There are situations that we deal with short text, probably messy, without a lot of training data. In that case, we need external semantic information. Instead of using the conventional bag-of-words (BOW) model, we should employ word-embedding models, such as Word2Vec, GloVe etc.

Suppose we want to perform supervised learning, with three subjects, described by the following Python dictionary:

classdict={'mathematics': ['linear algebra',
'topology',
'algebra',
'calculus',
'variational calculus',
'functional field',
'real analysis',
'complex analysis',
'differential equation',
'statistics',
'statistical optimization',
'probability',
'stochastic calculus',
'numerical analysis',
'differential geometry'],
'physics': ['renormalization',
'classical mechanics',
'quantum mechanics',
'statistical mechanics',
'functional field',
'path integral',
'quantum field theory',
'electrodynamics',
'condensed matter',
'particle physics',
'topological solitons',
'astrophysics',
'spontaneous symmetry breaking',
'atomic molecular and optical physics',
'quantum chaos'],
'theology': ['divine providence',
'soteriology',
'anthropology',
'pneumatology',
'Christology',
'Holy Trinity',
'eschatology',
'scripture',
'ecclesiology',
'predestination',
'divine degree',
'creedal confessionalism',
'scholasticism',
'prayer',
'eucharist']}


And we implemented Word2Vec here. To add external information, we use a pre-trained Word2Vec model from Google, downloaded here. We can use it with Python package gensim. To load it, enter

from gensim.models import Word2Vec


How do we represent a phrase in Word2Vec? How do we do the classification? Here I wrote two classes to do it.

Average

We can represent a sentence by summing the word-embedding representations of each word. The class, inside SumWord2VecClassification.py, is coded as follow:

from collections import defaultdict

import numpy as np
from nltk import word_tokenize
from scipy.spatial.distance import cosine

from utils import ModelNotTrainedException

class SumEmbeddedVecClassifier:
def __init__(self, wvmodel, classdict, vecsize=300):
self.wvmodel = wvmodel
self.classdict = classdict
self.vecsize = vecsize
self.trained = False

def train(self):
for classtype in self.classdict:
for shorttext in self.classdict[classtype]:
self.trained = True

def shorttext_to_embedvec(self, shorttext):
vec = np.zeros(self.vecsize)
tokens = word_tokenize(shorttext)
for token in tokens:
if token in self.wvmodel:
vec += self.wvmodel[token]
norm = np.linalg.norm(vec)
if norm!=0:
vec /= np.linalg.norm(vec)
return vec

def score(self, shorttext):
if not self.trained:
raise ModelNotTrainedException()
vec = self.shorttext_to_embedvec(shorttext)
scoredict = {}
try:
scoredict[classtype] = 1 - cosine(vec, self.addvec[classtype])
except ValueError:
scoredict[classtype] = np.nan
return scoredict


Here the exception ModelNotTrainedException is just an exception raised if the model has not been trained yet, but scoring function was called by the user. (Codes listed in my Github repository.) The similarity will be calculated by cosine similarity.

Such an implementation is easy to understand and carry out. It is good enough for a lot of application. However, it has the problem that it does not take the relation between words or word order into account.

Convolutional Neural Network

To tackle the problem of word relations, we have to use deeper neural networks. Yoon Kim published a well cited paper regarding this in EMNLP in 2014, titled “Convolutional Neural Networks for Sentence Classification.” The model architecture is as follow: (taken from his paper)

Each word is represented by an embedded vector, but neighboring words are related through the convolutional matrix. And MaxPooling and a dense neural network were implemented afterwards. His paper involves multiple filters with variable window sizes / spatial extent, but for our cases of short phrases, I just use one window of size 2 (similar to dealing with bigram). While Kim implemented using Theano (see his Github repository), I implemented using keras with Theano backend. The codes, inside CNNEmbedVecClassification.py, are as follow:

import numpy as np
from keras.layers import Convolution1D, MaxPooling1D, Flatten, Dense
from keras.models import Sequential
from nltk import word_tokenize

from utils import ModelNotTrainedException

class CNNEmbeddedVecClassifier:
def __init__(self,
wvmodel,
classdict,
n_gram,
vecsize=300,
nb_filters=1200,
maxlen=15):
self.wvmodel = wvmodel
self.classdict = classdict
self.n_gram = n_gram
self.vecsize = vecsize
self.nb_filters = nb_filters
self.maxlen = maxlen
self.trained = False

def convert_trainingdata_matrix(self):
classlabels = self.classdict.keys()
lblidx_dict = dict(zip(classlabels, range(len(classlabels))))

