report.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part I: Theory Questions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## k-Nearest Neighbor Classification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1-NN"
   ]
  },
  {
   "attachments": {
    "K1.PNG": {
     "image/png": 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    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![K1.PNG](attachment:K1.PNG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3-NN"
   ]
  },
  {
   "attachments": {
    "K3.PNG": {
     "image/png": 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    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![K3.PNG](attachment:K3.PNG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 2:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Answer A:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Value of k=3 minimizes training set error for given data set.Because we applied k-cross-validation method and we use to one item for test data, it will be obvious that it will be difficult to decide without looking at minimum 3 data.But training set error not a reasonable for this value of k, beacuse the data set not enough for the cross validation method."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Answer B:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Value of k=1 minimizes leave-one-out cross-validation error for given data set. Because items in data set mostly included in the class of the nearest neighbor. Cross-validation a better measure of test set performance because the whole data set is trained multiple times with new values and averaging this errors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Answer C:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yes, too large values k be bad in this data set because already data set too small. This stuation not effective for knn algorithm, but for too small values k more effective for this data set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lineer Regression\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Answer 1:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ X \\quad {shape}\\quad 23 \\times 6 \\\\\n",
    "Y \\quad {shape}\\quad 23 \\times 1 \\\\\n",
    "\\theta \\quad {shape}\\quad  6 \\times 1 $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Answer 2:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gradient descent, since $(X^{T}X)^{-1}$ will be very slow to compute in the normal equation. Inverting such a large matrix is computationally expensive, so gradient descent is better."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PART II: Book Recommendation System"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##   INTRODUCTIONS\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recommendation systems have an important place in our day.Many e-commerce and retail companies are leveraging the power of data and boosting sales by implementing recommender systems on their websites. These systems aim to predict users’ interests and recommend items that quite likely are interesting for them. Data required for recommender systems stems from explicit user ratings after watching a movie or listening to a song, from implicit search engine queries and purchase histories, or from other knowledge about the users/items themselves.\n",
    "\n",
    "Various machine learning applications are used when making these propositions. One of these collaborative filtering based systems.These kinds of systems utilize user interactions to filter for items of interest.  An interesting way of looking at collaborative filtering is to think of it as a generalization of classification and regression. While in these cases we aim to predict a variable that directly depends on other features, in collaborative filtering there is no such distinction of feature variables and class variables.\n",
    "\n",
    "Various algorithms can be used in such systems.The KNN algorithm is one of them.The logic of this algorithm is to take advantage of the data that is most similar to itself when rating.\n",
    "\n",
    "In this assignment, we aimed to write a rating prediction application using KNN and W-KNN algorithms with various similarity functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Book-Crossings is a book rating dataset compiled by Cai-Nicolas Ziegler . As mentioned\n",
