---
up:
  - "[[M1 LOGOS]]"
tags:
  - s/fac
  - s/informatique
aliases:
---

# Vocabulary

$\underbrace{(x_1, x_2, \dots, x_{n})}_{\text{vector of length } n} \in \mathbb{R}^{n}$

$x_{i} \in \mathbb{R}$ is a scalar

one-hot : boolean vector with all zeroes but one value. Usefull if each dimension represents a word of the vocabulary

BOW : Bag Of Words
You could represent sentences like that :
Let our vocabulary be : `V = 'le' 'un' 'garcon' 'lit' 'livre' 'regarde'`
Then "le garcon lit le livre" would be written by counting the number of occurences of each word of the sentence in a vector, so `2 0 1 1 1 0` (the formula is `sentence +⌿⍤(∘.≡) vocabulary`)

$\cos(u, v) = \frac{u\cdot v}{\|u\| \| v\|}$