docs/source/tuto_network_calibration/clustering_ckmeans.ipynb

   1 {
   2  "cells": [
   3   {
   4    "cell_type": "markdown",
   5    "metadata": {},
   6    "source": [
   7     "# Clustering data using Ckmeans.1d.dp"
   8    ]
   9   },
  10   {
  11    "cell_type": "markdown",
  12    "metadata": {},
  13    "source": [
  14     "Illustrates how to do the clustering using the library ckmeans.\n",
  15     "\n",
  16     "After the cluster created, we can calculate the mean and stddev of each one, creating the corresponding normal distributions."
  17    ]
  18   },
  19   {
  20    "cell_type": "code",
  21    "execution_count": 8,
  22    "metadata": {
  23     "tags": [
  24      "parameters"
  25     ]
  26    },
  27    "outputs": [],
  28    "source": [
  29     "seed=42\n",
  30     "quantreg_tau=0.05\n",
  31     "df_str=\"\"\n",
  32     "metric=\"\"\n",
  33     "coeff_col_name=\"\"\n",
  34     "output_file=\"/tmp/ckmeans.csv\""
  35    ]
  36   },
  37   {
  38    "cell_type": "code",
  39    "execution_count": 10,
  40    "metadata": {},
  41    "outputs": [],
  42    "source": [
  43     "library(Ckmeans.1d.dp)\n",
  44     "library(quantreg)\n",
  45     "\n",
  46     "set.seed(seed) #forcing seed for reproductibility"
  47    ]
  48   },
  49   {
  50    "cell_type": "markdown",
  51    "metadata": {},
  52    "source": [
  53     "## Reading dataframe"
  54    ]
  55   },
  56   {
  57    "cell_type": "code",
  58    "execution_count": 132,
  59    "metadata": {},
  60    "outputs": [
  61     {
  62      "name": "stdout",
  63      "output_type": "stream",
  64      "text": [
  65       "       X               op               msg_size     start        \n",
  66       " Min.   :  1130   Length:3500        Min.   :1   Min.   : 0.2003  \n",
  67       " 1st Qu.: 82565   Class :character   1st Qu.:2   1st Qu.:14.3932  \n",
  68       " Median :179094   Mode  :character   Median :4   Median :30.8789  \n",
  69       " Mean   :174237                      Mean   :4   Mean   :30.3998  \n",
  70       " 3rd Qu.:262094                      3rd Qu.:6   3rd Qu.:45.7296  \n",
  71       " Max.   :358579                      Max.   :7   Max.   :63.0828  \n",
  72       "    duration          experiment            type               index       \n",
  73       " Min.   :1.510e-07   Length:3500        Length:3500        Min.   :  2260  \n",
  74       " 1st Qu.:1.560e-07   Class :character   Class :character   1st Qu.:165130  \n",
  75       " Median :1.580e-07   Mode  :character   Mode  :character   Median :358189  \n",
  76       " Mean   :2.322e-07                                         Mean   :348475  \n",
  77       " 3rd Qu.:2.270e-07                                         3rd Qu.:524188  \n",
  78       " Max.   :1.452e-05                                         Max.   :717158  \n"
  79      ]
  80     },
  81     {
  82      "data": {
  83       "text/html": [
  84        "<table class=\"dataframe\">\n",
  85        "<caption>A data.frame: 6 × 8</caption>\n",
  86        "<thead>\n",
  87        "\t<tr><th></th><th scope=col>X</th><th scope=col>op</th><th scope=col>msg_size</th><th scope=col>start</th><th scope=col>duration</th><th scope=col>experiment</th><th scope=col>type</th><th scope=col>index</th></tr>\n",
  88        "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
  89        "</thead>\n",
  90        "<tbody>\n",
  91        "\t<tr><th scope=row>1</th><td>1130</td><td>MPI_Send</td><td>3</td><td>0.200334</td><td>2.57e-07</td><td>grenoble</td><td>exp/exp_PingPong.csv</td><td>2260</td></tr>\n",
  92        "\t<tr><th scope=row>2</th><td>1131</td><td>MPI_Send</td><td>3</td><td>0.200338</td><td>1.85e-07</td><td>grenoble</td><td>exp/exp_PingPong.csv</td><td>2262</td></tr>\n",
  93        "\t<tr><th scope=row>3</th><td>1132</td><td>MPI_Send</td><td>3</td><td>0.200342</td><td>1.63e-07</td><td>grenoble</td><td>exp/exp_PingPong.csv</td><td>2264</td></tr>\n",
  94        "\t<tr><th scope=row>4</th><td>1133</td><td>MPI_Send</td><td>3</td><td>0.200345</td><td>1.56e-07</td><td>grenoble</td><td>exp/exp_PingPong.csv</td><td>2266</td></tr>\n",