    "before, it contains 1.1 million ratings of 270,000 books by 90,000 users. The\n",
    "ratings are on a scale from 0 to 10.\n",
    "\n",
    "    • The data consists of three tables: ratings, books info, and users info.\n",
    "    • The ratings data set provides a list of ratings that users have given to books. It\n",
    "      includes 1,149,780 records and 3 fields: userID, ISBN, and bookRating.\n",
    "    • The books dataset provides book details. It includes 271,360 records and 8 fields:\n",
    "      ISBN, book title, book author, publisher and so on.\n",
    "    • The user dataset provides the user demographic information. It includes 278,858\n",
    "      records and 3 fields: user id, location, and age.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data we will use on this data are three;\n",
    "\n",
    "    • User-ID's   : Only include us and canada users.\n",
    "    • ISBN        : Contains books only in amazon.\n",
    "    • bookRatings : Books in the Amazon include ratings given by users of USA and Canada\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When using this filter, we passed the csv files to a dataframe, and then we were able to merge them with each other. After applying this filtering we have a 3-column and 66991-row  dataframe.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Functions & Data types"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### DfToDict() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function takes dataframe as parameter and returns two two-dimensional dictionary.\n",
    "\n",
    "First dictionary format :\n",
    "\n",
    "    { UserIDs : { User ISBNs : Ratings}} \n",
    "   \n",
    "Second dictionary format :\n",
    "    \n",
    "    { ISBNs : { Users vote this ISBN : Ratings}} \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Prediction()"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function contains main algorithm of this assignment and takes six parameter. These parameters;\n",
    "\n",
    "        1.TrainDict # type {trainuserid:{isbn:rating}}\n",
    "        2.TestDict # type {testuserid:{isbn:{rating}}\n",
    "        3.TrainISBNDict # type {isbn:{trainuserid:rating}}\n",
    "        4.neighbourNumber # K for KNN\n",
    "        5.smilarityName # name of similarity function to be used\n",
    "        6.predictDict # dictionary used to check predictions\n",
    "        \n",
    "In this function nearest neighbours are determined for all users with selected smilarity function first. Then through using of nearest neighbour algorithm the rating prediction will be made for every single book of each user. After these predictions, calculate mean absolute error with using these predictions. Two different KNN are used in this algorithm. One of them standart KNN algorithm, other one is Weighted KNN algorithm. Finally function returns two value. This values are mean absolute error and weighted mean absolute error.\n",
    "\n",
    "Mean Absolute error calculated as given below :\n",
    "\n",
    "![1111.JPG](attachment:1111.JPG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### cosineSim()"
   ]
  },
  {
   "attachments": {
    "cos.PNG": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function calculate smilarites for given users and takes four parameter.These are;\n",
    "\n",
    "    1.TestUserDict # type {isbn:rating}\n",
    "    2.TrainUserDict # type {trainuserid:{isbn:{rating}}\n",
    "    3.TrainBookDict # type {isbn:{trainuserid:{rating}}\n",
    "    4.TrainSquaresDict # type {trainuserid: root of sum of squares ratings}\n",
    "    \n",
    "In this function users accept as vector and calculate cosine smilarities as given formula below.\n",
    "\n",
    "![cos.PNG](attachment:cos.PNG)\n",
    "\n",
    "After calculated smilarities, function returns smilarity list for KNN algorithm. Because smilarities determine neighbour.\n",
    "\n",
    "This smilarity is suitable for Used-based collaborative filtering."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cosine smilarity list of testuser :\n",
      " [[0.9285051067780872 {'exampleisbn': 10, 'exampleisbn2': 4}\n",
      "  {'exampleisbn': 6}]\n",
      " [0.8948545861297539 {'exampleisbn': 4, 'exampleisbn3': 2}\n",
