{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sweep BookCrossing Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(readr)\n",
    "library(dplyr)\n",
    "library(reshape2)\n",
    "library(ggplot2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "options(repr.matrix.max.rows=15, repr.plot.height=4.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "bias.results = read_csv(\"build/bx-bias-sweep-results.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Damping</th><th scope=col>Metric</th><th scope=col>value</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1          </td><td>RMSE.ByUser</td><td>1.562261   </td></tr>\n",
       "\t<tr><td>2          </td><td>RMSE.ByUser</td><td>1.529473   </td></tr>\n",
       "\t<tr><td>3          </td><td>RMSE.ByUser</td><td>1.517921   </td></tr>\n",
       "\t<tr><td>4          </td><td>RMSE.ByUser</td><td>1.514028   </td></tr>\n",
       "\t<tr><td>5          </td><td>RMSE.ByUser</td><td>1.513653   </td></tr>\n",
       "\t<tr><td>6          </td><td>RMSE.ByUser</td><td>1.515096   </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " Damping & Metric & value\\\\\n",
       "\\hline\n",
       "\t 1           & RMSE.ByUser & 1.562261   \\\\\n",
       "\t 2           & RMSE.ByUser & 1.529473   \\\\\n",
       "\t 3           & RMSE.ByUser & 1.517921   \\\\\n",
       "\t 4           & RMSE.ByUser & 1.514028   \\\\\n",
       "\t 5           & RMSE.ByUser & 1.513653   \\\\\n",
       "\t 6           & RMSE.ByUser & 1.515096   \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Damping | Metric | value | \n",
       "|---|---|---|---|---|---|\n",
       "| 1           | RMSE.ByUser | 1.562261    | \n",
       "| 2           | RMSE.ByUser | 1.529473    | \n",
       "| 3           | RMSE.ByUser | 1.517921    | \n",
       "| 4           | RMSE.ByUser | 1.514028    | \n",
       "| 5           | RMSE.ByUser | 1.513653    | \n",
       "| 6           | RMSE.ByUser | 1.515096    | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  Damping Metric      value   \n",
       "1 1       RMSE.ByUser 1.562261\n",
       "2 2       RMSE.ByUser 1.529473\n",
       "3 3       RMSE.ByUser 1.517921\n",
       "4 4       RMSE.ByUser 1.514028\n",
       "5 5       RMSE.ByUser 1.513653\n",
       "6 6       RMSE.ByUser 1.515096"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bias.results.tall = bias.results %>%\n",
    "    select(Damping, RMSE.ByUser, Predict.nDCG) %>%\n",
    "    melt(id.vars = \"Damping\", variable.name = \"Metric\")\n",
    "head(bias.results.tall)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAAIcCAMAAAD7UX68AAADAFBMVEUAAAABAQECAgIDAwME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\nIAD8P/Hv7tuIZFH6AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(bias.results.tall) +\n",
    "    aes(x=Damping, y=value) +\n",
    "    geom_point() + geom_line() +\n",
    "    facet_grid(Metric ~ ., scales=\"free_y\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bias damping of **7** looks good. 5 wouldn't be bad either.\n",
    "\n",
    "We will feed this value foward into the other sweeps."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Explicit Feedback Recsys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Parsed with column specification:\n",
      "cols(\n",
      "  DataSet = col_character(),\n",
      "  Algorithm = col_character(),\n",
      "  Damping = col_integer(),\n",
      "  FeatureCount = col_integer(),\n",
      "  NNbrs = col_integer(),\n",
      "  BuildTime = col_double(),\n",
      "  TestTime = col_double(),\n",
      "  RMSE.ByUser = col_double(),\n",
      "  RMSE.ByRating = col_double(),\n",
      "  Predict.nDCG = col_double(),\n",
      "  TopN.nDCG = col_double(),\n",
      "  MAP = col_double()\n",
      ")\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>DataSet</th><th scope=col>Algorithm</th><th scope=col>Damping</th><th scope=col>FeatureCount</th><th scope=col>NNbrs</th><th scope=col>BuildTime</th><th scope=col>TestTime</th><th scope=col>RMSE.ByUser</th><th scope=col>RMSE.ByRating</th><th scope=col>Predict.nDCG</th><th scope=col>TopN.nDCG</th><th scope=col>MAP</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>bx-explicit </td><td>Bias        </td><td> 1          </td><td>NA          </td><td>NA          </td><td> 1.416      </td><td>158.961     </td><td>1.562261    </td><td>1.687230    </td><td>0.9592534   </td><td>0.0004137511</td><td>0.0002570759</td></tr>\n",
       "\t<tr><td>bx-explicit </td><td>Bias        </td><td> 2          </td><td>NA          </td><td>NA          </td><td> 0.645      </td><td>161.917     </td><td>1.529473    </td><td>1.654503    </td><td>0.9593112   </td><td>0.0007320124</td><td>0.0005007552</td></tr>\n",