  95        "\t<tr><th scope=row>5</th><td>1134</td><td>MPI_Send</td><td>3</td><td>0.200349</td><td>1.54e-07</td><td>grenoble</td><td>exp/exp_PingPong.csv</td><td>2268</td></tr>\n",
  96        "\t<tr><th scope=row>6</th><td>1135</td><td>MPI_Send</td><td>3</td><td>0.200352</td><td>1.64e-07</td><td>grenoble</td><td>exp/exp_PingPong.csv</td><td>2270</td></tr>\n",
  97        "</tbody>\n",
  98        "</table>\n"
  99       ],
 100       "text/latex": [
 101        "A data.frame: 6 × 8\n",
 102        "\\begin{tabular}{r|llllllll}\n",
 103        "  & X & op & msg\\_size & start & duration & experiment & type & index\\\\\n",
 104        "  & <int> & <chr> & <int> & <dbl> & <dbl> & <chr> & <chr> & <int>\\\\\n",
 105        "\\hline\n",
 106        "\t1 & 1130 & MPI\\_Send & 3 & 0.200334 & 2.57e-07 & grenoble & exp/exp\\_PingPong.csv & 2260\\\\\n",
 107        "\t2 & 1131 & MPI\\_Send & 3 & 0.200338 & 1.85e-07 & grenoble & exp/exp\\_PingPong.csv & 2262\\\\\n",
 108        "\t3 & 1132 & MPI\\_Send & 3 & 0.200342 & 1.63e-07 & grenoble & exp/exp\\_PingPong.csv & 2264\\\\\n",
 109        "\t4 & 1133 & MPI\\_Send & 3 & 0.200345 & 1.56e-07 & grenoble & exp/exp\\_PingPong.csv & 2266\\\\\n",
 110        "\t5 & 1134 & MPI\\_Send & 3 & 0.200349 & 1.54e-07 & grenoble & exp/exp\\_PingPong.csv & 2268\\\\\n",
 111        "\t6 & 1135 & MPI\\_Send & 3 & 0.200352 & 1.64e-07 & grenoble & exp/exp\\_PingPong.csv & 2270\\\\\n",
 112        "\\end{tabular}\n"
 113       ],
 114       "text/markdown": [
 115        "\n",
 116        "A data.frame: 6 × 8\n",
 117        "\n",
 118        "| <!--/--> | X &lt;int&gt; | op &lt;chr&gt; | msg_size &lt;int&gt; | start &lt;dbl&gt; | duration &lt;dbl&gt; | experiment &lt;chr&gt; | type &lt;chr&gt; | index &lt;int&gt; |\n",
 119        "|---|---|---|---|---|---|---|---|---|\n",
 120        "| 1 | 1130 | MPI_Send | 3 | 0.200334 | 2.57e-07 | grenoble | exp/exp_PingPong.csv | 2260 |\n",
 121        "| 2 | 1131 | MPI_Send | 3 | 0.200338 | 1.85e-07 | grenoble | exp/exp_PingPong.csv | 2262 |\n",
 122        "| 3 | 1132 | MPI_Send | 3 | 0.200342 | 1.63e-07 | grenoble | exp/exp_PingPong.csv | 2264 |\n",
 123        "| 4 | 1133 | MPI_Send | 3 | 0.200345 | 1.56e-07 | grenoble | exp/exp_PingPong.csv | 2266 |\n",
 124        "| 5 | 1134 | MPI_Send | 3 | 0.200349 | 1.54e-07 | grenoble | exp/exp_PingPong.csv | 2268 |\n",
 125        "| 6 | 1135 | MPI_Send | 3 | 0.200352 | 1.64e-07 | grenoble | exp/exp_PingPong.csv | 2270 |\n",
 126        "\n"
 127       ],
 128       "text/plain": [
 129        "  X    op       msg_size start    duration experiment type                \n",
 130        "1 1130 MPI_Send 3        0.200334 2.57e-07 grenoble   exp/exp_PingPong.csv\n",
 131        "2 1131 MPI_Send 3        0.200338 1.85e-07 grenoble   exp/exp_PingPong.csv\n",
 132        "3 1132 MPI_Send 3        0.200342 1.63e-07 grenoble   exp/exp_PingPong.csv\n",
 133        "4 1133 MPI_Send 3        0.200345 1.56e-07 grenoble   exp/exp_PingPong.csv\n",
 134        "5 1134 MPI_Send 3        0.200349 1.54e-07 grenoble   exp/exp_PingPong.csv\n",
 135        "6 1135 MPI_Send 3        0.200352 1.64e-07 grenoble   exp/exp_PingPong.csv\n",
 136        "  index\n",
 137        "1 2260 \n",
 138        "2 2262 \n",
 139        "3 2264 \n",
 140        "4 2266 \n",
 141        "5 2268 \n",
 142        "6 2270 "
 143       ]
 144      },
 145      "metadata": {},
 146      "output_type": "display_data"
 147     }
 148    ],
 149    "source": [
 150     "df = read.csv(text=df_str)\n",
 151     "print(summary(df))\n",
 152     "head(df)"
 153    ]
 154   },
 155   {
 156    "cell_type": "markdown",
 157    "metadata": {},
 158    "source": [
 159     "## Quantile regression"
 160    ]
 161   },
 162   {
 163    "cell_type": "markdown",
 164    "metadata": {},
 165    "source": [
 166     "Use quantile regression to get the lowest points in the duration graph.\n",
 167     "\n",
 168     "This is important to avoid having negative intercept which could lead to negative duration depending on the message size."