      "  {'exampleisbn': 6}]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "testuser={\"exampleisbn\":6}\n",
    "          \n",
    "trainuser = {1235:{\"exampleisbn\":10,\"exampleisbn2\":4},\n",
    "            1245:{\"exampleisbn\":4,\"exampleisbn3\":2}}\n",
    "          \n",
    "trainbook= {\"exampleisbn\":{1235:10,1245:4},\n",
    "            \"exampleisbn2\":{1235:4},\n",
    "            \"exampleisbn3\":{1245:4}\n",
    "           }\n",
    "trainsquares={1235:10.77,\n",
    "              1245:4.47}\n",
    "\n",
    "def cosineSim(TestData,TrainUserData,TrainBookData,TrainSquares):\n",
    "    \n",
    "    cossim=list() #smilarity list of testuser\n",
    "    setuser=set() # intersection trainUser set\n",
    "    vecttest=0 # sum of squares ratings\n",
    "    for x,y in TestData.items():\n",
    "        vecttest += y**2 \n",
    "        if x in TrainBookData:\n",
    "            setuser |= set(TrainBookData[x].keys())\n",
    "            \n",
    "    vecttest=vecttest**0.5 # root of sum of squares testuser ratings\n",
    "    for a in setuser:\n",
    "        dotproduct =0 # sum of common items ratings dots \n",
    "        for key,value in TestData.items():\n",
    "            if key in TrainUserData[a]:\n",
    "                dotproduct+= value * TrainUserData[a][key] # common item ratings dot\n",
    "        vecttrain=TrainSquares[a] # root of sum of squares trainuser ratings\n",
    "        if ( vecttrain !=0) & (vecttest !=0) :\n",
    "            cossim.append([dotproduct/(vecttrain*vecttest),TrainUserData[a],TestData])#calculate smilarity and append list\n",
    "        else:\n",
    "            cossim.append([0,TrainUserData[a],TestData])\n",
    "    cossim =sorted(cossim,key=lambda l:l[0], reverse=True)\n",
    "    return cossim\n",
    "testcosine=cosineSim(testuser,trainuser,trainbook,trainsquares)\n",
    "print(\"cosine smilarity list of testuser :\\n\",\n",
    "      np.array(testcosine))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### adjCosineSim()"
   ]
  },
  {
   "attachments": {
    "adjcos.PNG": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function calculate smilarites for given users and takes three parameter.These are;\n",
    "\n",
    "    1.TestUserDict # type {isbn:rating}\n",
    "    2.TrainUserDict # type {trainuserid:{isbn:{rating}}\n",
    "    3.TrainBookDict # type {isbn:{trainuserid:{rating}}\n",
    "    \n",
    "In this function users accept as vector and calculate adj-cosine smilarities as given formula below.\n",
    "\n",
    "![adjcos.PNG](attachment:adjcos.PNG)\n",
    "\n",
    "After calculated smilarities, function returns smilarity list for KNN algorithm. Because smilarities determine neighbour same as cosineSim function.\n",
    "\n",
    "This smilarity is suitable for Used-based collaborative filtering too."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "adj-cosine smilarity list of testuser :\n",
      " [[0 {'exampleisbn': 10, 'exampleisbn2': 4} {'exampleisbn': 6}]\n",
      " [0 {'exampleisbn': 4, 'exampleisbn3': 2} {'exampleisbn': 6}]]\n"
     ]
    }
   ],
   "source": [
    "def adjCosineSim(TestData,TrainUserData,TrainBookData):\n",
    "    \n",
    "    adjcossim=list() #smilarity list of testuser\n",
    "    setuser=set() #intersection trainUser set\n",
    "    meantest=sum(TestData.values())/len(TestData) # testuser ratings mean\n",
    "    \n",
    "    for x,y in TestData.items():\n",
    "        if x in TrainBookData:\n",
    "            setuser |= set(TrainBookData[x].keys())\n",
    "            \n",
    "  \n",
    "    for a in setuser:\n",
    "        vecttrain=0 # sum of substract common items ratings and trainuser mean\n",
    "        vecttest=0 # sum of substract common items ratings and testuser mean\n",
    "        dotproduct =0 # sum of common item rating dots\n",
    "        meantrain = sum(TrainUserData[a].values())/len(TrainUserData[a])\n",
    "        for key,value in TestData.items():\n",
    "            if key in TrainUserData[a]:\n",
    "               vect1= (value-meantest)\n",
    "               vect2=(TrainUserData[a][key]-meantrain)\n",
    "               dotproduct += vect1 *vect2\n",
    "               vecttest += vect1**2\n",
    "               vecttrain+= vect2**2\n",