       "\t<tr><td>bx-explicit </td><td>Bias        </td><td> 3          </td><td>NA          </td><td>NA          </td><td> 0.629      </td><td>169.447     </td><td>1.517921    </td><td>1.643064    </td><td>0.9594167   </td><td>0.0014005498</td><td>0.0008153528</td></tr>\n",
       "\t<tr><td>bx-explicit </td><td>Bias        </td><td> 4          </td><td>NA          </td><td>NA          </td><td> 0.656      </td><td>171.547     </td><td>1.514028    </td><td>1.639065    </td><td>0.9594397   </td><td>0.0018478931</td><td>0.0011493359</td></tr>\n",
       "\t<tr><td>bx-explicit </td><td>ItemItem    </td><td>NA          </td><td>NA          </td><td> 5          </td><td>99.924      </td><td>724.865     </td><td>1.548048    </td><td>1.815056    </td><td>0.5809573   </td><td>0.0014989007</td><td>0.0015909301</td></tr>\n",
       "\t<tr><td>bx-explicit </td><td>ItemItem    </td><td>NA          </td><td>NA          </td><td>10          </td><td>99.920      </td><td>725.641     </td><td>1.542411    </td><td>1.808310    </td><td>0.5810906   </td><td>0.0015100563</td><td>0.0015955714</td></tr>\n",
       "\t<tr><td>bx-explicit </td><td>ItemItem    </td><td>NA          </td><td>NA          </td><td>15          </td><td>99.916      </td><td>731.384     </td><td>1.541888    </td><td>1.807619    </td><td>0.5811162   </td><td>0.0015100221</td><td>0.0015954628</td></tr>\n",
       "\t<tr><td>bx-explicit </td><td>ItemItem    </td><td>NA          </td><td>NA          </td><td>20          </td><td>99.918      </td><td>732.711     </td><td>1.541953    </td><td>1.807609    </td><td>0.5811064   </td><td>0.0015101051</td><td>0.0015956590</td></tr>\n",
       "\t<tr><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td></tr>\n",
       "\t<tr><td>bx-explicit</td><td>Bias       </td><td>27         </td><td>NA         </td><td>NA         </td><td>0.601      </td><td>175.258    </td><td>1.576848   </td><td>1.699570   </td><td>0.9594186  </td><td>0.007322595</td><td>0.007162933</td></tr>\n",
       "\t<tr><td>bx-explicit</td><td>Bias       </td><td>26         </td><td>NA         </td><td>NA         </td><td>0.604      </td><td>175.058    </td><td>1.574590   </td><td>1.697321   </td><td>0.9594207  </td><td>0.007162322</td><td>0.006878786</td></tr>\n",
       "\t<tr><td>bx-explicit</td><td>Bias       </td><td>25         </td><td>NA         </td><td>NA         </td><td>0.583      </td><td>174.790    </td><td>1.572261   </td><td>1.695001   </td><td>0.9594660  </td><td>0.006972813</td><td>0.006851596</td></tr>\n",
       "\t<tr><td>bx-explicit</td><td>Bias       </td><td>24         </td><td>NA         </td><td>NA         </td><td>0.569      </td><td>174.880    </td><td>1.569855   </td><td>1.692610   </td><td>0.9595008  </td><td>0.006897759</td><td>0.006783868</td></tr>\n",
       "\t<tr><td>bx-explicit</td><td>Bias       </td><td>21         </td><td>NA         </td><td>NA         </td><td>0.616      </td><td>173.952    </td><td>1.562155   </td><td>1.684971   </td><td>0.9594732  </td><td>0.006728265</td><td>0.006577022</td></tr>\n",
       "\t<tr><td>bx-explicit</td><td>Bias       </td><td>23         </td><td>NA         </td><td>NA         </td><td>0.643      </td><td>174.208    </td><td>1.567372   </td><td>1.690142   </td><td>0.9595076  </td><td>0.006813821</td><td>0.006730331</td></tr>\n",
       "\t<tr><td>bx-explicit</td><td>Bias       </td><td>22         </td><td>NA         </td><td>NA         </td><td>0.637      </td><td>174.454    </td><td>1.564806   </td><td>1.687597   </td><td>0.9594914  </td><td>0.006789392</td><td>0.006689019</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllllllllll}\n",
       " DataSet & Algorithm & Damping & FeatureCount & NNbrs & BuildTime & TestTime & RMSE.ByUser & RMSE.ByRating & Predict.nDCG & TopN.nDCG & MAP\\\\\n",
       "\\hline\n",
       "\t bx-explicit  & Bias         &  1           & NA           & NA           &  1.416       & 158.961      & 1.562261     & 1.687230     & 0.9592534    & 0.0004137511 & 0.0002570759\\\\\n",
       "\t bx-explicit  & Bias         &  2           & NA           & NA           &  0.645       & 161.917      & 1.529473     & 1.654503     & 0.9593112    & 0.0007320124 & 0.0005007552\\\\\n",
       "\t bx-explicit  & Bias         &  3           & NA           & NA           &  0.629       & 169.447      & 1.517921     & 1.643064     & 0.9594167    & 0.0014005498 & 0.0008153528\\\\\n",
       "\t bx-explicit  & Bias         &  4           & NA           & NA           &  0.656       & 171.547      & 1.514028     & 1.639065     & 0.9594397    & 0.0018478931 & 0.0011493359\\\\\n",
