An Intuitive Understanding of Word Embeddings: From Count Vectors to Word2Vec

Introduction

Before we start, have a look at the below examples.

• You open Google and search for a news article on the ongoing Champions trophy and get hundreds of search results in return about it.
• Nate silver analysed millions of tweets and correctly predicted the results of 49 out of 50 states in 2008 U.S Presidential Elections.
• You type a sentence in google translate in English and get an Equivalent Chinese conversion.

So what do the above examples have in common?

You possible guessed it right – TEXT processing. All the above three scenarios deal with humongous amount of text to perform different range of tasks like clustering in the google search example, classification in the second and Machine Translation in the third.

Humans can deal with text format quite intuitively but provided we have millions of documents being generated in a single day, we cannot have humans performing the above the three tasks. It is neither scalable nor effective.

So, how do we make computers of today perform clustering, classification etc on a text data since we know that they are generally inefficient at handling and processing strings or texts for any fruitful outputs?

Sure, a computer can match two strings and tell you whether they are same or not. But how do we make computers tell you about football or Ronaldo when you search for Messi? How do you make a computer understand that “Apple” in “Apple is a tasty fruit” is a fruit that can be eaten and not a company?

The answer to the above questions lie in creating a representation for words that capture their meanings, semantic relationships and the different types of contexts they are used in.

And all of these are implemented by using Word Embeddings or numerical representations of texts so that computers may handle them.

Below, we will see formally what are Word Embeddings and their different types and how we can actually implement them to perform the tasks like returning efficient Google search results.

What are Word Embeddings?

In very simplistic terms, Word Embeddings are the texts converted into numbers and there may be different numerical representations of the same text. But before we dive into the details of Word Embeddings, the following question should be asked – Why do we need Word Embeddings?

As it turns out, many Machine Learning algorithms and almost all Deep Learning Architectures are incapable of processing strings or plain text in their raw form. They require numbers as inputs to perform any sort of job, be it classification, regression etc. in broad terms. And with the huge amount of data that is present in the text format, it is imperative to extract knowledge out of it and build applications. Some real world applications of text applications are – sentiment analysis of reviews by Amazon etc., document or news classification or clustering by Google etc.

Let us now define Word Embeddings formally. A Word Embedding format generally tries to map a word using a dictionary to a vector. Let us break this sentence down into finer details to have a clear view.

Take a look at this example – sentence=” Word Embeddings are Word converted into numbers ”

A word in this sentence may be “Embeddings” or “numbers ” etc.

A dictionary may be the list of all unique words in the sentence. So, a dictionary may look like – [‘Word’,’Embeddings’,’are’,’Converted’,’into’,’numbers’]

A vector representation of a word may be a one-hot encoded vector where 1 stands for the position where the word exists and 0 everywhere else. The vector representation of “numbers” in this format according to the above dictionary is [0,0,0,0,0,1] and of converted is[0,0,0,1,0,0].

This is just a very simple method to represent a word in the vector form. Let us look at different types of Word Embeddings or Word Vectors and their advantages and disadvantages over the rest.

Different types of Word Embeddings

The different types of word embeddings can be broadly classified into two categories-

• Frequency based Embedding
• Prediction based Embedding

Let us try to understand each of these methods in detail.

1 Frequency based Embedding

There are generally three types of vectors that we encounter under this category.

• Count Vector
• TF-IDF Vector
• Co-Occurrence Vector

Let us look into each of these vectorization methods in detail.

1.1 Count Vector

Consider a Corpus C of D documents {d1,d2…..dD} and N unique tokens extracted out of the corpus C. The N tokens will form our dictionary and the size of the Count Vector matrix M will be given by D X N. Each row in the matrix M contains the frequency of tokens in document D(i).

Let us understand this using a simple example.

D1: He is a lazy boy. She is also lazy.

D2: Neeraj is a lazy person.

The dictionary created may be a list of unique tokens(words) in the corpus =[‘He’,’She’,’lazy’,’boy’,’Neeraj’,’person’]

Here, D=2, N=6

The count matrix M of size 2 X 6 will be represented as –

	He	She	lazy	boy	Neeraj	person
D1	1	1	2	1	0	0
D2	0	0	1	0	1	1

Now, a column can also be understood as word vector for the corresponding word in the matrix M. For example, the word vector for ‘lazy’ in the above matrix is [2,1] and so on.Here, the rows correspond to the documents in the corpus and the columns correspond to the tokens in the dictionary. The second row in the above matrix may be read as – D2 contains ‘lazy’: once, ‘Neeraj’: once and ‘person’ once.

Now there may be quite a few variations while preparing the above matrix M. The variations will be generally in-

• The way dictionary is prepared.
• Why? Because in real world applications we might have a corpus which contains millions of documents. And with millions of document, we can extract hundreds of millions of unique words. So basically, the matrix that will be prepared like above will be a very sparse one and inefficient for any computation. So an alternative to using every unique word as a dictionary element would be to pick say top 10,000 words based on frequency and then prepare a dictionary.
• The way count is taken for each word.
• We may either take the frequency (number of times a word has appeared in the document) or the presence(has the word appeared in the document?) to be the entry in the count matrix M. But generally, frequency method is preferred over the latter.

Below is a representational image of the matrix M for easy understanding.

1.2 TF-IDF vectorization

This is another method which is based on the frequency method but it is different to the count vectorization in the sense that it takes into account not just the occurrence of a word in a single document but in the entire corpus. So, what is the rationale behind this? Let us try to understand.

Common words like ‘is’, ‘the’, ‘a’ etc. tend to appear quite frequently in comparison to the words which are important to a document. For example, a document A on Lionel Messi is going to contain more occurences of the word “Messi” in comparison to other documents. But common words like “the” etc. are also going to be present in higher frequency in almost every document.