    "               \n",
    "        vecttest=vecttest**0.5 # root of sum of squares testuser ratings\n",
    "        vecttrain=vecttrain**0.5 # root of sum of squares trainuser ratings\n",
    "        if ( vecttrain !=0) & (vecttest !=0) :\n",
    "            adjcossim.append([dotproduct/(vecttrain*vecttest),TrainUserData[a],TestData])#calculate smilarity and append list\n",
    "        else:\n",
    "            adjcossim.append([0,TrainUserData[a],TestData])\n",
    "    adjcossim =sorted(adjcossim,key=lambda l:l[0], reverse=True)\n",
    "    return adjcossim\n",
    "testadjcos=adjCosineSim(testuser,trainuser,trainbook)\n",
    "print(\"adj-cosine smilarity list of testuser :\\n\",\n",
    "      np.array(testadjcos))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Becomes smilarities 0 because adj-cosine formula use (item rating- usermean). given examples testuser has got one item and dot product becomes 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### correlation()"
   ]
  },
  {
   "attachments": {
    "cor.PNG": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAAASoAAAA/CAYAAABXVoWzAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABckSURBVHhe7Z15UFNZvsffP1M9f7+qqer3+lltV9v2ojM6Om8stXss26X6TSs9Mtoura9o04CIgK2iIAHR1mba6W42CZuyCREQlCUsxRpWbaAABQGLnUJEKmImkJekkjvfd29ysyeQQJDAnE/VKXJvknM493fP9yz33m/+DQQCgeDkEKEiEAhODxEqAoHg9BChIhAITg8RKgKB4PQQoSIQCE4PESoCgeD0EKEiEAhODxEqAoHg9BChIhAITg8RKgKB4PQQoSIQCE4PESoCgeD0EKEiEAhODxEqAoHg9BChIhAITg8RKgKB4PQQoSIQCE4PESrCkmdychKnTp2yK2VlZbHfdk66u7st/t+zpdraWjaH5QURKsKSRyKRICoqyq4kFArZbzsnw8PDFv/v2dLjx4/ZHJYXRKiWKrIq+K76NVbsPIkgLhdcbQoKwFlfL3x9YCd+9+Yb+NWaAPyiYL+zQCj7ipAkeAptMcpnrSgvLUFJCZ1Ky1D1oBNjUvbNhUT5DK3lpZpyS0pRVvUAndYKVvXhflQmOuXstg4l+oqSIHiqP2iLVh8Ge+rEYLVeSxsiVEsYcc0FbHxnL+KfKtk9JkieIPPbQwiulrE7FgBZC6JCUtCnYrcZ5C8g8HwfG85WYGC4D+3CdJzbuwdX6iTsBxYKOV4IPPH+hrOoGBhGX7sQ6ef2Ys+VOlgqWTWQiqDr9UbvyVqiEJLSB8PqLF59GOyrE4Olei11iFAtaRTojNiFtzeFoHGK3WWKagANjcPshqOhMH7bC6fzTZoENYKonWvgV6MdlSgg9FmNtecf6EZdCwOFkaidWONXoytHIfTB6rXn8cBiwVJUXnAHb5CVJWoct71Ow7Q6i1cfBnvrxGBSr2UAEaqlDjWKrKOr8cE3+Rin2H2vjUmkuXGQZdqwX/FxYNVR5LLiKelIAGePF/j9VkZ+FqDEvegetVcGXoF/YBWO6gtGAmcPvPj99ISOgYK4txuG2UrzPHCEN6rZmEyDGyfLfCTigPowUBPd6Hpub5BmqxMNNYHurud07fQY1WsZQIRqOSAWwn/DSuyJe6o/eV8HikYE7g9Gs0mh8rITWL3JB8nZfMQGuWL7wQT02PmPqZ6WofiJnVNWeRlOrN4En+Rs8GOD4Lr9IBKMClbhaVkxDLNVdl6Fq2+F+rWiMRD7g5vNjqEj6sMge1SEMqM5sg3MWica2SMUlRlPVw3rtRxYJKGiMFZ5C3darc1X5oakNROpNeNGPcu/CvJfArF1Vzi6HTjaVwwKkRoTCV5qNQboUYhqtBYpUZFIFrI9tbwCvvu+w2OjdqNEK3cjNl99omk49LQpYsdanKnXDGPk/XXI5pehR84MBJpQ1zGt3m+IrK+W/kwperSCongMfmggAgICTFIgghMa6DGHBmUrFxs3X8UTTcEYidiBtWfq2SmTDH21dGMv7aFf6VH1/wRX9wL1a3mFL/Z999hEqOZfH/pTGKy7B35OPZ6xJ6fiMR+hgab1oVNgMBIatDWarU50zoN1uMfPQb02YxbDei0H7BMqWrlTQ2JQL2a354i8PRLeV6p1J5gGGR6lhiDGrszFeBgXgvhftCfHKwivfYu4zjl0d0sZZS9unwtA9pD6bJ4DEnTc4+Hn8HCEh0ciqXpE0yhV/fhxtwvitNMVagx8XpZ+iqlsQ+h+f9RqWw0DNYSITz/Sr+fIq+C9aj2CWhRQTo2gvKgc6Z7HEDuqwljcUXjmmTRsSoTqwjJkeruBN2JPl0NhKOJTfKRby5GjynsV1ge1QKGUYmqsGoVlmfB248EwW2VLCA4GPtC8bgvFfv9a43Wn+daHRjVShaLmcWQfP4akl+xOm5i5TtL/G0FVUTPGs4/jmEnGhvVaDtglVNRYPi75xaJlPpdmVb24cewU7hurFJM58i/5IdaezFXDuMs9gxRDYRJl46RbPAbm2maXGnTDrrjii8hmSz05gwpSKXOtWo7+OnpEUdZDv6Iw0VQHTecvQ1tCKGKbJum9Jkym4cCuMPRoj+V0MdJzDNdCpCj15SBujN0j7UYJzwubf7MBnLRmiJjdzPRw/Ub45QoQk1gNsbwYJ49EYUglQTbnGBL7RHhlUjA1kQGO2y30iExPEmtI0V3Cg9fm32ADJw3NmoLRGLgeG/1yIYhJRLWYrnMGB263eiB6pa0QvS/la3jcZVelpKXw5cRBWx1H1UeNohb+h6/B9j7Uljoxn1Og1v8wrhllbFKvZcBrn/rJ689jr38d3VgWChkq/fbg4kLfPOQUyNER7wduwZi5yLDIO2NxNXWQ1jMhisrT4XksFqOqMcQd9YS685cVI+R0PGrq61GvTg1oGRCr85OVnMB2/wbdCEPRmIE7XcYtTVYbglPxQ1bLV6MQobejH5OMPshrEeoeisycWPi4cvB9ajG66SwVDy9hr7dmqqJ4GAI3v2gkCnrV23NHAVFvB/rVBSvwMMQNftGJEPSyQkWNI8XnPEp1KxAy1IacQvzQjLWxuz4Mqq4wHD4r1B3LuWNYJxpVF8IOn4XQMGOzei19zIWKmkR3dR7u3itD84i+l54erEd+fgOGdAMeGYYf5KOgYYjWfhUm2opwJzkZuS0T9BaFqaGHEGSkIrdpXDONUKNA/dmPwck3WSSdHkR9fj4a9JnPimK8HaX3BGh6Zi55kqyv8MnFJnZruUJhrCAQJyObMCmlpwHaNC3Gi6FutDUU49bFfVjz1meIYec68uKTOBI1BJUkG5xjieijRyyUTIBgHx4qhUL13dpCYQ0e9tL76aj1Xd+NQxnac0CKB2l8PDIdEVATEIRdQ5FdV7MUUDANi6L/6k6OSZTnV7Ov6amL+gOORqkpl0VcE46wfGORpyYECLtWBPsuzs1QH0kXmjpF6PzhIPxKrY1654IEXU2dEHX+gIN+pTDM2VK9ljrGQkWfdIUXT+FGmwQUPa1K5ZzCHREt2iMCJKS34knEbnzMLioqHyWDVz6Im39Zj0PfRSOjfgzy6WYEb9uJC0k3wRcOY1r6CJe3bcfftXMHahjhO3fiZ8MeSzUCQUI6Wp9EYPfH2kXDmVEN5CEquQmikWh8tvWKyWIu/X73Nfzpzzx2yxQJnpTxkX77Nm5bTem4U9FDN00nRtmFlNNf4fDhwzOmY5cKdWtK8tpQuIdmIifWB66c