md`# Understanding Word Vectors
//mm edits by M.M.
*A js/observable port of Allison Parrish's excellent [Jupyter notebook](https://gist.github.com/aparrish/2f562e3737544cf29aaf1af30362f469) of the same name.*
## Animal similarity and linear algebra
We'll begin by considering a small subset of English: words for animals. Our task is to be able to write programs to find similarities among these words and the creatures they designate. To do this, we might start by making a spreadsheet of some animals and their characteristics. For example:
`
distance2d = function(p1, p2){
let dx = p2[0] - p1[0];
let dy = p2[1] - p1[1];
return Math.sqrt(dx * dx + dy * dy);
}
distance2d(animal('capybara'), animal('panda bear')) // panda and capybara
distance2d(animal('tarantula'), animal('elephant')) // tarantula and elephant
colors['olive']
colors['red']
colors['black']
distance([10, 1], [5, 2]);
subtractv([10, 1], [5, 2])
addv([10, 1], [5, 2])
meanv([[0, 1], [2, 2], [4, 3]])
distance(colors['red'], colors['green']) > distance(colors['red'], colors['pink'])
closest(colors, colors.red)
closest(colors, [150, 60, 150])
closest(colors, subtractv(colors['purple'], colors['red']))
closest(colors, addv(colors['blue'], colors['green']))
// the average of black and white: medium grey
closest(colors, meanv([colors['black'], colors['white']]))
{
// an analogy: pink is to red as X is to blue
let pinkToRed = subtractv(colors['pink'], colors['red'])
return closest(colors, addv(pinkToRed, colors['blue']))
}
{
// another example:
let navyToBlue = subtractv(colors['navy'], colors['blue'])
return closest(colors, addv(navyToBlue, colors['green']))
}
avgColor = {
let doc = await gutenFetch('http://www.gutenberg.org/cache/epub/345/pg345.txt');
let words = RiTa.tokenize(doc), dracColors = [];
words.forEach((w,i) => colors[w.toLowerCase()]
&& dracColors.push(colors[w.toLowerCase()]));
return meanv(dracColors);
}
closest(colors, avgColor)
closest(colors, colors['mauve']).map(cname => cname + " trousers");
tokens = RiTa.tokens(await gutenFetch('http://www.gutenberg.org/cache/epub/345/pg345.txt'));
gloVe.getVector("cheese")
cosine = function(v1, v2) {
let vec1 = tf.tensor1d(v1);
let vec2 = tf.tensor1d(v2);
let dot = vec1.dot(vec2).asScalar();
let sim = dot.div(vec1.norm(2)).div(vec2.norm(2));
return 1 - sim.dataSync()[0];
}
cosine(vec('dog'), vec('puppy')) < cosine(vec('trousers'), vec('octopus'))
gloVeClosest = async function(tokenList, vector, n=10) {
let tensor = tf.tensor1d(vector);
let neighbors = await gloVe._getNearestNeighbors(tensor, n*100, true);
return neighbors.filter(t => tokenList.includes(t.word)).slice(0, n).map(n => n.word);
}
gloVeClosest(tokens, vec("basketball"))
gloVeClosest(tokens, meanv([vec("day"), vec("night")]))
gloVeClosest(tokens, vec("wine"))
gloVeClosest(tokens, subtractv(vec("wine"), vec("alcohol"))) // hmmm, something off here
gloVeClosest(tokens, vec("water"))
gloVeClosest(tokens, addv(vec("water"),vec("frozen")))
gloVeClosest(tokens, vec("grass"))
{
// analogy: blue is to sky as X is to grass
let blueToSky = subtractv(vec("blue"), vec("sky"))
return gloVeClosest(tokens, addv(blueToSky, vec("grass")))
}
sentVec = function(s) {
let words = RiTa.tokenize(s);
return meanv(words.map(w => gloVe.getVector(w)));
}
sentences = RiTa.sentences(await gutenFetch('http://www.gutenberg.org/cache/epub/345/pg345.txt'));
gloVeClosestSent = function(space, inputStr, n=10) {
let inputVec = sentVec(inputStr);
let dists = {};
console.time("cos");
space = space.slice(0,500);
space.forEach(x => dists[x] = cosine(sentVec(x), inputVec));
console.timeEnd("cos");
return Object.keys(dists).sort((a,b) => dists[a] - dists[b]).slice(0,n);
}
animal = function(name) { return data.filter(d => d.name === name).map(o => [o.cuteness, o.size])[0] }
RiTa = require('rita@2.4.86');
height = 400
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