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fabrizioc1/Learning_LSH.ipynb

Created March 29, 2018 09:00
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Learning_LSH.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 123,
"metadata": {},
"outputs": [],
"source": [
"import random\n",
"import numpy as np\n",
"import functools\n",
"from collections import defaultdict, OrderedDict\n",
"\n",
"BANDS_COUNT = 4\n",
"FEATURES_COUNT = 10\n",
"SAMPLES_COUNT = 200\n",
"HASH_FUNCTIONS_COUNT = 50\n",
"\n",
"P_VALUE = 15307\n",
"R_VALUE = HASH_FUNCTIONS_COUNT / BANDS_COUNT\n",
"\n",
"EXPECTED_JACCARD_SIMILARITY = (1.0 / BANDS_COUNT) ** (1.0 / R_VALUE)\n",
"\n",
"def generate_features():\n",
" return [int(round(random.random())) for i in range(FEATURES_COUNT)]\n",
"\n",
"def minhash(v, a, b, p):\n",
" row_numbers = np.arange(len(v), dtype = np.int)\n",
" hash_values = (a * row_numbers + b) % p\n",
" return min([hash_value for hash_value, feature in zip(hash_values, v) if feature])\n",
"\n",
"def get_lsh(sig, b, r):\n",
" lsh = []\n",
" for i, band in enumerate(range(b)):\n",
" lsh_hash_input = tuple(sig[i * r:i * r + r])\n",
" lsh_hash_value = hash(lsh_hash_input)\n",
" lsh.append(lsh_hash_value)\n",
" return lsh\n",
"\n",
"hash_functions_seeds = np.random.randint(0, P_VALUE + 1, size=(HASH_FUNCTIONS_COUNT,2))\n",
"hash_functions = [functools.partial(minhash, a = s[0], b = s[1], p = P_VALUE) for s in hash_functions_seeds]\n",
"\n",
"def create_signature(features):\n",
" return [hash_function(features) for hash_function in hash_functions]\n",
"\n",
"features = [generate_features() for i in range(SAMPLES_COUNT)]\n",
"signatures = [create_signature(item) for item in features]\n",
"lsh_values = [get_lsh(signature, BANDS_COUNT, R_VALUE) for signature in signatures]\n",
"lsh_groups = defaultdict(list)\n",
"\n",
"for i, lsh_hashes in enumerate(lsh_values):\n",
" for lsh_hash in lsh_hashes:\n",
" lsh_groups[lsh_hash].append(i)"
]
},
{
"cell_type": "code",
"execution_count": 124,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
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" 690183900078809008: array([98])\n",
"-6988302191411374157: array([99])\n",
" 63678250346071988: array([180])\n",
" 8985949513703303838: array([172])\n",
"-2348289424712001610: array([43])\n",
"-8417894611852292166: array([77])\n",
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" 726679056062449606: array([86])\n",
"-5024203455956938809: array([175])\n",
"-4995423867204231214: array([110])\n",
" 8498636628145590227: array([98])\n",
"-4263942708411076651: array([179])\n",
"-1735819078863671335: array([59])\n",
" 3821059279430873424: array([41])\n",
" 4578714089656546647: array([102])\n",
"-3181093704174411805: array([69])\n",
" 8640762441285853157: array([124])\n",
" 1275063547491753961: array([175])\n",
" 4122369044275421168: array([120])\n",
" -137982345661284013: array([146])\n",
" 4268678903566027433: array([107])\n",
" 519413400269240312: array([137])\n",
" -669122388335052806: array([169])\n"
]
}
],
"source": [
"lsh_groups_sorted = sorted(lsh_groups.iteritems(), key=lambda (lsh_hash, indices): len(indices), reverse=True)\n",
"for (h, i) in lsh_groups_sorted:\n",
" print(\"%20d: %r\" % (h, np.array(i)))"
]
},
{
"cell_type": "code",
"execution_count": 125,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[[1, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n",
" [1, 0, 1, 1, 1, 1, 0, 0, 1, 1],\n",
" [1, 0, 1, 1, 0, 1, 0, 1, 1, 1],\n",