75Fa3E03XSmaY0OR2Ga+Nqhoj4CnXxyKy3OQGB2DXPq8sIi8F5XV+jvT5wL1qgsdgwshTlZQDaG+qsuogWuR91ai2uDO9LmgrQ/TdmKjk5F6v83ylHCuMO0mNhrJqffRZpjxDPVayhgLlSgRe9e6o2CcbvnKViRyE9EqU6EnMx210y/BP/AO9qVM0B9U4klmBh5MtSBo/UocvcteaVN14sof38KBDHYdQ9WD77d+iNPa1VZFPc6sc0WawZBU1ZOJ9NppvOQfwDv7UsDkPjNS1Cal4hGdpeLhBaz771AzocJEPD7fGMhumEKPBJvKUap+JMFaKkV5y+i8Gp7TQnf9TL0o+q+uT6BH0a1Z0eaL6cxb08/R2zMCsekxJhBeI8ZCpWjDT7v/E2+88e9YvY2DhDa9LlPPb8Hl3UPInGR30FCj0di58jgKtUOPiVvY+19fIpPtnKkXN7F3xZe4o10TlVfCe90RZJsOVajnuOXyLg4ZZj4rKvT/uA2rTpSbr3dNp2P/ujPshuO5fv06tm3bRhJJJNmQXFxc2JYzdwyESo7xgRFI6Hn2eLsAMe5/wH98kQzNRU8Kwzd2Y5VbHiQqCSSsfokzv8QK+jP07FCNTMDBOzujMaoeTlEYv+WClfsz8JKSQCyhdyp/QcDGvyDJZJZBDd/A7lVuyJOoINFmPisipPxlBQ7wzacs1ItY/HlTCLtlAiWCMCYQ/ufO4ZzV5I/A+AaY56yhp6cH1dXVNqWioiIkJyeTtMApOzvb4vG3lCorKy3mQdLCJD6fz7acuaMTKmYa9bs3v0QGqzrKJi6+OFOtGa1Qw4jcsRoeJVN4nhODDPX9OnJUeL2Hj3/oZacJCjSeW4s/XHrE3jDHCMk7OJQ1iVclN3Czg9k7gQSXT3BF/VoLLYKRO7DaowRTz3MQkzGk3qsaLkUMrxRD1qYcskIcX7kDURbutVG2BWPr/lR2yxzF1CReikQQWU0vMTntiLmOEkmR0Xjvgw/x4YckLWT69ttv2WM+O/94XIuV731gMR+SHJ+2bNnCHvm5oxMqaqISN2/koLKhEcKCFPx4JRa1E6wIUGNIO/I5zmdlIyGzGeolJlUPwj7ZgItNbIOmxYy5MU63HgUJBN7/g1PJuUhMr6dHVcw+JTqubMeXtw3vj6EwlnYEn5/PQnZCJprZ9aupAg+89+Y6+FdZvpFB8cAfv90YgnYLeiK6uQ+7/z7fS9sOQFaJ4AvZsGdCS1hoZKgMvoBsEpQlhfEaFY3sxTDG6CmYOVJ6FDKtWSRXQ0E8ITJYH6IwNfnKZAFajkmRRL9oS6Pq/gEu/3tHN13UIn0pwrTJ4EjVx8dtoSWhUuHp3z7GeycrDMpnYZ6AP3YA0U7w5LisIhgX7tp60yLhtSCroDuPuyZPRRCcHTOhWnheotDvOG70zyYkSnRn3EKFbqGIgqjsEo4G5GFc1oZLH2/GpWbz63Kq7p9w/HyV+RPwrx0ZyoMDkENahBFxcXGIjo62Od27d4/9pmOQlQcjgATFDGYt1dLxny29LhZBqGjJeVEErm8cnsxw/Z+afAiB8JnRCO5Zphc+P34ZPwadRuj9AXYtzAB5O6J9r6BKM89cXGTlCA7Itbog/6/KmTNn4O3tbXOKiIhgv2mMZKARFbVdEM1wDpmj6TxySVDMiI+Pt3j8Z0v//Oc/2RwMkAygsaIWXfYFZ0YWRagYlKN1qHrs2NvSxG2VaHi++FM+BmlZMALvMS1ChirfVfj1ip04GWRgGcwNQsBZX3h9fQA7f/cm3vjVGgQs8GM/TmMZTHcxz1r197KVllXhQeeYlRtsVei7H4VMA29dWUMkLqd3YrA9E34ux5Ghucw8O9IyBAfeozsP54kJHRQUJQmgu7/UXuthh2JPXDSo+u4jKrNTvwQja0Dk5XR0DrYj088FxzMc44m1aEK1vJGiLDgQ97U9t7gGFza+g73x1vyiJHiS+S0OBesfIXE4TmUZzBQtgOf7G3C2YgDDfe0Qpp/D3j1XYLFo1QBSg66jnn1P+jAZSWpLUxlKPLfiVKWldUxz1J2HNijOEBP6/2+JCkGKcVDsth52JHbFRY0KA6lBuK4PDpKTGtUX3GQlnth6qlKzf54QoVoIpKXgBuYZnViKzgjsensTQqx7BmOgoZF97WiczTKYKToKO9f4QV+0ED6r1+K8FX9daeUFuPMG2S0N0vZouHun2GhiJ0UpNxB5BodgcWNCH4Px2/A6nW8iQHOxHnYc9sZFjbQSF9x5MLp+JW1HtLs3UubiMGgBIlQLgLSEi4vmxtsYzTqK1R98g/zX7hm8cJbBc+UV/wBWHc3V3OpCN9WOBA72ePFhtWhpHjyO6J/fFLffRXRKHcbFXei0xdNHWgLuRXNRWLyYMC46buCYB2V26+EFxO64qJEiz+MIeNopuLgdd6NTUDcuRlfngGbfPCFC5XCmUcK9aP4DAWrEEPpvwMo9cbD2wzELwgJaBoMSo7fb3uci5Sg7sRqbfJKRzY9FkOt2HEzoMWiI5t7mUHbiqquv+qX04TVs/2gdtn26Hdv++FeE22BrOm2x82BYpJjQR6wxcD+CzYMyu/WwLVjwUZ+d2eKiwdz7XYnOq67wraCn4PTU79r2j7Bu26fYvu2P+Gt4N/uZ+UGEas5QeC4IQViRyck/XQxuUAHbI1lA/gsCt+6yqXHZjGIQwtQYRPJSUa3xDEZtShQik4UYZYqZg2Wwzaieoqz4CdTGPTZaBjMPvHM3bsZV1iqDGonAjrVnoC/a3NuccRv9ydWd3bAO9VyAkLAik5HTNIq5QSiwFpSFiAktRIPCVMRE8pBaPUBvqTBam4KoyGQINUFBhe8+fGfyRP1s1sM2Y+SjrsBjfigCzeISgMDgBOicj2eNiwZz73cV+n9yhXuBiX2TAyFCNUfknbmI8NiCdzkCo6si00VcBBVaaxFK9N4+h4DsIfYEsh9Jxz3wfmZcDsIRmVSNEXVGzAPau+ESp+1BKYzxecjSTmfstQyWSqGQ96OOHmmVaczA0VTXYW4dIutDLf2ZUp25uW1QQxH49CP9Ooi8yhur1gehRaGEVPoPi97mULYg5KA1RwwWeSdyIzyw5V0OBMZBoTuPQiudx/xjwkzP7vF+VsckPDIJ1Zqg0Nr6I3a7xOm8ragxPnhZWk9/JdpC98PfOCgzWw8rrLm0GmPNR302Zo4Ls9Pc+12DEi0hBxG4gItoRKjmARPYHe+fBDPi1TANAZcLgcW7LiiIKq7AN7LZqleQihYI5mSwdjLK2hIQGtuESbPzbxJpB3YhTO8ZjOL0HAPzN3stgysxICxCebonjsWOQjUWh6OeeSb/N12f6kKUZXrDjTdCb9mGtLsEPK/N+M0GDtKaRervMb/+sn6jH3IFMYjPK7TobU5NpOBrj7vs1gwwArzjfZzUBwXTAi64FoNia0zoqFj7EQdZGxJCY9FkHhRMph3ArrAenQBOF6cjx2DKJC31BSdOa3A3u/Vw5YAVl1ZDVNZ91GditrgkVovprK14v9MdWcrXHlhI52MiVPOBnvb88InBdGlaAC63yOJJL++Ihx+3QO/HbQo9Goi9mmrdMpgeXxSHnEZ8jdYyuB4NLQMQM/nJSnBiuz8atB0aLToZd7rofk6P3ZbBtEwWnzyCqCEVJNkcHEvsg8jc3BwZHDfc6hFBZ0M+RxSiXnT0T9KN2rK3+XiKD87b5K1LTxt/+MRguqTpPIosBMXWmKgdN6z8iIOsOASn42t0MalvaMGAJigoObEd/vqgoDHjDoycnGW1CDkVj5mdj42thy26tKrfMcSSj/rc0MeFxYL3OzWeAp/zpdaXOxwAEap5oUTH5U34/UXNb8FNFXIRXGzeIqixAgSejKR7XQPLYOk0xC+G0N3WgOJbF7FvzVv4LGZE/XnLJ6MMgmAf8Cq1lsFC1DzsVbtGqvquY/ehDJ1ASh+kgW/qGUyLin2WwXLUhrojNDMHsT6u4HyfimKNGTgu7fVGAXM7Ev06xM0P0YkCaG3I548Fb3NxDcLD8q0LignKjsvY9PuLmosHU4XgBhebdR72xoQOisUfcZAJguHDq9TFRFjzEL2aoOD67kPQOzk/QBpf6yyihRZlQRiuFdm+6G3RpdUwJgyWfNQdhLn3uxg14WHItzU4c4QI1TxRNgdhw6bL6FBOoSAoGCVmOqVEV8ppfGXBJtgoHbuEQnZNybJlMH2uN8ciNLHN/LEcRTsiPP0QV1yOnMRoxOS2mSwms8zBMlihMQOn/+qVaLI8H9Xa7lOpcQx1LIbe5ioM1Vehy1z/raNsRtCGTbjcocRUQRCCzYJif0ys/YgDHRTEhibC3MlZgfYIT/jFFaM8JxHRMbmw7OQsR29ltf7OdFuw4NKqiYl1H/V5Y8X7XTVUjyq7gjM3iFDNF0UDzv72T/hbex64IaVGC+vzwsLJyAjGZGsWos0W05m3pvG8twcjC+0ZTL1CV8fgAoiTI1Gg4exv8ae/tSOPG4JSxwVFI6BGP+JAb062IivafDGdidf08170jIhNRlIORhsTaz7qDmDBvN9thAjVvGGuzHyALV9wwHVciyDME+aK1QdbvgCH68DOg7BoEKFyANLib7DibQ8H9tyEeSMtxjcr3oYHCcqygAiVI5DWIeFmEz22IjgPUtQl3EQTCcqygAgVgUBweohQEQgEp4cIFYFAcHqIUBEIBKeHCBWBQHB6iFARCASnhwgVgUBweohQEQgEp4cIFYFAcHKA/wdVcnuv/WWMwQAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function calculate smilarites for given users and takes three parameter.These are;\n",