       "\t bx-explicit  & ItemItem     & NA           & NA           &  5           & 99.924       & 724.865      & 1.548048     & 1.815056     & 0.5809573    & 0.0014989007 & 0.0015909301\\\\\n",
       "\t bx-explicit  & ItemItem     & NA           & NA           & 10           & 99.920       & 725.641      & 1.542411     & 1.808310     & 0.5810906    & 0.0015100563 & 0.0015955714\\\\\n",
       "\t bx-explicit  & ItemItem     & NA           & NA           & 15           & 99.916       & 731.384      & 1.541888     & 1.807619     & 0.5811162    & 0.0015100221 & 0.0015954628\\\\\n",
       "\t bx-explicit  & ItemItem     & NA           & NA           & 20           & 99.918       & 732.711      & 1.541953     & 1.807609     & 0.5811064    & 0.0015101051 & 0.0015956590\\\\\n",
       "\t ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮\\\\\n",
       "\t bx-explicit & Bias        & 27          & NA          & NA          & 0.601       & 175.258     & 1.576848    & 1.699570    & 0.9594186   & 0.007322595 & 0.007162933\\\\\n",
       "\t bx-explicit & Bias        & 26          & NA          & NA          & 0.604       & 175.058     & 1.574590    & 1.697321    & 0.9594207   & 0.007162322 & 0.006878786\\\\\n",
       "\t bx-explicit & Bias        & 25          & NA          & NA          & 0.583       & 174.790     & 1.572261    & 1.695001    & 0.9594660   & 0.006972813 & 0.006851596\\\\\n",
       "\t bx-explicit & Bias        & 24          & NA          & NA          & 0.569       & 174.880     & 1.569855    & 1.692610    & 0.9595008   & 0.006897759 & 0.006783868\\\\\n",
       "\t bx-explicit & Bias        & 21          & NA          & NA          & 0.616       & 173.952     & 1.562155    & 1.684971    & 0.9594732   & 0.006728265 & 0.006577022\\\\\n",
       "\t bx-explicit & Bias        & 23          & NA          & NA          & 0.643       & 174.208     & 1.567372    & 1.690142    & 0.9595076   & 0.006813821 & 0.006730331\\\\\n",
       "\t bx-explicit & Bias        & 22          & NA          & NA          & 0.637       & 174.454     & 1.564806    & 1.687597    & 0.9594914   & 0.006789392 & 0.006689019\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "DataSet | Algorithm | Damping | FeatureCount | NNbrs | BuildTime | TestTime | RMSE.ByUser | RMSE.ByRating | Predict.nDCG | TopN.nDCG | MAP | \n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| bx-explicit  | Bias         |  1           | NA           | NA           |  1.416       | 158.961      | 1.562261     | 1.687230     | 0.9592534    | 0.0004137511 | 0.0002570759 | \n",
       "| bx-explicit  | Bias         |  2           | NA           | NA           |  0.645       | 161.917      | 1.529473     | 1.654503     | 0.9593112    | 0.0007320124 | 0.0005007552 | \n",
       "| bx-explicit  | Bias         |  3           | NA           | NA           |  0.629       | 169.447      | 1.517921     | 1.643064     | 0.9594167    | 0.0014005498 | 0.0008153528 | \n",
       "| bx-explicit  | Bias         |  4           | NA           | NA           |  0.656       | 171.547      | 1.514028     | 1.639065     | 0.9594397    | 0.0018478931 | 0.0011493359 | \n",
       "| bx-explicit  | ItemItem     | NA           | NA           |  5           | 99.924       | 724.865      | 1.548048     | 1.815056     | 0.5809573    | 0.0014989007 | 0.0015909301 | \n",
       "| bx-explicit  | ItemItem     | NA           | NA           | 10           | 99.920       | 725.641      | 1.542411     | 1.808310     | 0.5810906    | 0.0015100563 | 0.0015955714 | \n",
       "| bx-explicit  | ItemItem     | NA           | NA           | 15           | 99.916       | 731.384      | 1.541888     | 1.807619     | 0.5811162    | 0.0015100221 | 0.0015954628 | \n",
       "| bx-explicit  | ItemItem     | NA           | NA           | 20           | 99.918       | 732.711      | 1.541953     | 1.807609     | 0.5811064    | 0.0015101051 | 0.0015956590 | \n",
       "| ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | \n",
       "| bx-explicit | Bias        | 27          | NA          | NA          | 0.601       | 175.258     | 1.576848    | 1.699570    | 0.9594186   | 0.007322595 | 0.007162933 | \n",
       "| bx-explicit | Bias        | 26          | NA          | NA          | 0.604       | 175.058     | 1.574590    | 1.697321    | 0.9594207   | 0.007162322 | 0.006878786 | \n",
       "| bx-explicit | Bias        | 25          | NA          | NA          | 0.583       | 174.790     | 1.572261    | 1.695001    | 0.9594660   | 0.006972813 | 0.006851596 | \n",
       "| bx-explicit | Bias        | 24          | NA          | NA          | 0.569       | 174.880     | 1.569855    | 1.692610    | 0.9595008   | 0.006897759 | 0.006783868 | \n",
