"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#set up standard corpora + vectors\n",
"vfair_all = Setup.make_standard_sampler_and_vecs('vfair',5,100,1) #window=5, dims=100, min_count=1\n",
"heartd_all = Setup.make_standard_sampler_and_vecs('heartd',5,100,1) #window=5, dims=100, min_count=1\n",
"\n",
"what = [['Vanity Fair (vfair)'],['Heart of Darkness (heartd)']]\n",
"for i,c in enumerate([vfair_all,heartd_all]):\n",
" sampler = c['sampler']\n",
" what[i].extend([sum(sampler.counts.values()), len(sampler.counts)])\n",
"\n",
"show_table(what, headers=['Corpus','Tokens','Types'], title=\"Corpora sizes\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Background\n",
"\n",
"[[1]](#ref1) is a nice paper which examines some aspects of the distribution of word vectors in vector space. Although the emphasis of the paper is on skip ngrams with negative sampling (sgns), they also consistently compare sgns with the GLoVe approach. Here I will also include the FastText and PPMI approaches that I have been considering throughout this series of posts. By expanding the number of methods, and by using the small corpora, we can see to what extent the observations from [[1]](#ref1) hold more broadly. As mentioned above, mostly they do."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Distribution with respect to the mean\n",
"\n",
"The first aspect I'll look at is distribution with respect to the mean. [[1]](#ref1) take the mean of vectors. They then compute the dot products of all the vectors with the mean, and plot the resulting distributions by 4 frequency bands. Their frequency bands are:\n",
"\n",
"
\n",
"
Frequency range
Name
\n",
"
1-100
ultra hight
\n",
"
100-500
high
\n",
"
500-5000
moderate
\n",
"
5000 and up
low
\n",
"
\n",
"\n",
"What they observe for their large (~70,000 word vocabulary) corpus is that:\n",
"\n",
"* \"SGNS vector inner products are all positive, with low-frequency words the most positive\"\n",
"* \"GloVe inner products become positive for low-frequency words and negative for high-frequency words\"\n",
"\n",
"Note that since the dot product is the cosine of the angle between the vectors times their lengths, the sign of the distributions, which is what we're interested in, would be the same if we just took the cosine similarity. However, I'll use the dot product to be consistent. (Also note that since I've normalized the vectors, the dot product here is just the cosine similarity scaled by the length of the mean vector.)\n",
"\n",
"Rather than using absolute frequencies for the frequency bands, I'll use percentiles, since this allows for easier comparison across corpora of different sizes. Here I've arbitrarily chose 10 percentiles as the band width.\n",
"\n",
"This is what we get for _Vanity Fair_ (_vfair_) with the 4 different methods."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"Skip down"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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3lUnbsNGy3EaqrN+d8630lkNEzCA9mPAj0vq5k7SuyFcOv0v6v5hDapj+p2HO8gxSu5j6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\nNIQs4iRJkoaQRZwkSdIQsoiTJEkaQv8/zSju7+Q7IboAAAAASUVORK5CYII=\n",
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