    "\n",
    "    1.TestUserDict # type {isbn:rating}\n",
    "    2.TrainUserDict # type {trainuserid:{isbn:{rating}}\n",
    "    3.TrainBookDict # type {isbn:{trainuserid:{rating}}\n",
    "    \n",
    "In this function users accept as vector and calculate adj-cosine smilarities as given formula below.\n",
    "\n",
    "![cor.PNG](attachment:cor.PNG)\n",
    "\n",
    "After calculated smilarities, function returns smilarity list for KNN algorithm. Because smilarities determine neighbour same as cosineSim and adjcosinesim function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "correlation smilarity list of testuser :\n",
      " [[1.0 {'exampleisbn': 4, 'exampleisbn3': 2} {'exampleisbn': 6}]\n",
      " [-1.0 {'exampleisbn': 10, 'exampleisbn2': 4} {'exampleisbn': 6}]]\n"
     ]
    }
   ],
   "source": [
    "def correlation(TestData,TrainUserData,TrainBookData):\n",
    "    \n",
    "    correlation=list() # smilarity list for testuser\n",
    "    meanitem={} # item means in training data dictionry \n",
    "    setuser=set() # intersection trainUser set\n",
    "    \n",
    "    for x,y in TestData.items():\n",
    "        if x in TrainBookData:\n",
    "            setuser |= set(TrainBookData[x].keys())\n",
    "            mean=sum(TrainBookData[x].values())/len(TrainBookData[x])\n",
    "            meanitem.update({x:mean}) # item means updated here\n",
    "        else:\n",
    "            meanitem.update({x:0})\n",
    "            \n",
    "    for a in setuser:\n",
    "        vectx =0 #  sum of substract common items ratings and trainusers common itemmean\n",
    "        vecty=0 # sum of substract common items ratings and trainusers common itemmean\n",
    "        dotproduct =0\n",
    "        for key,value in TestData.items():\n",
    "            if key in TrainUserData[a] :\n",
    "                vect1= (value-meanitem[key])\n",
    "                vect2=(TrainUserData[a][key]-meanitem[key])\n",
    "                dotproduct += vect1 *vect2\n",
    "                vectx += vect1**2\n",
    "                vecty+= vect2**2\n",
    "        vectx=vectx**0.5 # root of sum of squares testuser ratings\n",
    "        vecty=vecty**0.5 # root of sum of squares trainuser ratings\n",
    "        if (vectx !=0) & (vecty !=0) :\n",
    "            correlation.append([dotproduct/(vecty*vectx),TrainUserData[a],TestData])#calculate smilarity and append list\n",
    "        else:\n",
    "            correlation.append([0,TrainUserData[a],TestData])\n",
    "            \n",
    "    correlation =sorted(correlation,key=lambda l:l[0], reverse=True)\n",
    "    return correlation\n",
    "testcorrelation=correlation(testuser,trainuser,trainbook)\n",
    "print(\"correlation smilarity list of testuser :\\n\",\n",
    "      np.array(testcorrelation))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When the calculate correlation smilarity dot product calculated with common items and this items means in train data.I think this is for Item-based collaborative filtering.Not suitable for Used-based collaborative filtering."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### squareforcos()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function is only used to help cossime and increase the algorithm run time.\n",
    "Take one paramater as type :\n",
    "\n",
    "        trainData # {userid:{isbn:rating}}\n",
    "        \n",
    "Function calculate sum of ratings square for each user and return dict as type:\n",
    "\n",
    "    {userid : sumofratingsquares}\n",
    "        \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "example transform:\n",
      " input: {1235: {'exampleisbn': 10, 'exampleisbn2': 4}, 1245: {'exampleisbn': 4, 'exampleisbn3': 2}} \n",