" [1, 1, 1, 1, 1, 1, 0, 1, 1, 0],\n",
" [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n",
" [1, 1, 1, 1, 1, 1, 0, 0, 1, 1],\n",
" [1, 0, 1, 1, 1, 1, 0, 1, 1, 1],\n",
" [1, 1, 1, 1, 0, 1, 0, 1, 1, 0],\n",
" [1, 0, 1, 1, 0, 1, 0, 0, 1, 1],\n",
" [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]]"
]
},
"execution_count": 125,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"[features[idx] for idx in lsh_groups_sorted[0][1]]"
]
},
{
"cell_type": "code",
"execution_count": 126,
"metadata": {},
"outputs": [],
"source": [
"def jaccard(x, y):\n",
" a = np.array(x)\n",
" b = np.array(y)\n",
" union = float(sum(a | b)) \n",
" intersection = float(sum(a & b))\n",
" return round(intersection / union, 4)"
]
},
{
"cell_type": "code",
"execution_count": 127,
"metadata": {},
"outputs": [],
"source": [
"def calculate_similarities(rows):\n",
" sims = [(jaccard(a,b), a, b) for a in rows for b in rows]\n",
" sims = sorted(sims, key=lambda (j, a, b): j, reverse=True)\n",
" return sims"
]
},
{
"cell_type": "code",
"execution_count": 128,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1.0000: [1, 0, 1, 1, 1, 1, 1, 1, 1, 1] [1, 0, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"1.0000: [1, 0, 1, 1, 1, 1, 0, 0, 1, 1] [1, 0, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"1.0000: [1, 0, 1, 1, 0, 1, 0, 1, 1, 1] [1, 0, 1, 1, 0, 1, 0, 1, 1, 1]\n",
"1.0000: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"1.0000: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"1.0000: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"1.0000: [1, 1, 1, 1, 1, 1, 0, 0, 1, 1] [1, 1, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"1.0000: [1, 0, 1, 1, 1, 1, 0, 1, 1, 1] [1, 0, 1, 1, 1, 1, 0, 1, 1, 1]\n",
"1.0000: [1, 1, 1, 1, 0, 1, 0, 1, 1, 0] [1, 1, 1, 1, 0, 1, 0, 1, 1, 0]\n",
"1.0000: [1, 0, 1, 1, 0, 1, 0, 0, 1, 1] [1, 0, 1, 1, 0, 1, 0, 0, 1, 1]\n",
"1.0000: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"1.0000: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"0.9000: [1, 0, 1, 1, 1, 1, 1, 1, 1, 1] [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"0.9000: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] [1, 0, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"0.8889: [1, 0, 1, 1, 1, 1, 1, 1, 1, 1] [1, 0, 1, 1, 1, 1, 0, 1, 1, 1]\n",
"0.8889: [1, 0, 1, 1, 1, 1, 0, 1, 1, 1] [1, 0, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"0.8750: [1, 0, 1, 1, 1, 1, 0, 0, 1, 1] [1, 1, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"0.8750: [1, 0, 1, 1, 1, 1, 0, 0, 1, 1] [1, 0, 1, 1, 1, 1, 0, 1, 1, 1]\n",
"0.8750: [1, 0, 1, 1, 0, 1, 0, 1, 1, 1] [1, 0, 1, 1, 1, 1, 0, 1, 1, 1]\n",
"0.8750: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 1, 1, 1, 0, 1, 0, 1, 1, 0]\n",
"0.8750: [1, 1, 1, 1, 1, 1, 0, 0, 1, 1] [1, 0, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"0.8750: [1, 0, 1, 1, 1, 1, 0, 1, 1, 1] [1, 0, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"0.8750: [1, 0, 1, 1, 1, 1, 0, 1, 1, 1] [1, 0, 1, 1, 0, 1, 0, 1, 1, 1]\n",
"0.8750: [1, 1, 1, 1, 0, 1, 0, 1, 1, 0] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"0.8750: [1, 1, 1, 1, 0, 1, 0, 1, 1, 0] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"0.8750: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 1, 1, 1, 0, 1, 0, 1, 1, 0]\n",
"0.8571: [1, 0, 1, 1, 1, 1, 0, 0, 1, 1] [1, 0, 1, 1, 0, 1, 0, 0, 1, 1]\n",
"0.8571: [1, 0, 1, 1, 0, 1, 0, 1, 1, 1] [1, 0, 1, 1, 0, 1, 0, 0, 1, 1]\n",
