Solution file Hackerday December 2017_R.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Science Project in Python- Build a machine learning algorithm that automatically suggests the right product prices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mercari, Japan’s biggest community-powered shopping app, knows this problem deeply. They’d like to offer pricing suggestions to sellers, but this is tough because their sellers are enabled to put just about anything, or any bundle of things, on Mercari's marketplace.\n",
    "\n",
    "## In this machine learning project, we will build an algorithm that automatically suggests the right product prices. You’ll be provided user-inputted text descriptions of their products, including details like product category name, brand name, and item condition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "library(data.table)\n",
    "library(stringr)\n",
    "library(ggplot2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "test = fread('https://s3.amazonaws.com/hackerday.datascience/109/test.tsv')\n",
    "train = fread('https://s3.amazonaws.com/hackerday.datascience/109/train.tsv')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>29999</li>\n",
       "\t<li>7</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 29999\n",
       "\\item 7\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 29999\n",
       "2. 7\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 29999     7"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>29999</li>\n",
       "\t<li>8</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 29999\n",
       "\\item 8\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 29999\n",
       "2. 8\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 29999     8"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Exploratory Data Analysis\n",
    "# univariate\n",
    "# bivariate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "    train_id         name           item_condition_id category_name     \n",
       " Min.   :    0   Length:29999       Min.   :1.000     Length:29999      \n",
       " 1st Qu.: 7500   Class :character   1st Qu.:1.000     Class :character  \n",
       " Median :14999   Mode  :character   Median :2.000     Mode  :character  \n",
       " Mean   :14999                      Mean   :1.906                       \n",
       " 3rd Qu.:22498                      3rd Qu.:3.000                       \n",
       " Max.   :29998                      Max.   :5.000                       \n",
       "  brand_name            price            shipping      item_description  \n",
       " Length:29999       Min.   :   0.00   Min.   :0.0000   Length:29999      \n",
       " Class :character   1st Qu.:  10.00   1st Qu.:0.0000   Class :character  \n",
       " Mode  :character   Median :  17.00   Median :0.0000   Mode  :character  \n",
       "                    Mean   :  26.95   Mean   :0.4477                     \n",
       "                    3rd Qu.:  29.00   3rd Qu.:1.0000                     \n",
       "                    Max.   :1506.00   Max.   :1.0000                     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "    test_id          name           item_condition_id category_name     \n",
       " Min.   :    0   Length:29999       Min.   :1.000     Length:29999      \n",
       " 1st Qu.: 7500   Class :character   1st Qu.:1.000     Class :character  \n",
       " Median :14999   Mode  :character   Median :2.000     Mode  :character  \n",
       " Mean   :14999                      Mean   :1.911                       \n",
       " 3rd Qu.:22498                      3rd Qu.:3.000                       \n",
       " Max.   :29998                      Max.   :5.000                       \n",
       "  brand_name           shipping      item_description  \n",
       " Length:29999       Min.   :0.0000   Length:29999      \n",
       " Class :character   1st Qu.:0.0000   Class :character  \n",
       " Mode  :character   Median :0.0000   Mode  :character  \n",
       "                    Mean   :0.4484                     \n",
       "                    3rd Qu.:1.0000                     \n",
       "                    Max.   :1.0000                     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Guided approach:\n",
    "#1. what is the variation in prices?\n",
    "#2. How good the products are?\n",
    "#3. Comment of the shipping condition, how good the shipping condition is?\n",
    "#4. What are the most expensive brands present?\n",
    "#5. does expensive brands posses higher prices?\n",
    "#6. How many product categories are there?\n",