      " output: {1235: 10.770329614269007, 1245: 4.47213595499958}\n"
     ]
    }
   ],
   "source": [
    "def squareforcos(TrainUsers):\n",
    "    \n",
    "    squareddict={}\n",
    "    for key,value in TrainUsers.items():\n",
    "        vecttrain = np.array(list(value.values()))\n",
    "        vecttrain = np.sum(np.square(vecttrain))**0.5\n",
    "        squareddict[key]=vecttrain\n",
    "    \n",
    "    \n",
    "    return squareddict\n",
    "\n",
    "print(\"example transform:\\n\",\n",
    "      \"input:\",trainuser,\n",
    "      \"\\n output:\",squareforcos(trainuser))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### KNN Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def Knn(CosSim_BooksNumpy,number_K,trainBook,predictdict):\n",
    "    Numpylen =  len(CosSim_BooksNumpy)\n",
    "    if Numpylen < number_K: # controlling list length for loop\n",
    "        number_K = Numpylen \n",
    "    \n",
    "    Keylist=CosSim_BooksNumpy[0][2].keys() # testuser isbn list\n",
    "    IsbnList=[]# isbns data \n",
    "    meanisbn=0\n",
    "    for k in Keylist: \n",
    "        IsbnList.append([k,0,0,0,0,0])# [\"isbn\",\"neighbours mean\",\"real rating of testuser\",\"weighted mean\",\"neighbours weight sum\",\"neighbours lengt\"]\n",
    "    for i in range(number_K):\n",
    "        item = CosSim_BooksNumpy[i][1].keys()\n",
    "        meanisbn=0 #testuser mean \n",
    "        for isbninlist in IsbnList:\n",
    "            isbninlist[2]= CosSim_BooksNumpy[i][2][isbninlist[0]] # real item rating uploaded\n",
    "            meanisbn += isbninlist[2] # add item rating for user mean\n",
    "            if isbninlist[0] in item:\n",
    "                \n",
    "                trainmean = sum(CosSim_BooksNumpy[i][1].values())/len(CosSim_BooksNumpy[i][1]) # trainUser mean calculating\n",
    "    \n",
    "                isbninlist[1]+=CosSim_BooksNumpy[i][1][isbninlist[0]]-trainmean # neighbour trainusers deviation for this item\n",
    "                \n",
    "                isbninlist[3]+=((1/(1.1-CosSim_BooksNumpy[i][0]))**2)*(CosSim_BooksNumpy[i][1][isbninlist[0]]-trainmean)#weighted trainusers deviation for this item\n",
    "                \n",
    "                isbninlist[5] += 1 # how many users rate this book count decreasing\n",
    "                \n",
    "                isbninlist[4] += (1/(1.1-CosSim_BooksNumpy[i][0]))**2# neighbours distance for total weight \n",
    "                    \n",
    "    MeanAbsolute=0 \n",
    "    WeightedMeanAbsolute=0\n",
    "    meanisbn = meanisbn/len(IsbnList) # testuser mean\n",
    "   \n",
    "    for isbninlist in IsbnList:\n",
    "        if isbninlist[5]!=0: # if at least one neighbour rate this book\n",
    "            isbninlist[1] = round(meanisbn + (isbninlist[1] / isbninlist[5])) # calculate predict value\n",
    "            \n",
    "            if isbninlist[1] <0: # predict range will be 0 to 10\n",
    "                isbninlist[1]=0\n",
    "            if isbninlist[1]>10: # predict range will be 0 to 10\n",
    "                isbninlist[1]=10\n",
    "        \n",
    "        else: \n",
    "            isbninlist[1] = round(meanisbn)# anybody dont rate update predict userMean\n",
    "            \n",
    "        if isbninlist[4]!=0: #if at least one neighbour rate this book\n",
    "            \n",
    "            isbninlist[3] = round(meanisbn+ (isbninlist[3] / isbninlist[4])) # calculate predict value\n",
    "            if isbninlist[3] <0: # predict range will be 0 to 10\n",
    "                isbninlist[3]=0\n",
    "            if isbninlist[3]>10: # predict range will be 0 to 10\n",
    "                isbninlist[3]=10\n",
    "            \n",
    "        else:\n",
    "            isbninlist[3] = round(meanisbn) # anybody dont rate this item, update predict userMean\n",
    "        \n",
    "        predictdict[isbninlist[0]][1],predictdict[isbninlist[0]][2]=isbninlist[1],isbninlist[3]# update prediction dict\n",
    "        WeightedMeanAbsolute += abs(isbninlist[3]-isbninlist[2]) # calculating user MAE\n",
    "        MeanAbsolute += abs(isbninlist[1]-isbninlist[2]) # calculating weighted User MAE\n",
    "    \n",
    "    MeanAbsolute=MeanAbsolute/len(IsbnList) # calculating user MAE\n",
