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# Word Representation

Approaches of word representation

## 🌚 Word Representation

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• One Hot Encoding
• Featurized Representation (Word Embedding)
• Word2Vec
• Skip Gram Model
• GloVe (Global Vectors for Word Representation)

## 🚀 One Hot Encoding

A way to represent words so we can treat with them easily

### 🔎 Example

Let's say that we have a dictionary that consists of 10 words (🤭) and the words of the dictionary are:
• Car, Pen, Girl, Berry, Apple, Likes, The, And, Boy, Book.
Our $$X^{(i)}$$ is: The Girl Likes Apple And Berry
So we can represent this sequence like the following 👀
Car -0) ⌈ 0 ⌉ ⌈ 0 ⌉ ⌈ 0 ⌉ ⌈ 0 ⌉ ⌈ 0 ⌉ ⌈ 0 ⌉
Pen -1) | 0 | | 0 | | 0 | | 0 | | 0 | | 0 |
Girl -2) | 0 | | 1 | | 0 | | 0 | | 0 | | 0 |
Berry -3) | 0 | | 0 | | 0 | | 0 | | 0 | | 1 |
Apple -4) | 0 | | 0 | | 0 | | 1 | | 0 | | 0 |
Likes -5) | 0 | | 0 | | 1 | | 0 | | 0 | | 0 |
The -6) | 1 | | 0 | | 0 | | 0 | | 0 | | 0 |
And -7) | 0 | | 0 | | 0 | | 0 | | 1 | | 0 |
Boy -8) | 0 | | 0 | | 0 | | 0 | | 0 | | 0 |
Book -9) ⌊ 0 ⌋ ⌊ 0 ⌋ ⌊ 0 ⌋ ⌊ 0 ⌋ ⌊ 0 ⌋ ⌊ 0 ⌋
By representing sequences in this way we can feed our data to neural networks✨

• If our dictionary consists of 10,000 words so each vector will be 10,000 dimensional 🤕
• This representation can not capture semantic features 💔

## 🎎 Featurized Representation (Word Embedding)

• Representing words by associating them with features such as gender, age, royal, food, cost, size.... and so on
• Every feature is represented as a range between [-1, 1]
• Thus, every word can be represented as a vector of these features
• The dimension of each vector is related to the number of features that we pick

### 🔢 Embedded Matrix

For a given word w, the embedding matrix E is a matrix that maps its 1-hot representation $$o_w$$ to its embedding $$e_w$$ as follows:
$$e_w=Eo_w$$

• Words that have the similar meaning have a similar representation.
• This model can capture semantic features ✨
• Vectors are smaller than vectors in one hot representation.
TODO: Subtracting vectors of oppsite words

### 🔄 Word2Vec

• Word2vec is a strategy to learn word embeddings by estimating the likelihood that a given word is surrounded by other words.
• This is done by making context and target word pairs which further depends on the window size we take.
• Window size: a parameter that looks to the left and right of the context word for as many as window_size words Creating Context to Target pairs with window size = 2 🙌

## Skip Gram Model

The skip-gram word2vec model is a supervised learning task that learns word embeddings by assessing the likelihood of any given target word t happening with a context word c. By noting $$θ_{t}$$ a parameter associated with t, the probability P(t|c) is given by:
$$P(t|c)=\frac{exp(\theta^T_te_c)}{\sum_{j=1}^{|V|}exp(\theta^T_je_c)}$$
Remark: summing over the whole vocabulary in the denominator of the softmax part makes this model computationally expensive

## 🚀 One Hot Rep. vs Word Embedding ## 🧤 GloVe

The GloVe model, short for global vectors for word representation, is a word embedding technique that uses a co-occurence matrix X where each $$X_{ij}$$ denotes the number of times that a target i occurred with a context j. Its cost function J is as follows:
$$J(\theta)=\frac{1}{2}\sum_{i,j=1}^{|V|}f(X_{ij})(\theta^T_ie_j+b_i+b'j-log(X{ij}))^2$$
where f is a weighting function such that $$X_{ij}=0$$ ⟹ $$f(X_{ij})$$ = 0. Given the symmetry that e and θ play in this model, the final word embedding e $$e^{(final)}_w$$ is given by:
$$e^{(final)}_w=\frac{e_w+\theta_w}{2}$$

## 👩‍🏫 Conclusion of Word Embeddings

• If this is your first try, you should try to download a pre-trained model that has been made and actually works best.
• If you have enough data, you can try to implement one of the available algorithms.
• Because word embeddings are very computationally expensive to train, most ML practitioners will load a pre-trained set of embeddings.