# One-hot vector for fixed vocabulary

given a vocabulary with $$|V|=4$$ and V = {I, want, this, cat} for example.

How does the bag-of-words representation with this vocabulary and one-hot encoding look like regarding example sentences:

1. You are the dog here
2. I am fifty
3. Cat cat cat

I suppose it would look like this

1. $$V_1 = \begin{pmatrix} 0 \\ 0 \\ 0 \\ 0 \\ \end{pmatrix}$$

2. $$V_2 = \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \\ \end{pmatrix}$$

3. $$V_3=\begin{pmatrix} 0 \\ 0 \\ 0 \\ 1 \\ \end{pmatrix}$$

But what exactly is the point of this representation? Does is show the weakness of one-hot encoding with a fixed vocabulary or did I miss something?

• I think this is correct – Peter Nov 17 '20 at 8:26

library(quanteda)

mytext <- c(oldtext = "I want this cat")
dtm_old <- dfm(mytext)
dtm_old

newtext <- c(newtext = "You are the dog here")
dtm_new <- dfm(newtext)
dtm_new

dtm_matched <- dfm_match(dtm_new, featnames(dtm_old))
dtm_matched


$$V_1$$

Document-feature matrix of: 1 document, 4 features (100.0% sparse).
features
docs      i want this cat
newtext 0    0    0   0


$$V_2$$

Document-feature matrix of: 1 document, 4 features (75.0% sparse).
features
docs      i want this cat
newtext 1    0    0   0


$$V_3$$

Document-feature matrix of: 1 document, 4 features (75.0% sparse).
features
docs      i want this cat
newtext 0    0    0   3


Of course when using a "one hot" vectorizer, "cat" in $$V_3$$ would be 1 (instead of the count).