# tokenize the words, and determine the word length
phrases = []
indices = []
for label in classlabels:
for shorttext in self.classdict[label]:
category_bucket = [0]*len(classlabels)
category_bucket[lblidx_dict[label]] = 1
indices.append(category_bucket)
phrases.append(word_tokenize(shorttext))

# store embedded vectors
train_embedvec = np.zeros(shape=(len(phrases), self.maxlen, self.vecsize))
for i in range(len(phrases)):
for j in range(min(self.maxlen, len(phrases[i]))):
train_embedvec[i, j] = self.word_to_embedvec(phrases[i][j])
indices = np.array(indices, dtype=np.int)

return classlabels, train_embedvec, indices

def train(self):
# convert classdict to training input vectors
self.classlabels, train_embedvec, indices = self.convert_trainingdata_matrix()

# build the deep neural network model
model = Sequential()
filter_length=self.n_gram,
border_mode='valid',
activation='relu',
input_shape=(self.maxlen, self.vecsize)))
model.compile(loss='categorical_crossentropy', optimizer='rmsprop')

# train the model
model.fit(train_embedvec, indices)

# flag switch
self.model = model
self.trained = True

def word_to_embedvec(self, word):
return self.wvmodel[word] if word in self.wvmodel else np.zeros(self.vecsize)

def shorttext_to_matrix(self, shorttext):
tokens = word_tokenize(shorttext)
matrix = np.zeros((self.maxlen, self.vecsize))
for i in range(min(self.maxlen, len(tokens))):
matrix[i] = self.word_to_embedvec(tokens[i])
return matrix

def score(self, shorttext):
if not self.trained:
raise ModelNotTrainedException()

# retrieve vector
matrix = np.array([self.shorttext_to_matrix(shorttext)])

# classification using the neural network
predictions = self.model.predict(matrix)

# wrangle output result
scoredict = {}
for idx, classlabel in zip(range(len(self.classlabels)), self.classlabels):
scoredict[classlabel] = predictions[0][idx]
return scoredict


The output is a vector of length equal to the number of class labels, 3 in our example. The elements of the output vector add up to one, indicating its score, and a nature of probability.

Evaluation

A simple cross-validation to the example data set does not tell a difference between the two algorithms:

However, we can test the algorithm with a few examples:

Example 1: “renormalization”

• Average: {‘mathematics’: 0.54135105096749336, ‘physics’: 0.63665460856632494, ‘theology’: 0.31014049736087901}
• CNN: {‘mathematics’: 0.093827009201049805, ‘physics’: 0.85451591014862061, ‘theology’: 0.051657050848007202}

As renormalization was a strong word in the training data, it gives an easy result. CNN can distinguish much more clearly.

Example 2: “salvation”

• Average: {‘mathematics’: 0.14939650156482298, ‘physics’: 0.21692765541184023, ‘theology’: 0.5698233329716329}
• CNN: {‘mathematics’: 0.012395491823554039, ‘physics’: 0.022725773975253105, ‘theology’: 0.96487873792648315}

“Salvation” is not found in the training data, but it is closely related to “soteriology,” which means the doctrine of salvation. So it correctly identifies it with theology.

Example 3: “coffee”

• Average: {‘mathematics’: 0.096820211601723272, ‘physics’: 0.081567332119268032, ‘theology’: 0.15962682945135631}
• CNN: {‘mathematics’: 0.27321341633796692, ‘physics’: 0.1950736939907074, ‘theology’: 0.53171288967132568}

Coffee is not related to all subjects. The first architecture correctly indicates the fact, but CNN, with its probabilistic nature, has to roughly equally distribute it (but not so well.)