"0.8571: [1, 0, 1, 1, 0, 1, 0, 0, 1, 1] [1, 0, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"0.8571: [1, 0, 1, 1, 0, 1, 0, 0, 1, 1] [1, 0, 1, 1, 0, 1, 0, 1, 1, 1]\n",
"0.8000: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"0.8000: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"0.8000: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] [1, 1, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"0.8000: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] [1, 0, 1, 1, 1, 1, 0, 1, 1, 1]\n",
"0.8000: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"0.8000: [1, 1, 1, 1, 1, 1, 0, 0, 1, 1] [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"0.8000: [1, 0, 1, 1, 1, 1, 0, 1, 1, 1] [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"0.8000: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"0.7778: [1, 0, 1, 1, 1, 1, 1, 1, 1, 1] [1, 0, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"0.7778: [1, 0, 1, 1, 1, 1, 1, 1, 1, 1] [1, 0, 1, 1, 0, 1, 0, 1, 1, 1]\n",
"0.7778: [1, 0, 1, 1, 1, 1, 0, 0, 1, 1] [1, 0, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"0.7778: [1, 0, 1, 1, 0, 1, 0, 1, 1, 1] [1, 0, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"0.7778: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 1, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"0.7778: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 0, 1, 1, 1, 1, 0, 1, 1, 1]\n",
"0.7778: [1, 1, 1, 1, 1, 1, 0, 0, 1, 1] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"0.7778: [1, 1, 1, 1, 1, 1, 0, 0, 1, 1] [1, 0, 1, 1, 1, 1, 0, 1, 1, 1]\n",
"0.7778: [1, 1, 1, 1, 1, 1, 0, 0, 1, 1] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"0.7778: [1, 0, 1, 1, 1, 1, 0, 1, 1, 1] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"0.7778: [1, 0, 1, 1, 1, 1, 0, 1, 1, 1] [1, 1, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"0.7778: [1, 0, 1, 1, 1, 1, 0, 1, 1, 1] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"0.7778: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 1, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"0.7778: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 0, 1, 1, 1, 1, 0, 1, 1, 1]\n",
"0.7500: [1, 0, 1, 1, 1, 1, 0, 0, 1, 1] [1, 0, 1, 1, 0, 1, 0, 1, 1, 1]\n",
"0.7500: [1, 0, 1, 1, 0, 1, 0, 1, 1, 1] [1, 0, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"0.7500: [1, 0, 1, 1, 0, 1, 0, 1, 1, 1] [1, 1, 1, 1, 0, 1, 0, 1, 1, 0]\n",
"0.7500: [1, 1, 1, 1, 1, 1, 0, 0, 1, 1] [1, 0, 1, 1, 0, 1, 0, 0, 1, 1]\n",
"0.7500: [1, 0, 1, 1, 1, 1, 0, 1, 1, 1] [1, 0, 1, 1, 0, 1, 0, 0, 1, 1]\n",
"0.7500: [1, 1, 1, 1, 0, 1, 0, 1, 1, 0] [1, 0, 1, 1, 0, 1, 0, 1, 1, 1]\n",
"0.7500: [1, 0, 1, 1, 0, 1, 0, 0, 1, 1] [1, 1, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"0.7500: [1, 0, 1, 1, 0, 1, 0, 0, 1, 1] [1, 0, 1, 1, 1, 1, 0, 1, 1, 1]\n",
"0.7000: [1, 0, 1, 1, 1, 1, 1, 1, 1, 1] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"0.7000: [1, 0, 1, 1, 1, 1, 1, 1, 1, 1] [1, 1, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"0.7000: [1, 0, 1, 1, 1, 1, 1, 1, 1, 1] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"0.7000: [1, 0, 1, 1, 1, 1, 0, 0, 1, 1] [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"0.7000: [1, 0, 1, 1, 0, 1, 0, 1, 1, 1] [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"0.7000: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 0, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"0.7000: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] [1, 0, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"0.7000: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] [1, 0, 1, 1, 0, 1, 0, 1, 1, 1]\n",
