”: {“i”: 1, “believe”: 1, “my”: 1, “is”: 1, “diseased”: 1},
… }
with as many keys as there are distinct words in the passage.
Subpart (c) build_semantic_descriptors_from_files(filenames) (20%)
This function takes a list of filenames of strings, which contains the names of files (the first one can
be opened using open(filenames[0], “r”, encoding=”latin1″)), and returns the a dictionary of the
semantic descriptors of all the words in the files filenames, with the files treated as a single text.
You should assume that the following punctuation always separates sentences: “.”, “!”, “?”, and that
is the only punctuation that separates sentences. You should also assume that that is the only punctuation
that separates sentences. Assume that only the following punctuation is present in the texts:
[“,”, “-“, “–“, “:”, “;”]
Engineering Science, University of Toronto Page 4 of 6
CSC 180 H1F Project # 3 — Semantic Similarity
Subpart (d) most_similar_word(word, choices, semantic_descriptors, similarity_fn) (15%)
This function takes in a string word, a list of strings choices, and a dictionary semantic_descriptors
which is built according to the requirements for build_semantic_descriptors, and returns the element
of choices which has the largest semantic similarity to word, with the semantic similarity computed using
the data in semantic_descriptors and the similarity function similarity_fn. The similarity function is
a function which takes in two sparse vectors stored as dictionaries and returns a float. An example of such
a function is cosine_similarity. If the semantic similarity between two words cannot be computed, it is
considered to be −1. In case of a tie between several elements in choices, the one with the smallest index
in choices should be returned (e.g., if there is a tie between choices[5] and choices[7], choices[5] is
returned).
Subpart (e) run_similarity_test(filename, semantic_descriptors, similarity_fn) (10%)
This function takes in a string filename which is the name of a file in the same format as test.txt, and
returns the percentage (i.e., float between 0.0 and 100.0) of questions on which most_similar_word()
guesses the answer correctly using the semantic descriptors stored in semantic_descriptors, using the
similarity function similariy_fn.
The format of test.txt is as follows. On each line, we are given a word (all-lowercase), the correct
answer, and the choices. For example, the line:
feline cat dog cat horse
represents the question:
feline:
(a) dog
(b) cat
(c) horse
and indicates that the correct answer is “cat”.
Subpart (f) Efficiency
You will receive at most 90% of the available marks for Subpart b and c and if
build_semantic_descriptors_from_files(filenames) takes over 120 seconds to run on an ECF
workstation when the files are the novels specified in Part 2.
Part 2.
For this part, a detailed report is not required. One-sentence answers and (clearly-labelled) graphs are
sufficient. In your report, for each subpart, include the code used to generate the results you report. You
do not have to use matplotlib to generate your graphs, although we recommend that you learn to use it
at some point.
Subpart (a) Experimenting on a large corpus of text (4%)
Download the novels Swann’s Way by Marcel Proust, and War and Peace by Leo Tolstoy from Project
Gutenberg, and use them to build a semantic descriptors dictionary. Report how well the program performs
(using the cosine similarity similarity function) on the questions in test.txt, using those two novels at
Engineering Science, University of Toronto Page 5 of 6
CSC 180 H1F Project # 3 — Semantic Similarity Fall 2016
the same time. Note: the program may take several minutes to run (or more, if the implementation is
inefficient). The novels are available at the following URLs:
http://www.gutenberg.org/cache/epub/7178/pg7178.txt
http://www.gutenberg.org/cache/epub/2600/pg2600.txt
If your program takes too long to run, report the results on a shorter text.
Subpart (b) Experimenting with alternative similarity measures (3%)
Two alternative similarity measures between two vectors are: the negative distance in Euclidean space
between the vectors, and the negative distances in Euclidean space between the normalized versions of the
vectors:
simeuc(v1, v2) = −||v1 − v2||
simeucnorm(v1, v2) = −||v1/|v1| − v2/|v2|||.
Report on the performance of the algorithm (in terms of the percent of questions answered correctly)
using the text of the two novels on text.txt using these two similarity measures, and compare that to the
performance using the cosine similarity measure.
Subpart (c) Experimenting with smaller corpora of text: efficiency and performance (3%)
Plot the performance (in terms of the percent of questions answered correctly) on test.txt and the runtime
of the algorithm (including the time to build the descriptor dictionary) on 10%, 20%, …., 90%, 100% of the
text of the two novels, using the cosine similarity measure. Clearly label the axes of your graphs. The
runtime can be measured on any computer you like, not necessarily on ECF.
Engineering Science, University of Toronto Page 6 of 6