    "#7. Does the prices vary by product categories?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Use hypothesis testing process and answer the questions.\n",
    "x = c(12,12,32,34,43)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://s3.amazonaws.com/hackerday.datascience/109/test.tsv\n",
    "https://s3.amazonaws.com/hackerday.datascience/109/train.tsv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9708592 bytes"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "object.size(train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0</li>\n",
       "\t<li>1506</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0\n",
       "\\item 1506\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0\n",
       "2. 1506\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1]    0 1506"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "range(train$price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AAEQJAABECQAARAkAAEQJAABECQAARA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\nAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title “density.default(x = train$price)”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(density(train$price))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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s7XGx55IdAhBClqjSYzHPzDIgcZjg7MIEhRY7Njg0thfbWLVINuIUjRumj9kuXw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\n",
      "text/plain": [
       "Plot with title “density.default(x = log(train$price))”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(density(log(train$price)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "ggplot(data=train,aes(x=price)) + geom_histogram(fill='red') + labs(title='Histogram of Prices')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.3 Mb\n",
      "9 Mb\n"
     ]
    }
   ],
   "source": [
    "print(object.size(train),units='Mb')\n",
    "print(object.size(test),units='Mb')\n",
    "\n",
    "library(ggplot2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Guided approach:\n",
    "#1. what is the variation in prices?\n",
    "ggplot(data=train,aes(x=price)) + \n",
    "  geom_histogram(fill='red') + \n",
    "  labs(title='Histogram of Prices')\n",
    "\n",
    "ggplot(data=train,aes(x=log(price))) + \n",
    "  geom_histogram(fill='red') + \n",
    "  labs(title='Histogram of Prices')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#2. How good the products are (condition of the products)?\n",
    "table(train$item_condition_id)\n",
    "library(dplyr)\n",
    "train[,.N, by= item_condition_id] %>%\n",
    "  ggplot(aes(x=as.factor(item_condition_id),y=N/1000)) +\n",
    "  geom_bar(stat = 'identity',fill='blue') \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# which condition ID is superior in terms of prices?\n",
    "train[,.(.N,Med_price=median(price),Mean_price = mean(price)), \n",
    "      by= item_condition_id] \n",
    "\n",
    "ggplot(data=train,aes(x=as.factor(item_condition_id),y=log(price+1))) +\n",
    "  geom_boxplot(fill='orange',color='blue') \n",
    "\n",
    "ggplot(data=train,aes(x=as.factor(item_condition_id),y=price)) +\n",
    "  geom_boxplot(fill='orange',color='blue') \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "        0         1 \n",
       "0.5522851 0.4477149 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#3. Comment on the shipping condition, how good the shipping condition is?\n",
    "#OR\n",
    "# The items that are paid by the seller has better price than not paid by \n",
    "# the seller?\n",
    "table(train$shipping)/nrow(train)\n",
    "\n",
    "train %>%\n",
    "  ggplot(aes(x=log(price+1),fill=factor(shipping))) +\n",
    "  geom_density(alpha=0.5)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tWelch Two Sample t-test\n",
       "\n",
       "data:  train$price by train$shipping\n",
       "t = 17.581, df = 29996, p-value < 2.2e-16\n",
       "alternative hypothesis: true difference in means is not equal to 0\n",
       "95 percent confidence interval:\n",
       " 7.137901 8.929136\n",
       "sample estimates:\n",
       "mean in group 0 mean in group 1 \n",
       "       30.55031        22.51679 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# t-test helps in checking the statistical significance of two group means\n",
    "t.test(train$price~train$shipping)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in ContinuousRange$new(): `inherit` must be a R6ClassGenerator.\n",
     "output_type": "error",
     "traceback": [
      "Error in ContinuousRange$new(): `inherit` must be a R6ClassGenerator.\nTraceback:\n",
