Lab_ex_1_2_solution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ex 1.2: A simple parallel MapReduce framework in Python\n",
    "Now we use the [*multiprocessing*](https://docs.python.org/3/library/multiprocessing.html) lib to actually do things in parallel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "import collections\n",
    "import itertools\n",
    "import multiprocessing\n",
    "\n",
    "\n",
    "class SimpleMapReduce:\n",
    "\n",
    "    def __init__(self, map_func, reduce_func, num_workers=None):\n",
    "        \"\"\"\n",
    "        map_func\n",
    "\n",
    "          Function to map inputs to intermediate data. Takes as\n",
    "          argument one input value and returns a tuple with the\n",
    "          key and a value to be reduced.\n",
    "\n",
    "        reduce_func\n",
    "\n",
    "          Function to reduce partitioned version of intermediate\n",
    "          data to final output. Takes as argument a key as\n",
    "          produced by map_func and a sequence of the values\n",
    "          associated with that key.\n",
    "\n",
    "        num_workers\n",
    "\n",
    "          The number of workers to create in the pool. Defaults\n",
    "          to the number of CPUs available on the current host.\n",
    "        \"\"\"\n",
    "        self.map_func = map_func\n",
    "        self.reduce_func = reduce_func\n",
    "        self.pool = multiprocessing.Pool(num_workers)\n",
    "\n",
    "    def partition(self, mapped_values):\n",
    "        \"\"\"Organize the mapped values by their key.\n",
    "        Returns an unsorted sequence of tuples with a key\n",
    "        and a sequence of values.\n",
    "        \"\"\"\n",
    "        partitioned_data = collections.defaultdict(list)\n",
    "        for key, value in mapped_values:\n",
    "            partitioned_data[key].append(value)\n",
    "        return partitioned_data.items()\n",
    "\n",
    "    def __call__(self, inputs, chunksize=1):\n",
    "        \"\"\"Process the inputs through the map and reduce functions\n",
    "        given.\n",
    "\n",
    "        inputs\n",
    "          An iterable containing the input data to be processed.\n",
    "\n",
    "        chunksize=1\n",
    "          The portion of the input data to hand to each worker.\n",
    "          This can be used to tune performance during the mapping\n",
    "          phase.\n",
    "        \"\"\"\n",
    "        map_responses = self.pool.map(\n",
    "            self.map_func,\n",
    "            inputs,\n",
    "            chunksize=chunksize,\n",
    "        )\n",
    "        partitioned_data = self.partition(\n",
    "            itertools.chain(*map_responses)\n",
    "        )\n",
    "        reduced_values = self.pool.map(\n",
    "            self.reduce_func,\n",
    "            partitioned_data,\n",
    "        )\n",
    "        return reduced_values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A Word Count example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "import string\n",
    "\n",
    "# map - read file and count words\n",
    "def file_to_words(filename):\n",
    "    \"\"\"Read a file and return a sequence of\n",
    "    (word, occurences) values.\n",
    "    \"\"\"\n",
    "    STOP_WORDS = set([\n",
    "        'a', 'an', 'and', 'are', 'as', 'be', 'by', 'for', 'if',\n",
    "        'in', 'is', 'it', 'of', 'or', 'py', 'rst', 'that', 'the',\n",
    "        'to', 'with',\n",
    "    ])\n",
    "    TR = str.maketrans({\n",
    "        p: ' '\n",
    "        for p in string.punctuation\n",
    "    })\n",
    "\n",
    "    print('{} reading {}'.format(\n",
    "        multiprocessing.current_process().name, filename))\n",
    "    output = []\n",
    "\n",
    "    with open(filename, 'rt') as f:\n",
    "        for line in f:\n",
    "            # Skip comment lines.\n",
    "            if line.lstrip().startswith('..'):\n",
    "                continue\n",
    "            line = line.translate(TR)  # Strip punctuation\n",
    "            for word in line.split():\n",
    "                word = word.lower()\n",
    "                if word.isalpha() and word not in STOP_WORDS:\n",
    "                    output.append((word, 1))\n",
    "    return output\n",
    "\n",
    "# reduce\n",
    "def count_words(item):\n",
    "    \"\"\"Convert the partitioned data for a word to a\n",
    "    tuple containing the word and the number of occurences.\n",
    "    \"\"\"\n",
    "    word, occurences = item\n",
    "    return (word, sum(occurences))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ForkPoolWorker-93 reading text3.rst\n",
      "ForkPoolWorker-95 reading text2.rst\n",
      "ForkPoolWorker-94 reading text4.rst\n",
      "ForkPoolWorker-96 reading text1.rst\n",
      "\n",
      "TOP 20 WORDS BY FREQUENCY\n",
      "\n",
      "my    :    67\n",
