Compute the aggregate similarity of two question token sets according to ontological graph distances in WordNet.
Based on the implementation of the paper "Sentence Similarity based on Semantic Nets and Corpus Statistics" by Li et al..
This utility package imports numpy, pandas, matplotlib and a helper kg module into the root namespace.
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from pygoose import *
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import math
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import nltk
Automatically discover the paths to various data folders and compose the project structure.
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project = kg.Project.discover()
Identifier for storing these features on disk and referring to them later.
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feature_list_id = 'wordnet_similarity'
Download auxiliary NLTK models and corpora.
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nltk.download('brown')
nltk.download('wordnet')
nltk.download('averaged_perceptron_tagger')
Preprocessed and tokenized questions.
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tokens_train = kg.io.load(project.preprocessed_data_dir + 'tokens_lowercase_spellcheck_train.pickle')
tokens_test = kg.io.load(project.preprocessed_data_dir + 'tokens_lowercase_spellcheck_test.pickle')
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tokens = tokens_train + tokens_test
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brown_freqs = dict()
N = 0
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def get_batch_similarities(pairs, _):
from nltk.corpus import brown
from nltk.corpus import wordnet as wn
# Parameters to the algorithm. Currently set to values that was reported
# in the paper to produce "best" results.
ALPHA = 0.2
BETA = 0.45
ETA = 0.4
PHI = 0.2
DELTA = 0.85
######################### word similarity ##########################
def get_best_synset_pair(word_1, word_2):
"""
Choose the pair with highest path similarity among all pairs.
Mimics pattern-seeking behavior of humans.
"""
max_sim = -1.0
synsets_1 = wn.synsets(word_1)
synsets_2 = wn.synsets(word_2)
if len(synsets_1) == 0 or len(synsets_2) == 0:
return None, None
else:
max_sim = -1.0
best_pair = None, None
for synset_1 in synsets_1:
for synset_2 in synsets_2:
sim = wn.path_similarity(synset_1, synset_2)
if sim is not None and sim > max_sim:
max_sim = sim
best_pair = synset_1, synset_2
return best_pair
def length_dist(synset_1, synset_2):
"""
Return a measure of the length of the shortest path in the semantic
ontology (Wordnet in our case as well as the paper's) between two
synsets.
"""
l_dist = 1e9
if synset_1 is None or synset_2 is None:
return 0.0
if synset_1 == synset_2:
# if synset_1 and synset_2 are the same synset return 0
l_dist = 0.0
else:
wset_1 = set([str(x.name()) for x in synset_1.lemmas()])
wset_2 = set([str(x.name()) for x in synset_2.lemmas()])
if len(wset_1.intersection(wset_2)) > 0:
# if synset_1 != synset_2 but there is word overlap, return 1.0
l_dist = 1.0
else:
# just compute the shortest path between the two
l_dist = synset_1.shortest_path_distance(synset_2)
if l_dist is None:
l_dist = 0.0
# normalize path length to the range [0,1]
return math.exp(-ALPHA * l_dist)
def hierarchy_dist(synset_1, synset_2):
"""
Return a measure of depth in the ontology to model the fact that
nodes closer to the root are broader and have less semantic similarity
than nodes further away from the root.
"""
h_dist = 1e9
if synset_1 is None or synset_2 is None:
return h_dist
if synset_1 == synset_2:
# return the depth of one of synset_1 or synset_2
h_dist = max([x[1] for x in synset_1.hypernym_distances()])
else:
# find the max depth of least common subsumer
hypernyms_1 = {x[0]:x[1] for x in synset_1.hypernym_distances()}
hypernyms_2 = {x[0]:x[1] for x in synset_2.hypernym_distances()}
lcs_candidates = set(hypernyms_1.keys()).intersection(
set(hypernyms_2.keys()))
if len(lcs_candidates) > 0:
lcs_dists = []
for lcs_candidate in lcs_candidates:
lcs_d1 = 0
if lcs_candidate in hypernyms_1:
lcs_d1 = hypernyms_1[lcs_candidate]
lcs_d2 = 0
if lcs_candidate in hypernyms_2:
lcs_d2 = hypernyms_2[lcs_candidate]
lcs_dists.append(max([lcs_d1, lcs_d2]))
h_dist = max(lcs_dists)
else:
h_dist = 0
return ((math.exp(BETA * h_dist) - math.exp(-BETA * h_dist)) /
(math.exp(BETA * h_dist) + math.exp(-BETA * h_dist)))
def word_similarity(word_1, word_2):
synset_pair = get_best_synset_pair(word_1, word_2)
return (length_dist(synset_pair[0], synset_pair[1]) *
hierarchy_dist(synset_pair[0], synset_pair[1]))
######################### sentence similarity ##########################
def most_similar_word(word, word_set):
"""
Find the word in the joint word set that is most similar to the word
passed in. We use the algorithm above to compute word similarity between
the word and each word in the joint word set, and return the most similar
word and the actual similarity value.