      "1. scale_y_continuous(labels = scales::dollar)",
      "2. continuous_scale(c(\"y\", \"ymin\", \"ymax\", \"yend\", \"yintercept\", \n .     \"ymin_final\", \"ymax_final\"), \"position_c\", identity, ..., \n .     expand = expand, guide = \"none\")",
      "3. structure(list(call = match.call(), aesthetics = aesthetics, \n .     scale_name = scale_name, palette = palette, range = ContinuousRange$new(), \n .     limits = limits, trans = trans, na.value = na.value, expand = expand, \n .     rescaler = rescaler, oob = oob, name = name, breaks = breaks, \n .     minor_breaks = minor_breaks, labels = labels, legend = legend, \n .     guide = guide), class = c(scale_name, \"continuous\", \"scale\"))",
      "4. ContinuousRange$new()",
      "5. stop(\"`inherit` must be a R6ClassGenerator.\")"
     ]
    }
   ],
   "source": [
    "#4. What are the top 10 most expensive brands present?\n",
    "par(mfrow=c(1,2))\n",
    "\n",
    "train[,.(med_price = median(price)), by= brand_name] %>%\n",
    "  head(10) %>%\n",
    "  ggplot(aes(x= reorder(brand_name,med_price),y=med_price)) +\n",
    "  geom_point(color='red') +\n",
    "  coord_flip() +\n",
    "  scale_y_continuous(labels = scales::dollar)\n",
    "\n",
    "train[,.(mean_price = mean(price)), by= brand_name] %>%\n",
    "  head(10) %>%\n",
    "  ggplot(aes(x= reorder(brand_name,mean_price),y=mean_price)) +\n",
    "  geom_point(color='red') +\n",
    "  coord_flip() +\n",
    "  scale_y_continuous(labels = scales::dollar)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#5. does expensive brands posses higher prices?\n",
    "train[,.(mean_price = mean(price)), by= brand_name]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#6. How many product categories are there?\n",
    "table(train$category_name)\n",
    "\n",
    "unique(train$category_name)\n",
    "\n",
    "length(unique(train$category_name))\n",
    "\n",
    "sort(table(train$category_name),decreasing = T)[1:10]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#7. Does the prices vary by product categories? Analyze the prices\n",
    "# by different category?\n",
    "\n",
    "# what are the product categories with the highest selling price?\n",
    "train[,.(median_price = median(price)), by= category_name][order(median_price,decreasing = T)][1:15] %>%\n",
    "  ggplot(aes(x=reorder(category_name,median_price),y=median_price)) +\n",
    "  geom_point(color = 'blue') +\n",
    "  coord_flip() \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# splitting the columns based on regex '/'\n",
    "library(data.table)\n",
    "train[,c('level1_cat','level2_cat') := tstrsplit(train$category_name,split='/',keep = c(1,2))]\n",
    "\n",
    "head(train[,c('level1_cat','level2_cat')])\n",
    "\n",
    "table(train$level1_cat)\n",
    "\n",
    "table(train$level2_cat)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#average prices by level 1 category\n",
    "train %>%\n",
    "ggplot(aes(x=level1_cat,y=log(price+1))) +\n",
    "  geom_boxplot(fill='orange',color = 'blue') +\n",
    "  coord_flip() \n",
    "\n",
    "train %>%\n",
    "  ggplot(aes(x=level2_cat,y=log(price+1))) +\n",
    "  geom_boxplot(fill='orange',color = 'blue') +\n",
    "  coord_flip() \n",
    "\n",
    "head(train)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fit <- lm(price~factor(item_condition_id)+factor(shipping),data=train)\n",
    "summary(fit)\n",
    "\n",
    "fit <- lm(price~factor(item_condition_id)+\n",
    "            factor(shipping)+\n",
    "            factor(level1_cat)+\n",
    "            factor(level2_cat),data=train)\n",
    "summary(fit)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# we cannot train a regression based model since the R-square value is less than 1%\n",
    "\n",
    "# we need to create better features\n",
    "# calculate the item description length\n",
    "train[,desc_len := nchar(item_description)]\n",
    "\n",
    "summary(train$desc_len)\n",
    "\n",
    "cor(train$desc_len,train$price)\n",
    "\n",
    "cor.test(train$desc_len,train$price)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# spurious correlation\n",
    "\n",
    "#let's do some text analysis\n",
    "train[item_description == 'No Description Found', item_description := NA]\n",
    "\n",
    "# create a text corpus to perform text analysis\n",
    "library(tm)\n",
    "library(quanteda)\n",
    "dcorpus <- corpus(train$item_description)\n",
    "summary(dcorpus)[1:5,]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create a context\n",
    "kwic(dcorpus,phrase('Computers and Tablets'),valuetype = 'fixed') %>%\n",