       "| bx-explicit | Bias        | 21          | NA          | NA          | 0.616       | 173.952     | 1.562155    | 1.684971    | 0.9594732   | 0.006728265 | 0.006577022 | \n",
       "| bx-explicit | Bias        | 23          | NA          | NA          | 0.643       | 174.208     | 1.567372    | 1.690142    | 0.9595076   | 0.006813821 | 0.006730331 | \n",
       "| bx-explicit | Bias        | 22          | NA          | NA          | 0.637       | 174.454     | 1.564806    | 1.687597    | 0.9594914   | 0.006789392 | 0.006689019 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "    DataSet     Algorithm Damping FeatureCount NNbrs BuildTime TestTime\n",
       "1   bx-explicit Bias       1      NA           NA     1.416    158.961 \n",
       "2   bx-explicit Bias       2      NA           NA     0.645    161.917 \n",
       "3   bx-explicit Bias       3      NA           NA     0.629    169.447 \n",
       "4   bx-explicit Bias       4      NA           NA     0.656    171.547 \n",
       "5   bx-explicit ItemItem  NA      NA            5    99.924    724.865 \n",
       "6   bx-explicit ItemItem  NA      NA           10    99.920    725.641 \n",
       "7   bx-explicit ItemItem  NA      NA           15    99.916    731.384 \n",
       "8   bx-explicit ItemItem  NA      NA           20    99.918    732.711 \n",
       "⋮   ⋮           ⋮         ⋮       ⋮            ⋮     ⋮         ⋮       \n",
       "139 bx-explicit Bias      27      NA           NA    0.601     175.258 \n",
       "140 bx-explicit Bias      26      NA           NA    0.604     175.058 \n",
       "141 bx-explicit Bias      25      NA           NA    0.583     174.790 \n",
       "142 bx-explicit Bias      24      NA           NA    0.569     174.880 \n",
       "143 bx-explicit Bias      21      NA           NA    0.616     173.952 \n",
       "144 bx-explicit Bias      23      NA           NA    0.643     174.208 \n",
       "145 bx-explicit Bias      22      NA           NA    0.637     174.454 \n",
       "    RMSE.ByUser RMSE.ByRating Predict.nDCG TopN.nDCG    MAP         \n",
       "1   1.562261    1.687230      0.9592534    0.0004137511 0.0002570759\n",
       "2   1.529473    1.654503      0.9593112    0.0007320124 0.0005007552\n",
       "3   1.517921    1.643064      0.9594167    0.0014005498 0.0008153528\n",
       "4   1.514028    1.639065      0.9594397    0.0018478931 0.0011493359\n",
       "5   1.548048    1.815056      0.5809573    0.0014989007 0.0015909301\n",
       "6   1.542411    1.808310      0.5810906    0.0015100563 0.0015955714\n",
       "7   1.541888    1.807619      0.5811162    0.0015100221 0.0015954628\n",
       "8   1.541953    1.807609      0.5811064    0.0015101051 0.0015956590\n",
       "⋮   ⋮           ⋮             ⋮            ⋮            ⋮           \n",
       "139 1.576848    1.699570      0.9594186    0.007322595  0.007162933 \n",
       "140 1.574590    1.697321      0.9594207    0.007162322  0.006878786 \n",
       "141 1.572261    1.695001      0.9594660    0.006972813  0.006851596 \n",
       "142 1.569855    1.692610      0.9595008    0.006897759  0.006783868 \n",
       "143 1.562155    1.684971      0.9594732    0.006728265  0.006577022 \n",
       "144 1.567372    1.690142      0.9595076    0.006813821  0.006730331 \n",
       "145 1.564806    1.687597      0.9594914    0.006789392  0.006689019 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.explicit = read_csv(\"build/bx-ratings-sweep-results.csv\") %>%\n",
    "    rename(TopN.nDCG=nDCG)\n",
    "results.explicit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summarize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'Bias'</li>\n",
       "\t<li>'ItemItem'</li>\n",
       "\t<li>'UserUser'</li>\n",
       "\t<li>'FunkSVD'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'Bias'\n",
       "\\item 'ItemItem'\n",
       "\\item 'UserUser'\n",
       "\\item 'FunkSVD'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'Bias'\n",
       "2. 'ItemItem'\n",
       "3. 'UserUser'\n",
       "4. 'FunkSVD'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"Bias\"     \"ItemItem\" \"UserUser\" \"FunkSVD\" "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "unique(results.explicit$Algorithm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### User-User CF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAAIcCAMAAAD7UX68AAADAFBMVEUAAAABAQECAgIDAwME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\nBEgIxSFAQigO/T/pdwWj3dmS+AAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(results.explicit %>% filter(Algorithm==\"UserUser\")) +\n",
    "    aes(x=NNbrs, y=RMSE.ByUser) +\n",
