Count-Min sketch

count_min_sketch.ipynb

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   "source": [
    "## Count-Min Sketch\n",
    "\n",
    "Thanks to [A practical introduction to the Count-Min Sketch](https://hkorte.github.io/slides/cmsketch/#/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bar 1\n",
      "billy 1\n",
      "foo 2\n",
      "bing 1\n"
     ]
    }
   ],
   "source": [
    "L = 100\n",
    "counter = [0] * L\n",
    "\n",
    "def counter_index(word):\n",
    "    return sum(map(ord, word)) % L\n",
    "\n",
    "def get_count(word):\n",
    "    return counter[counter_index(word)]\n",
    "\n",
    "def count(word):\n",
    "    counter[counter_index(word)] += 1\n",
    "\n",
    "words = ['foo', 'bar', 'bing', 'foo', 'billy']\n",
    "\n",
    "for word in words:\n",
    "    count(word)\n",
    "    \n",
    "for word in set(words):\n",
    "    print(word, get_count(word))\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**There will be collisions!**\n",
    "We can minimize these by:\n",
    "- Use multiple arrays with different hash functions\n",
    "- When queried return the minimum of the numbers of the arrays (error correction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bar 1\n",
      "billy 1\n",
      "foo 2\n",
      "bing 1\n"
     ]
    }
   ],
   "source": [
    "import hashlib\n",
    "\n",
    "L = 100\n",
    "N = 5\n",
    "counter = [[0] * L] * N\n",
    "\n",
    "_hash_algos = [\n",
    "    hashlib.md5,\n",
    "    hashlib.sha1,\n",
    "    hashlib.sha224,\n",
    "    hashlib.sha256,\n",
    "    hashlib.sha384,\n",
    "]\n",
    "\n",
    "def counter_index(word, n):\n",
    "    return int(_hash_algos[n](word.encode()).hexdigest(), 16) % L\n",
    "\n",
    "\n",
    "def get_count(word):\n",
    "    return min(\n",
    "        counter[n][counter_index(word, n)]\n",
    "        for n in range(N))\n",
    "\n",
    "\n",
    "def count(word):\n",
    "    # Error correction, only update lowest counters.\n",
    "    counts = [counter[n][counter_index(word, n)] for n in range(N)]\n",
    "    min_ = min(counts)\n",
    "    to_update = [i for i, e in enumerate(counts) if e == min_]\n",
    "    for i in to_update:\n",
    "        counter[i][counter_index(word, i)] += 1\n",
    "    \n",
    "    \n",
    "words = ['foo', 'bar', 'bing', 'foo', 'billy']\n",
    "\n",
    "for word in words:\n",
    "    count(word)\n",
    "    \n",
    "for word in set(words):\n",
    "    print(word, get_count(word))"
   ]
  }
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