    "  head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# term document matrix/document frequency matrix to extract features from the text data\n",
    "dfm1 <- dfm(\n",
    "  dcorpus,\n",
    "  ngrams=1,\n",
    "  remove = c('rm',stopwords('english')),\n",
    "  remove_punct=T,\n",
    "  remove_numbers = T,\n",
    "  stem=T)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# N-gram approach to extract the top features\n",
    "tf <- topfeatures(dfm1,n=30)\n",
    "\n",
    "#let's visualize the top features\n",
    "data.frame(term=names(tf),freq=unname(tf)) %>%\n",
    "  ggplot(aes(x=reorder(term,freq),y=freq/1000)) +\n",
    "  geom_bar(stat = 'identity',fill='red') +\n",
    "  coord_flip()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#visualize the word cloud representation\n",
    "#textplot_wordcloud(dfm1,min.freq=2,rot.per=0.2)\n",
    "\n",
    "# term document matrix/document frequency matrix to extract features from the text data\n",
    "dfm2 <- dfm(\n",
    "  dcorpus,\n",
    "  ngrams=2,\n",
    "  remove = c('rm',stopwords('english')),\n",
    "  remove_punct=T,\n",
    "  remove_numbers = T,\n",
    "  concatenator=' ')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# N-gram approach to extract the top features\n",
    "tf <- topfeatures(dfm2,n=30)\n",
    "\n",
    "#let's visualize the top features\n",
    "data.frame(term=names(tf),freq=unname(tf)) %>%\n",
    "  ggplot(aes(x=reorder(term,freq),y=freq/1000)) +\n",
    "  geom_bar(stat = 'identity',fill='red') +\n",
    "  coord_flip()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#visualize the word cloud representation\n",
    "#textplot_wordcloud(dfm1,min.freq=2,rot.per=0.2)\n",
    "\n",
    "# term document matrix/document frequency matrix to extract features from the text data\n",
    "dfm3 <- dfm(\n",
    "  dcorpus,\n",
    "  ngrams=3,\n",
    "  remove = c('rm',stopwords('english')),\n",
    "  remove_punct=T,\n",
    "  remove_numbers = T,\n",
    "  concatenator=' ')\n",
    "\n",
    "# N-gram approach to extract the top features\n",
    "tf <- topfeatures(dfm3,n=30)\n",
    "\n",
    "#let's visualize the top features\n",
    "data.frame(term=names(tf),freq=unname(tf)) %>%\n",
    "  ggplot(aes(x=reorder(term,freq),y=freq/1000)) +\n",
    "  geom_bar(stat = 'identity',fill='red') +\n",
    "  coord_flip()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#visualize the word cloud representation\n",
    "#textplot_wordcloud(dfm1,min.freq=2,rot.per=0.2)\n",
    "# term document matrix/document frequency matrix to extract features from the text data\n",
    "dfm4 <- dfm(\n",
    "  dcorpus,\n",
    "  ngrams=4,\n",
    "  remove = c('rm',stopwords('english')),\n",
    "  remove_punct=T,\n",
    "  remove_numbers = T,\n",
    "  concatenator=' ')\n",
    "\n",
    "# N-gram approach to extract the top features\n",
    "tf <- topfeatures(dfm4,n=30)\n",
    "\n",
    "#let's visualize the top features\n",
    "data.frame(term=names(tf),freq=unname(tf)) %>%\n",
    "  ggplot(aes(x=reorder(term,freq),y=freq/1000)) +\n",
    "  geom_bar(stat = 'identity',fill='red') +\n",
    "  coord_flip()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#visualize the word cloud representation\n",
    "#textplot_wordcloud(dfm1,min.freq=2,rot.per=0.2)\n",
    "\n",
    "train %>% head()\n",
    "\n",
    "\n",
    "\n",
    "feat_brand_new <- ifelse(grepl('brand new with tags',train$item_description) |\n",
    "                           grepl('brand new',train$item_description),1,0)\n",
    "table(feat_brand_new)\n",
    "\n",
    "train$brand_new <- feat_brand_new\n",
    "\n",
    "feat_free_ship <- ifelse(grepl('free shipping',train$item_description) |\n",
    "                           grepl('free',train$item_description),1,0)\n",
    "table(feat_free_ship)\n",
    "\n",
    "train$free_ship <- feat_free_ship\n",
    "\n",
    "feat_condition <- ifelse(grepl('great condition',train$item_description) |\n",
    "                           grepl('good condition',train$item_description),1,0)\n",
    "table(feat_condition)\n",
    "\n",
    "train$condition <- feat_condition\n",
    "\n",
    "feat_gold <- ifelse(grepl('gold',train$name) |\n",
    "                           grepl('jewelery',train$category_name),1,0)\n",
    "table(feat_gold)\n",
    "\n",
    "train$gold_item <- feat_gold\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# please fix the errors related to the library, if possible run it locally."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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