    "    geom_point() + geom_line()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAAIcCAMAAAD7UX68AAADAFBMVEUAAAABAQECAgIDAwME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\nQaIQQEKQKASQECQKASQEiUL+Hx/hjRzpcLEQAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(results.explicit %>% filter(Algorithm==\"UserUser\")) +\n",
    "    aes(x=NNbrs, y=MAP) +\n",
    "    geom_point() + geom_line()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAAIcCAMAAAD7UX68AAADAFBMVEUAAAABAQECAgIDAwME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\nAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(results.explicit %>% filter(Algorithm==\"UserUser\")) +\n",
    "    aes(x=NNbrs, y=TopN.nDCG) +\n",
    "    geom_point() + geom_line()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAAIcCAMAAAD7UX68AAADAFBMVEUAAAABAQECAgIDAwME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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(results.explicit %>% filter(Algorithm==\"UserUser\")) +\n",
    "    aes(x=NNbrs, y=Predict.nDCG) +\n",
    "    geom_point() + geom_line()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Results\n",
    "\n",
    "Resulting configuration: **15** neighbors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Item-Item CF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAAIcCAMAAAD7UX68AAADAFBMVEUAAAABAQECAgIDAwME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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(results.explicit %>% filter(Algorithm==\"ItemItem\")) +\n",
    "    aes(x=NNbrs, y=RMSE.ByUser) +\n",
    "    geom_point() + geom_line()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAAIcCAMAAAD7UX68AAADAFBMVEUAAAABAQECAgIDAwME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\nrkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(results.explicit %>% filter(Algorithm==\"ItemItem\")) +\n",
    "    aes(x=NNbrs, y=MAP) +\n",
    "    geom_point() + geom_line()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAAIcCAMAAAD7UX68AAADAFBMVEUAAAABAQECAgIDAwME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\nKEBCoSwoQEKhLKj/B9eWdWxhtuF0AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(results.explicit %>% filter(Algorithm==\"ItemItem\")) +\n",
    "    aes(x=NNbrs, y=TopN.nDCG) +\n",
    "    geom_point() + geom_line()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAAIcCAMAAAD7UX68AAADAFBMVEUAAAABAQECAgIDAwME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\nBRESYymIkBhLQf8PNruojkHWuSYAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(results.explicit %>% filter(Algorithm==\"ItemItem\")) +\n",
    "    aes(x=NNbrs, y=Predict.nDCG) +\n",
    "    geom_point() + geom_line()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Results\n",
    "\n",
    "Resulting configuration: **15** neighbors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### FunkSVD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAAIcCAMAAAD7UX68AAADAFBMVEUAAAABAQECAgIDAwME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\nB8GA4dpvZ0Q+AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(results.explicit %>% filter(Algorithm==\"FunkSVD\")) +\n",
    "    aes(x=FeatureCount, y=RMSE.ByUser) +\n",
    "    geom_point() + geom_line()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAAIcCAMAAAD7UX68AAADAFBMVEUAAAABAQECAgIDAwME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\nAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(results.explicit %>% filter(Algorithm==\"FunkSVD\")) +\n",
    "    aes(x=FeatureCount, y=MAP) +\n",
    "    geom_point() + geom_line()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAAIcCAMAAAD7UX68AAADAFBMVEUAAAABAQECAgIDAwME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\nL/iF93iI0AAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(results.explicit %>% filter(Algorithm==\"FunkSVD\")) +\n",
    "    aes(x=FeatureCount, y=TopN.nDCG) +\n",
    "    geom_point() + geom_line()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAAIcCAMAAAD7UX68AAADAFBMVEUAAAABAQECAgIDAwME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\nAAkhEwIkhEwIkBAyof8H6GdyeLdsqa8AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(results.explicit %>% filter(Algorithm==\"FunkSVD\")) +\n",
    "    aes(x=FeatureCount, y=Predict.nDCG) +\n",
    "    geom_point() + geom_line()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Results\n",
    "\n",
    "Let's use **60** features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ggplot(results.explicit.pf %>% filter(Algorithm==\"PF\")) +\n",
    "    aes(x=FeatureCount, y=RMSE.ByUser) +\n",
    "    geom_point() + geom_line()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ggplot(results.explicit.pf %>% filter(Algorithm==\"PF\")) +\n",