"""
max_sim = -1.0
sim_word = ""
for ref_word in word_set:
sim = word_similarity(word, ref_word)
if sim > max_sim:
max_sim = sim
sim_word = ref_word
return sim_word, max_sim
def info_content(lookup_word):
"""
Uses the Brown corpus available in NLTK to calculate a Laplace
smoothed frequency distribution of words, then uses this information
to compute the information content of the lookup_word.
"""
global N
if N == 0:
# poor man's lazy evaluation
for sent in brown.sents():
for word in sent:
word = word.lower()
if word not in brown_freqs:
brown_freqs[word] = 0
brown_freqs[word] = brown_freqs[word] + 1
N = N + 1
lookup_word = lookup_word.lower()
n = 0 if lookup_word not in brown_freqs else brown_freqs[lookup_word]
return 1.0 - (math.log(n + 1) / math.log(N + 1))
def semantic_vector(words, joint_words, info_content_norm):
"""
Computes the semantic vector of a sentence. The sentence is passed in as
a collection of words. The size of the semantic vector is the same as the
size of the joint word set. The elements are 1 if a word in the sentence
already exists in the joint word set, or the similarity of the word to the
most similar word in the joint word set if it doesn't. Both values are
further normalized by the word's (and similar word's) information content
if info_content_norm is True.
"""
sent_set = set(words)
semvec = np.zeros(len(joint_words))
i = 0
for joint_word in joint_words:
if joint_word in sent_set:
# if word in union exists in the sentence, s(i) = 1 (unnormalized)
semvec[i] = 1.0
if info_content_norm:
semvec[i] = semvec[i] * math.pow(info_content(joint_word), 2)
else:
# find the most similar word in the joint set and set the sim value
sim_word, max_sim = most_similar_word(joint_word, sent_set)
semvec[i] = PHI if max_sim > PHI else 0.0
if info_content_norm:
semvec[i] = semvec[i] * info_content(joint_word) * info_content(sim_word)
i = i + 1
return semvec
def semantic_similarity(words_1, words_2, info_content_norm):
"""
Computes the semantic similarity between two sentences as the cosine
similarity between the semantic vectors computed for each sentence.
"""
joint_words = set(words_1).union(set(words_2))
vec_1 = semantic_vector(words_1, joint_words, info_content_norm)
vec_2 = semantic_vector(words_2, joint_words, info_content_norm)
return np.dot(vec_1, vec_2.T) / (np.linalg.norm(vec_1) * np.linalg.norm(vec_2))
######################### word order similarity ##########################
def word_order_vector(words, joint_words, windex):
"""
Computes the word order vector for a sentence. The sentence is passed
in as a collection of words. The size of the word order vector is the
same as the size of the joint word set. The elements of the word order
vector are the position mapping (from the windex dictionary) of the
word in the joint set if the word exists in the sentence. If the word
does not exist in the sentence, then the value of the element is the
position of the most similar word in the sentence as long as the similarity
is above the threshold ETA.
"""
wovec = np.zeros(len(joint_words))
i = 0
wordset = set(words)
for joint_word in joint_words:
if joint_word in wordset:
# word in joint_words found in sentence, just populate the index
wovec[i] = windex[joint_word]
else:
# word not in joint_words, find most similar word and populate
# word_vector with the thresholded similarity
sim_word, max_sim = most_similar_word(joint_word, wordset)
if max_sim > ETA:
wovec[i] = windex[sim_word]
else:
wovec[i] = 0
i = i + 1
return wovec
def word_order_similarity(words_1, words_2):
"""
Computes the word-order similarity between two sentences as the normalized
difference of word order between the two sentences.
"""
joint_words = list(set(words_1).union(set(words_2)))
windex = {x[1]: x[0] for x in enumerate(joint_words)}
r1 = word_order_vector(words_1, joint_words, windex)
r2 = word_order_vector(words_2, joint_words, windex)
return 1.0 - (np.linalg.norm(r1 - r2) / np.linalg.norm(r1 + r2))
######################### overall similarity ##########################
def similarity(words_1, words_2, info_content_norm):
"""
Calculate the semantic similarity between two sentences. The last
parameter is True or False depending on whether information content
normalization is desired or not.
"""
return DELTA * semantic_similarity(words_1, words_2, info_content_norm) + \
(1.0 - DELTA) * word_order_similarity(words_1, words_2)
######################### main / test ##########################
return [
[similarity(pair[0], pair[1], False), similarity(pair[0], pair[1], True)]
for pair in pairs
]
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similarities = kg.jobs.map_batch_parallel(
tokens,
batch_mapper=get_batch_similarities,
batch_size=1000,
)
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similarities = np.array(similarities)
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X_train = similarities[:len(tokens_train)]
X_test = similarities[len(tokens_train):]
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print('X_train:', X_train.shape)
print('X_test: ', X_test.shape)
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feature_names = [
'wordnet_similarity_raw',
'wordnet_similarity_brown',
]
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project.save_features(X_train, X_test, feature_names, feature_list_id)