Ideally, what we would want is to down weight the common words occurring in almost all documents and give more importance to words that appear in a subset of documents.

TF-IDF works by penalising these common words by assigning them lower weights while giving importance to words like Messi in a particular document.

So, how exactly does TF-IDF work?

Consider the below sample table which gives the count of terms(tokens/words) in two documents.

Now, let us define a few terms related to TF-IDF.

TF = (Number of times term t appears in a document)/(Number of terms in the document)

So, TF(This,Document1) = 1/8

TF(This, Document2)=1/5

It denotes the contribution of the word to the document i.e words relevant to the document should be frequent. eg: A document about Messi should contain the word ‘Messi’ in large number.

IDF = log(N/n), where, N is the number of documents and n is the number of documents a term t has appeared in.

where N is the number of documents and n is the number of documents a term t has appeared in.

So, IDF(This) = log(2/2) = 0.

So, how do we explain the reasoning behind IDF? Ideally, if a word has appeared in all the document, then probably that word is not relevant to a particular document. But if it has appeared in a subset of documents then probably the word is of some relevance to the documents it is present in.

Let us compute IDF for the word ‘Messi’.

IDF(Messi) = log(2/1) = 0.301.

Now, let us compare the TF-IDF for a common word ‘This’ and a word ‘Messi’ which seems to be of relevance to Document 1.

TF-IDF(This,Document1) = (1/8) * (0) = 0

TF-IDF(This, Document2) = (1/5) * (0) = 0

TF-IDF(Messi, Document1) = (4/8)*0.301 = 0.15

As, you can see for Document1 , TF-IDF method heavily penalises the word ‘This’ but assigns greater weight to ‘Messi’. So, this may be understood as ‘Messi’ is an important word for Document1 from the context of the entire corpus.

1.3 Co-Occurrence Matrix with a fixed context window

The big idea – Similar words tend to occur together and will have similar context for example – Apple is a fruit. Mango is a fruit.

Apple and mango tend to have a similar context i.e fruit.

Before I dive into the details of how a co-occurrence matrix is constructed, there are two concepts that need to be clarified – Co-Occurrence and Context Window.

Co-occurrence – For a given corpus, the co-occurrence of a pair of words say w1 and w2 is the number of times they have appeared together in a Context Window.

Context Window – Context window is specified by a number and the direction. So what does a context window of 2 (around) means? Let us see an example below,

Quick

Brown

Fox

Jump

Over

The

Lazy

Dog

The green words are a 2 (around) context window for the word ‘Fox’ and for calculating the co-occurrence only these words will be counted. Let us see context window for the word ‘Over’.

Quick

Brown

Fox

Jump

Over

The

Lazy

Dog

Now, let us take an example corpus to calculate a co-occurrence matrix.

Corpus = He is not lazy. He is intelligent. He is smart.

	He	is	not	lazy	intelligent	smart
He	0	4	2	1	2	1
is	4	0	1	2	2	1
not	2	1	0	1	0	0
lazy	1	2	1	0	0	0
intelligent	2	2	0	0	0	0
smart	1	1	0	0	0	0

Let us understand this co-occurrence matrix by seeing two examples in the table above. Red and the blue box.

Red box- It is the number of times ‘He’ and ‘is’ have appeared in the context window 2 and it can be seen that the count turns out to be 4. The below table will help you visualise the count.

He	is	not	lazy	He	is	intelligent	He	is	smart
He	is	not	lazy	He	is	intelligent	He	is	smart
He	is	not	lazy	He	is	intelligent	He	is	smart
He	is	not	lazy	He	is	intelligent	He	is	smart

while the word ‘lazy’ has never appeared with ‘intelligent’ in the context window and therefore has been assigned 0 in the blue box.

Variations of Co-occurrence Matrix

Let’s say there are V unique words in the corpus. So Vocabulary size = V. The columns of the Co-occurrence matrix form the context words. The different variations of Co-Occurrence Matrix are-

• A co-occurrence matrix of size V X V. Now, for even a decent corpus V gets very large and difficult to handle. So generally, this architecture is never preferred in practice.
• A co-occurrence matrix of size V X N where N is a subset of V and can be obtained by removing irrelevant words like stopwords etc. for example. This is still very large and presents computational difficulties.

But, remember this co-occurrence matrix is not the word vector representation that is generally used. Instead, this Co-occurrence matrix is decomposed using techniques like PCA, SVD etc. into factors and combination of these factors forms the word vector representation.

Let me illustrate this more clearly. For example, you perform PCA on the above matrix of size VXV. You will obtain V principal components. You can choose k components out of these V components. So, the new matrix will be of the form V X k.

And, a single word, instead of being represented in V dimensions will be represented in k dimensions while still capturing almost the same semantic meaning. k is generally of the order of hundreds.

So, what PCA does at the back is decompose Co-Occurrence matrix into three matrices, U,S and V where U and V are both orthogonal matrices. What is of importance is that dot product of U and S gives the word vector representation and V gives the word context representation.

Advantages of Co-occurrence Matrix

• It preserves the semantic relationship between words. i.e man and woman tend to be closer than man and apple.
• It uses SVD at its core, which produces more accurate word vector representations than existing methods.
• It uses factorization which is a well-defined problem and can be efficiently solved.
• It has to be computed once and can be used anytime once computed. In this sense, it is faster in comparison to others.

Disadvantages of Co-Occurrence Matrix

• It requires huge memory to store the co-occurrence matrix.
• But, this problem can be circumvented by factorizing the matrix out of the system for example in Hadoop clusters etc. and can be saved.

Source: https://www.analyticsvidhya.com/blog/2017/06/word-embeddings-count-word2veec/