    "    aes(x=FeatureCount, y=MAP) +\n",
    "    geom_point() + geom_line()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ggplot(results.explicit.pf %>% filter(Algorithm==\"PF\")) +\n",
    "    aes(x=FeatureCount, y=TopN.nDCG) +\n",
    "    geom_point() + geom_line()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ggplot(results.explicit.pf %>% filter(Algorithm==\"PF\")) +\n",
    "    aes(x=FeatureCount, y=Predict.nDCG) +\n",
    "    geom_point() + geom_line()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implicit Feedback Recsys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Parsed with column specification:\n",
      "cols(\n",
      "  DataSet = col_character(),\n",
      "  Algorithm = col_character(),\n",
      "  FeatureCount = col_integer(),\n",
      "  NNbrs = col_integer(),\n",
      "  BuildTime = col_double(),\n",
      "  TestTime = col_double(),\n",
      "  TopN.nDCG = col_double(),\n",
      "  MAP = col_double()\n",
      ")\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>DataSet</th><th scope=col>Algorithm</th><th scope=col>FeatureCount</th><th scope=col>NNbrs</th><th scope=col>BuildTime</th><th scope=col>TestTime</th><th scope=col>TopN.nDCG</th><th scope=col>MAP</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>bx-implicit </td><td>Popular     </td><td>NA          </td><td>NA          </td><td>  0.126     </td><td> 280.653    </td><td>NaN         </td><td>0.0275296610</td></tr>\n",
       "\t<tr><td>bx-implicit </td><td>FunkSVD     </td><td> 5          </td><td>NA          </td><td> 17.835     </td><td> 514.071    </td><td>NaN         </td><td>0.0023827009</td></tr>\n",
       "\t<tr><td>bx-implicit </td><td>FunkSVD     </td><td>10          </td><td>NA          </td><td> 33.888     </td><td> 653.060    </td><td>NaN         </td><td>0.0023842993</td></tr>\n",
       "\t<tr><td>bx-implicit </td><td>FunkSVD     </td><td>15          </td><td>NA          </td><td> 83.161     </td><td> 765.781    </td><td>NaN         </td><td>0.0010217565</td></tr>\n",
       "\t<tr><td>bx-implicit </td><td>FunkSVD     </td><td>20          </td><td>NA          </td><td>138.252     </td><td> 868.644    </td><td>NaN         </td><td>0.0007949715</td></tr>\n",
       "\t<tr><td>bx-implicit </td><td>FunkSVD     </td><td>25          </td><td>NA          </td><td>150.413     </td><td> 938.087    </td><td>NaN         </td><td>0.0006026655</td></tr>\n",
       "\t<tr><td>bx-implicit </td><td>FunkSVD     </td><td>30          </td><td>NA          </td><td>183.245     </td><td> 986.339    </td><td>NaN         </td><td>0.0005462069</td></tr>\n",
       "\t<tr><td>bx-implicit </td><td>ItemItem    </td><td>NA          </td><td> 5          </td><td>902.692     </td><td>5308.040    </td><td>NaN         </td><td>0.0465582003</td></tr>\n",
       "\t<tr><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td></tr>\n",
       "\t<tr><td>bx-implicit </td><td>UserUser    </td><td> NA         </td><td>80          </td><td>  0.018     </td><td>5774.407    </td><td>NaN         </td><td>0.0676743655</td></tr>\n",
       "\t<tr><td>bx-implicit </td><td>UserUser    </td><td> NA         </td><td>70          </td><td>  0.010     </td><td>5733.256    </td><td>NaN         </td><td>0.0684868456</td></tr>\n",
       "\t<tr><td>bx-implicit </td><td>FunkSVD     </td><td> 60         </td><td>NA          </td><td>260.564     </td><td>1425.950    </td><td>NaN         </td><td>0.0004521693</td></tr>\n",
       "\t<tr><td>bx-implicit </td><td>FunkSVD     </td><td> 70         </td><td>NA          </td><td>308.124     </td><td>1523.590    </td><td>NaN         </td><td>0.0005131640</td></tr>\n",
       "\t<tr><td>bx-implicit </td><td>FunkSVD     </td><td> 80         </td><td>NA          </td><td>322.225     </td><td>1647.682    </td><td>NaN         </td><td>0.0005751916</td></tr>\n",
       "\t<tr><td>bx-implicit </td><td>FunkSVD     </td><td> 90         </td><td>NA          </td><td>375.793     </td><td>1779.107    </td><td>NaN         </td><td>0.0006707972</td></tr>\n",
       "\t<tr><td>bx-implicit </td><td>FunkSVD     </td><td>100         </td><td>NA          </td><td>414.155     </td><td>1907.430    </td><td>NaN         </td><td>0.0000000000</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllllll}\n",
       " DataSet & Algorithm & FeatureCount & NNbrs & BuildTime & TestTime & TopN.nDCG & MAP\\\\\n",
       "\\hline\n",
       "\t bx-implicit  & Popular      & NA           & NA           &   0.126      &  280.653     & NaN          & 0.0275296610\\\\\n",
       "\t bx-implicit  & FunkSVD      &  5           & NA           &  17.835      &  514.071     & NaN          & 0.0023827009\\\\\n",