The code can be found in my Github repository: stephenhky/PyShortTextCategorization. (This repository has been updated since this article was published. The link shows the version of the code when this appeared online.)

One fascinating application of deep learning is the training of a model that outputs vectors representing words. A project written in Google, named Word2Vec, is one of the best tools regarding this. The vector representation captures the word contexts and relationships among words. This tool has been changing the landscape of natural language processing (NLP).

Let’s have some demonstration. To use Word2Vec in Python, you need to have the package gensim installed. (Installation instruction: here) And you have to download a trained model (GoogleNews-vectors-negative300.bin.gz), which is 3.6 GB big!! When you get into a Python shell (e.g., IPython), type

from gensim.models.word2vec import Word2Vec


This model enables the user to extract vector representation of length 300 of an English word. So what is so special about this vector representation from the traditional bag-of-words representation? First, the representation is standard. Once trained, we can use it in future training or testing dataset. Second, it captures the context of the word in a way that the algebraic operation of these vectors has meanings.

Here I give 5 examples.

A Juvenile Cat

What is a juvenile cat? We know that a juvenile dog is a puppy. Then we can get it by carry out the algebraic calculation $\text{puppy} - \text{dog} + \text{cat}$ by running

model.most_similar(positive=['puppy', 'cat'], negative=['dog'], topn=5)


This outputs:

[(u'kitten', 0.7634989619255066),
(u'puppies', 0.7110899686813354),
(u'pup', 0.6929495334625244),
(u'kittens', 0.6888389587402344),
(u'cats', 0.6796488761901855)]


which indicates that “kitten” is the answer (correctly!) The numbers are similarities of these words with the vector representation  $\text{puppy} - \text{dog} + \text{cat}$ in descending order. You can verify it by calculating the cosine distance:

from scipy.spatial import distance
print (1-distance.cosine(model['kitten'], model['puppy']+model['cat']-model['dog']))


which outputs 0.763498957413.

This demonstration shows that in the model, $\text{puppy}-\text{dog}$ and $\text{kitten}-\text{cat}$ are of similar semantic relations.

Capital of Taiwan

Where is the capital of Taiwan? We can find it if we know the capital of another country. For example, we know that Beijing is the capital of China. Then we can run the following:

model.most_similar(positive=['Beijing', 'Taiwan'], negative=['China'], topn=5)


which outputs

[(u'Taipei', 0.7866502404212952),
(u'Taiwanese', 0.6805002093315125),
(u'Kaohsiung', 0.6034111976623535),
(u'Chen', 0.5905819535255432),
(u'Seoul', 0.5865181684494019)]


Obviously, the answer is “Taipei.” And interestingly, the model sees Taiwan in the same footing of China!

Taipei (taken from Airasia: http://www.airasia.com/mo/en/destinations/taipei.page)

Past Participle of “eat”

We can extract grammatical information too. We know that the past participle of “go” is “gone”. With this, we can find that of “eat” by running:

model.most_similar(positive=[‘gone’, ‘eat’], negative=[‘go’], topn=5)

which outputs:

[(u'eaten', 0.7462186217308044),
(u'eating', 0.6516293287277222),
(u'ate', 0.6457351446151733),
(u'overeaten', 0.5853317975997925),
(u'eats', 0.5830586552619934)]


Capital of the State of Maryland

However, this model does not always work. If it can find the capital of Taiwan, can it find those for any states in the United States? We know that the capital of California is Sacramento. How about Maryland? Let’s run:

model.most_similar(positive=['Sacramento', 'Maryland'], negative=['California'], topn=5)


[(u'Towson', 0.7032245397567749),
(u'Baltimore', 0.6951349973678589),
(u'Hagerstown', 0.6367553472518921),
(u'Anne_Arundel', 0.5931429266929626),
(u'Oxon_Hill', 0.5879474878311157)]


But the correct answer should be Annapolis!

Downtown Annapolis (taken from Wikipedia)