"0.7000: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] [1, 1, 1, 1, 0, 1, 0, 1, 1, 0]\n",
"0.7000: [1, 1, 1, 1, 1, 1, 0, 0, 1, 1] [1, 0, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"0.7000: [1, 1, 1, 1, 0, 1, 0, 1, 1, 0] [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"0.7000: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 0, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"0.6667: [1, 0, 1, 1, 1, 1, 1, 1, 1, 1] [1, 0, 1, 1, 0, 1, 0, 0, 1, 1]\n",
"0.6667: [1, 0, 1, 1, 1, 1, 0, 0, 1, 1] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"0.6667: [1, 0, 1, 1, 1, 1, 0, 0, 1, 1] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"0.6667: [1, 0, 1, 1, 0, 1, 0, 1, 1, 1] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"0.6667: [1, 0, 1, 1, 0, 1, 0, 1, 1, 1] [1, 1, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"0.6667: [1, 0, 1, 1, 0, 1, 0, 1, 1, 1] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"0.6667: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 0, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"0.6667: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 0, 1, 1, 0, 1, 0, 1, 1, 1]\n",
"0.6667: [1, 1, 1, 1, 1, 1, 0, 0, 1, 1] [1, 0, 1, 1, 0, 1, 0, 1, 1, 1]\n",
"0.6667: [1, 1, 1, 1, 1, 1, 0, 0, 1, 1] [1, 1, 1, 1, 0, 1, 0, 1, 1, 0]\n",
"0.6667: [1, 0, 1, 1, 1, 1, 0, 1, 1, 1] [1, 1, 1, 1, 0, 1, 0, 1, 1, 0]\n",
"0.6667: [1, 1, 1, 1, 0, 1, 0, 1, 1, 0] [1, 1, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"0.6667: [1, 1, 1, 1, 0, 1, 0, 1, 1, 0] [1, 0, 1, 1, 1, 1, 0, 1, 1, 1]\n",
"0.6667: [1, 0, 1, 1, 0, 1, 0, 0, 1, 1] [1, 0, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"0.6667: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 0, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"0.6667: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 0, 1, 1, 0, 1, 0, 1, 1, 1]\n",
"0.6250: [1, 1, 1, 1, 0, 1, 0, 1, 1, 0] [1, 0, 1, 1, 0, 1, 0, 0, 1, 1]\n",
"0.6250: [1, 0, 1, 1, 0, 1, 0, 0, 1, 1] [1, 1, 1, 1, 0, 1, 0, 1, 1, 0]\n",
"0.6000: [1, 0, 1, 1, 1, 1, 1, 1, 1, 1] [1, 1, 1, 1, 0, 1, 0, 1, 1, 0]\n",
"0.6000: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] [1, 0, 1, 1, 0, 1, 0, 0, 1, 1]\n",
"0.6000: [1, 1, 1, 1, 0, 1, 0, 1, 1, 0] [1, 0, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"0.6000: [1, 0, 1, 1, 0, 1, 0, 0, 1, 1] [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n",
"0.5556: [1, 0, 1, 1, 1, 1, 0, 0, 1, 1] [1, 1, 1, 1, 0, 1, 0, 1, 1, 0]\n",
"0.5556: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 0, 1, 1, 0, 1, 0, 0, 1, 1]\n",
"0.5556: [1, 1, 1, 1, 0, 1, 0, 1, 1, 0] [1, 0, 1, 1, 1, 1, 0, 0, 1, 1]\n",
"0.5556: [1, 0, 1, 1, 0, 1, 0, 0, 1, 1] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"0.5556: [1, 0, 1, 1, 0, 1, 0, 0, 1, 1] [1, 1, 1, 1, 1, 1, 0, 1, 1, 0]\n",
"0.5556: [1, 1, 1, 1, 1, 1, 0, 1, 1, 0] [1, 0, 1, 1, 0, 1, 0, 0, 1, 1]\n"
]
}
],
"source": [
"for (j, a, b) in calculate_similarities([features[idx] for idx in lsh_groups_sorted[0][1]]):\n",
" print(\"%.4f: %r %r\" % (j, a, b))"
]
},
{
"cell_type": "code",
"execution_count": 122,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.8908987181403393"
]
},
"execution_count": 122,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"EXPECTED_JACCARD_SIMILARITY"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.10"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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