       "\t bx-implicit  & FunkSVD      & 10           & NA           &  33.888      &  653.060     & NaN          & 0.0023842993\\\\\n",
       "\t bx-implicit  & FunkSVD      & 15           & NA           &  83.161      &  765.781     & NaN          & 0.0010217565\\\\\n",
       "\t bx-implicit  & FunkSVD      & 20           & NA           & 138.252      &  868.644     & NaN          & 0.0007949715\\\\\n",
       "\t bx-implicit  & FunkSVD      & 25           & NA           & 150.413      &  938.087     & NaN          & 0.0006026655\\\\\n",
       "\t bx-implicit  & FunkSVD      & 30           & NA           & 183.245      &  986.339     & NaN          & 0.0005462069\\\\\n",
       "\t bx-implicit  & ItemItem     & NA           &  5           & 902.692      & 5308.040     & NaN          & 0.0465582003\\\\\n",
       "\t ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮\\\\\n",
       "\t bx-implicit  & UserUser     &  NA          & 80           &   0.018      & 5774.407     & NaN          & 0.0676743655\\\\\n",
       "\t bx-implicit  & UserUser     &  NA          & 70           &   0.010      & 5733.256     & NaN          & 0.0684868456\\\\\n",
       "\t bx-implicit  & FunkSVD      &  60          & NA           & 260.564      & 1425.950     & NaN          & 0.0004521693\\\\\n",
       "\t bx-implicit  & FunkSVD      &  70          & NA           & 308.124      & 1523.590     & NaN          & 0.0005131640\\\\\n",
       "\t bx-implicit  & FunkSVD      &  80          & NA           & 322.225      & 1647.682     & NaN          & 0.0005751916\\\\\n",
       "\t bx-implicit  & FunkSVD      &  90          & NA           & 375.793      & 1779.107     & NaN          & 0.0006707972\\\\\n",
       "\t bx-implicit  & FunkSVD      & 100          & NA           & 414.155      & 1907.430     & NaN          & 0.0000000000\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "DataSet | Algorithm | FeatureCount | NNbrs | BuildTime | TestTime | TopN.nDCG | MAP | \n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| bx-implicit  | Popular      | NA           | NA           |   0.126      |  280.653     | NaN          | 0.0275296610 | \n",
       "| bx-implicit  | FunkSVD      |  5           | NA           |  17.835      |  514.071     | NaN          | 0.0023827009 | \n",
       "| bx-implicit  | FunkSVD      | 10           | NA           |  33.888      |  653.060     | NaN          | 0.0023842993 | \n",
       "| bx-implicit  | FunkSVD      | 15           | NA           |  83.161      |  765.781     | NaN          | 0.0010217565 | \n",
       "| bx-implicit  | FunkSVD      | 20           | NA           | 138.252      |  868.644     | NaN          | 0.0007949715 | \n",
       "| bx-implicit  | FunkSVD      | 25           | NA           | 150.413      |  938.087     | NaN          | 0.0006026655 | \n",
       "| bx-implicit  | FunkSVD      | 30           | NA           | 183.245      |  986.339     | NaN          | 0.0005462069 | \n",
       "| bx-implicit  | ItemItem     | NA           |  5           | 902.692      | 5308.040     | NaN          | 0.0465582003 | \n",
       "| ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | \n",
       "| bx-implicit  | UserUser     |  NA          | 80           |   0.018      | 5774.407     | NaN          | 0.0676743655 | \n",
       "| bx-implicit  | UserUser     |  NA          | 70           |   0.010      | 5733.256     | NaN          | 0.0684868456 | \n",
       "| bx-implicit  | FunkSVD      |  60          | NA           | 260.564      | 1425.950     | NaN          | 0.0004521693 | \n",
       "| bx-implicit  | FunkSVD      |  70          | NA           | 308.124      | 1523.590     | NaN          | 0.0005131640 | \n",
       "| bx-implicit  | FunkSVD      |  80          | NA           | 322.225      | 1647.682     | NaN          | 0.0005751916 | \n",
       "| bx-implicit  | FunkSVD      |  90          | NA           | 375.793      | 1779.107     | NaN          | 0.0006707972 | \n",
       "| bx-implicit  | FunkSVD      | 100          | NA           | 414.155      | 1907.430     | NaN          | 0.0000000000 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   DataSet     Algorithm FeatureCount NNbrs BuildTime TestTime TopN.nDCG\n",
       "1  bx-implicit Popular   NA           NA      0.126    280.653 NaN      \n",
       "2  bx-implicit FunkSVD    5           NA     17.835    514.071 NaN      \n",
       "3  bx-implicit FunkSVD   10           NA     33.888    653.060 NaN      \n",
       "4  bx-implicit FunkSVD   15           NA     83.161    765.781 NaN      \n",
       "5  bx-implicit FunkSVD   20           NA    138.252    868.644 NaN      \n",