    "    WeightedMeanAbsolute=WeightedMeanAbsolute/len(IsbnList) # calculating weighted User MAE\n",
    "    IsbnList=np.array(IsbnList)\n",
    "    \n",
    "    return MeanAbsolute,WeightedMeanAbsolute,len(IsbnList)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function takes four parameter. These parameters;\n",
    "\n",
    "    1.CosSim_BooksNumpy # type [[smilarity,{trainuserisbn: trainuserrate},{testuserisbn: testuserrating}] 3-dimensional array\n",
    "    2.number_K # K for KNN\n",
    "    3.TrainBook # type {isbn:{trainuserid:rating}}\n",
    "    4.predictDict # dictionary used to check predictions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### About K-NN and WK-NN"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's first start by establishing some definitions and notations. We will use x to denote a feature (aka. predictor, attribute) and y to denote the target (aka. label, class) we are trying to predict.\n",
    "\n",
    "KNN falls in the supervised learning family of algorithms. Informally, this means that we are given a labelled dataset consiting of training observations (x,y) and would like to capture the relationship between x and y. More formally, our goal is to learn a function h:X→Y so that given an unseen observation x, h(x) can confidently predict the corresponding output y.\n",
    "\n",
    "Given a positive integer K my KNN algorithm performs the following two steps:\n",
    "\n",
    "First convert smilarities to distance for weighted prediction. I used this transfer function given below:\n",
    "\n",
    "$$   d = \\frac{1}{1.1-Smilarity}$$\n",
    "\n",
    "Secondly predictions are computed as weighted and non-weighted average of deviations from neighbour's mean and adding it to active user's mean rating. Deviations are used to adjust for the user associated biases. User biases occur as certain users may tend to always give high or low ratings to all items.\n",
    "\n",
    "$ x = TestUser $\n",
    "\n",
    "$ y = TrainUser $\n",
    "\n",
    "$ i = TestUser items$\n",
    "\n",
    "$ k = neighbour  $\n",
    "\n",
    "$ d= distance $\n",
    "\n",
    "\n",
    "\n",
    "Non-Weighted Formula:\n",
    "$$ P_i = \\overline{x} + \\frac{{\\underset{n \\epsilon K}{{\\displaystyle\\sum}}}(y_{n,i} - \\overline{y_n})}{k}$$\n",
    "\n",
    "\n",
    "\n",
    "Weighted Formula\n",
    "$$ wP_i = \\overline{x} + \\frac{{\\underset{n \\epsilon K}{{\\displaystyle\\sum}}}(y_{n,i} - \\overline{y_n})*d(x,y)}{{\\underset{n \\epsilon K}{{\\displaystyle\\sum}}}d(x,y)}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thanks to this approach, I can make more successful predictions and get fewer errors. I tried to implement my code by thinking that it would be more logical for User-based CF to evaluate personal behaviors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cross Validation"
   ]
  },
  {
   "attachments": {
    "result.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this part splitting the training data into ten pieces and providing the test-train error control for each piece.\n",
    "\n",
    "I save the error values obtained for each k value.\n",
    "\n",
    "I repeated the cross-validation test for one to fifty k values.\n",
    "\n",
    "I repeated this process by using weighted-knn and unweighted-knn for all smilarity functions.\n",
    "\n",
    "I saved the result of these calculations in a graph as below:\n",
    "\n",
    "\n",
    "![result.png](attachment:result.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I have found that the minimum error margin has been reached when the algorithm works with the Adjusted-Cosine similarity function.\n",
    "\n",
    "I've found that it works for k = 45 with the lowest error when working with adjusted cosine.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TestData"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I tried for given test data.The results are;"
   ]
  },
  {
   "attachments": {
    "testresult.PNG": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![testresult.PNG](attachment:testresult.PNG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##                          $$\\\\Muhammed\\,Enes\\\\KOÇAK\\\\21427119$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Raw Cell Format",
  "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}