      "i     :    60\n",
      "her   :    43\n",
      "he    :    41\n",
      "quiz  :    33\n",
      "was   :    28\n",
      "quick :    28\n",
      "his   :    23\n",
      "fox   :    22\n",
      "she   :    21\n",
      "from  :    20\n",
      "when  :    20\n",
      "blind :    19\n",
      "would :    18\n",
      "so    :    18\n",
      "but   :    18\n",
      "have  :    18\n",
      "vex   :    18\n",
      "on    :    17\n",
      "which :    16\n"
     ]
    }
   ],
   "source": [
    "import operator\n",
    "import glob #easy file access\n",
    "\n",
    "input_files = glob.glob('*.rst')#get all text files names \n",
    "\n",
    "mapper = SimpleMapReduce(file_to_words, count_words)#get mapreduce instance with custom map and reduce functions\n",
    "word_counts = mapper(input_files)#call parallel mapreduce on files\n",
    "\n",
    "word_counts.sort(key=operator.itemgetter(1))#sort results\n",
    "word_counts.reverse()\n",
    "\n",
    "print('\\nTOP 20 WORDS BY FREQUENCY\\n')\n",
    "top20 = word_counts[:20]\n",
    "longest = max(len(word) for word, count in top20)\n",
    "for word, count in top20:\n",
    "    print('{word:<{len}}: {count:5}'.format(\n",
    "            len=longest + 1,\n",
    "            word=word,\n",
    "            count=count)\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## K-Means implementation\n",
    "Use the simple frame work to implement K-Means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.datasets import make_blobs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7faf414d7050>"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#generate data with K=4\n",
    "X, y = make_blobs(n_samples=1500, centers=4)\n",
    "plt.scatter(X[:, 0], X[:, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7faf41532490>"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#K-Means ref implementation\n",
    "k = KMeans(n_clusters=4)\n",
    "y_pred = k.fit_predict(X)\n",
    "\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-8.91460098, -5.44137271],\n",
       "       [-6.23283648,  7.73816223],\n",
       "       [-2.17305153, -2.59736126],\n",
       "       [ 0.14007764,  5.17995039]])"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k.cluster_centers_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 2)"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.shape(k.cluster_centers_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [],
   "source": [
    "#implement map -> assign data to center \n",
    "def kMap( data, centers):\n",
    "    #print('{} mapping {}'.format(\n",
    "    #    multiprocessing.current_process().name, data))\n",
    "    output=[]\n",
    "    center = 0\n",
    "    min_dist = 999999999\n",
    "    for c in range(np.shape(centers)[0]):\n",
    "            dist = (data[0]-centers[c][0])*(data[0]-centers[c][0]) + (data[1]-centers[c][1])*(data[1]-centers[c][1])\n",
    "            dist=np.sqrt(dist) \n",
    "            if dist<min_dist:\n",
    "                min_dist=dist\n",
    "                center = c\n",
    "    output.append((center,data)) #map to tuple of center ID and data\n",
    "    \n",
    "    return output\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [],
   "source": [
    "#implement reduce -> compute new centers\n",
    "def kReduce( item, centers ):\n",
    "    #print('{} reducing {}'.format(\n",
    "    #    multiprocessing.current_process().name, item))\n",
    "    center = item[1][0]\n",
    "    \n",
    "    for i in range(np.shape(item[1])[0]):\n",
    "        center += item[1][i]\n",
    "    \n",
    "    center/=np.shape(item[1])[0]\n",
    "    return center\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "init center [[-5.45992164  6.59859873]\n",
      " [-6.50677515  7.6064767 ]\n",
      " [-7.08121091  9.0635928 ]\n",
      " [-2.55154962 -3.14428744]]\n"
     ]
    }
   ],
   "source": [
    "#init centers\n",
    "center = X[np.random.randint(X.shape[0], size=4), :]#get 4 random datapoints\n",
    "print('init center', center)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [],
   "source": [
    "#use framework\n",
    "from functools import partial\n",
    "mapper = SimpleMapReduce(partial(kMap,centers=center), partial(kReduce, centers=center))#get mapreduce instance with custom map and reduce functions\n",
    "new_center = mapper(X)#call parallel mapreduce oo data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([-5.51508808, -3.98598111]),\n",
       " array([-6.79353516,  9.05853112]),\n",
       " array([-0.96134478,  5.53738408]),\n",
       " array([-6.43883259,  7.69966261])]"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_center #new centers "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [],
   "source": [
    "#now run int in a loop to get K-Means iterations ...\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}