       "6  bx-implicit FunkSVD   25           NA    150.413    938.087 NaN      \n",
       "7  bx-implicit FunkSVD   30           NA    183.245    986.339 NaN      \n",
       "8  bx-implicit ItemItem  NA            5    902.692   5308.040 NaN      \n",
       "⋮  ⋮           ⋮         ⋮            ⋮     ⋮         ⋮        ⋮        \n",
       "40 bx-implicit UserUser   NA          80      0.018   5774.407 NaN      \n",
       "41 bx-implicit UserUser   NA          70      0.010   5733.256 NaN      \n",
       "42 bx-implicit FunkSVD    60          NA    260.564   1425.950 NaN      \n",
       "43 bx-implicit FunkSVD    70          NA    308.124   1523.590 NaN      \n",
       "44 bx-implicit FunkSVD    80          NA    322.225   1647.682 NaN      \n",
       "45 bx-implicit FunkSVD    90          NA    375.793   1779.107 NaN      \n",
       "46 bx-implicit FunkSVD   100          NA    414.155   1907.430 NaN      \n",
       "   MAP         \n",
       "1  0.0275296610\n",
       "2  0.0023827009\n",
       "3  0.0023842993\n",
       "4  0.0010217565\n",
       "5  0.0007949715\n",
       "6  0.0006026655\n",
       "7  0.0005462069\n",
       "8  0.0465582003\n",
       "⋮  ⋮           \n",
       "40 0.0676743655\n",
       "41 0.0684868456\n",
       "42 0.0004521693\n",
       "43 0.0005131640\n",
       "44 0.0005751916\n",
       "45 0.0006707972\n",
       "46 0.0000000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.implicit = read_csv(\"build/bx-implicit-sweep-results.csv\")\n",
    "results.implicit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summarize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'Popular'</li>\n",
       "\t<li>'FunkSVD'</li>\n",
       "\t<li>'ItemItem'</li>\n",
       "\t<li>'UserUser'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'Popular'\n",
       "\\item 'FunkSVD'\n",
       "\\item 'ItemItem'\n",
       "\\item 'UserUser'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'Popular'\n",
       "2. 'FunkSVD'\n",
       "3. 'ItemItem'\n",
       "4. 'UserUser'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"Popular\"  \"FunkSVD\"  \"ItemItem\" \"UserUser\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "unique(results.implicit$Algorithm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### User-User CF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAAIcCAMAAAD7UX68AAAC+lBMVEUAAAABAQECAgIDAwME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\n6P8D9gHpqwhyNRcAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(results.implicit %>% filter(Algorithm==\"UserUser\")) +\n",
    "    aes(x=NNbrs, y=MAP) +\n",
    "    geom_point() + geom_line() +\n",
    "    geom_hline(data=filter(results.implicit, Algorithm == \"Popular\"), mapping=aes(yintercept=MAP))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "More neighbors = worse. Let's use 5."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Item-Item CF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAAIcCAMAAAD7UX68AAAC/VBMVEUAAAABAQECAgIDAwME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\nAYkoCQGJKAkBiSgJAYkoCQGJKAn9P7IXEUCHnPLjAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(results.implicit %>% filter(Algorithm==\"ItemItem\")) +\n",
    "    aes(x=NNbrs, y=MAP) +\n",
    "    geom_point() + geom_line() +\n",
    "    geom_hline(data=filter(results.implicit, Algorithm == \"Popular\"), mapping=aes(yintercept=MAP))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Neighborhood count doesn't make much difference, but 15 is bad. Let's use 30."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### FunkSVD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAAIcCAMAAAD7UX68AAADAFBMVEUAAAABAQECAgIDAwME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\n8hCQiPLQ/wPxir+mkHW2XgAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(results.implicit %>% filter(Algorithm==\"FunkSVD\")) +\n",
    "    aes(x=FeatureCount, y=MAP) +\n",
    "    geom_point() + geom_line() +\n",
    "    geom_hline(data=filter(results.implicit, Algorithm == \"Popular\"), mapping=aes(yintercept=MAP))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use 10 features? Or just keep using 55 from the implicit data, since there isn't a *lot* of difference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### PF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ggplot(results.implicit %>% filter(Algorithm==\"PF-Implicit\")) +\n",
    "    aes(x=FeatureCount, y=MAP) +\n",
    "    geom_point() + geom_line() +\n",
    "    geom_hline(data=filter(results.implicit, Algorithm == \"Popular\"), mapping=aes(yintercept=MAP))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.4.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}