 169    ]
 170   },
 171   {
 172    "cell_type": "code",
 173    "execution_count": 13,
 174    "metadata": {},
 175    "outputs": [
 176     {
 177      "data": {
 178       "text/plain": [
 179        "Call:\n",
 180        "rq(formula = formula, tau = quantreg_tau, data = df)\n",
 181        "\n",
 182        "Coefficients:\n",
 183        " (Intercept)     msg_size \n",
 184        "1.526667e-07 3.333333e-10 \n",
 185        "\n",
 186        "Degrees of freedom: 3500 total; 3498 residual"
 187       ]
 188      },
 189      "metadata": {},
 190      "output_type": "display_data"
 191     }
 192    ],
 193    "source": [
 194     "formula = paste0(metric, \"~\", coeff_col_name)\n",
 195     "rqResult = rq(formula=formula, data=df, tau=quantreg_tau)\n",
 196     "rqResult"
 197    ]
 198   },
 199   {
 200    "cell_type": "markdown",
 201    "metadata": {},
 202    "source": [
 203     "## Clustering"
 204    ]
 205   },
 206   {
 207    "cell_type": "markdown",
 208    "metadata": {},
 209    "source": [
 210     "Calculating the intercept for the duration of each message considering the quantile regression."
 211    ]
 212   },
 213   {
 214    "cell_type": "code",
 215    "execution_count": 136,
 216    "metadata": {},
 217    "outputs": [],
 218    "source": [
 219     "df$intercept_estimate = df[[metric]] - df[[coeff_col_name]]*coef(rqResult)[coeff_col_name]"
 220    ]
 221   },
 222   {
 223    "cell_type": "markdown",
 224    "metadata": {},
 225    "source": [
 226     "Running ckmeans to identify clusters."
 227    ]
 228   },
 229   {
 230    "cell_type": "code",
 231    "execution_count": 138,
 232    "metadata": {},
 233    "outputs": [
 234     {
 235      "name": "stderr",
 236      "output_type": "stream",
 237      "text": [
 238       "Warning message in cluster.1d.dp(x, k, y, method, estimate.k, \"L2\", deparse(substitute(x)), :\n",
 239       "“Max number of clusters used. Consider increasing k!\n",
 240       "”\n"
 241      ]
 242     },
 243     {
 244      "data": {
 245       "text/html": [
 246        "<style>\n",
 247        ".list-inline {list-style: none; margin:0; padding: 0}\n",
 248        ".list-inline>li {display: inline-block}\n",
 249        ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
 250        "</style>\n",
 251        "<ol class=list-inline><li>1.5597630040012e-07</li><li>1.91602355072463e-07</li><li>2.30976303317536e-07</li><li>2.79305128205128e-07</li><li>4.37588105726872e-07</li><li>5.10460317460317e-07</li><li>5.9379012345679e-07</li><li>7.0548427672956e-07</li><li>1.4518e-05</li></ol>\n"
 252       ],
 253       "text/latex": [
 254        "\\begin{enumerate*}\n",
 255        "\\item 1.5597630040012e-07\n",
 256        "\\item 1.91602355072463e-07\n",
 257        "\\item 2.30976303317536e-07\n",
 258        "\\item 2.79305128205128e-07\n",
 259        "\\item 4.37588105726872e-07\n",
 260        "\\item 5.10460317460317e-07\n",
 261        "\\item 5.9379012345679e-07\n",
 262        "\\item 7.0548427672956e-07\n",
 263        "\\item 1.4518e-05\n",
 264        "\\end{enumerate*}\n"
 265       ],
 266       "text/markdown": [
 267        "1. 1.5597630040012e-07\n",
 268        "2. 1.91602355072463e-07\n",
 269        "3. 2.30976303317536e-07\n",
 270        "4. 2.79305128205128e-07\n",
 271        "5. 4.37588105726872e-07\n",
 272        "6. 5.10460317460317e-07\n",
 273        "7. 5.9379012345679e-07\n",
 274        "8. 7.0548427672956e-07\n",
 275        "9. 1.4518e-05\n",
 276        "\n",
 277        "\n"
 278       ],
 279       "text/plain": [
 280        "[1] 1.559763e-07 1.916024e-07 2.309763e-07 2.793051e-07 4.375881e-07\n",
 281        "[6] 5.104603e-07 5.937901e-07 7.054843e-07 1.451800e-05"
 282       ]
 283      },
 284      "metadata": {},
 285      "output_type": "display_data"
 286     }
 287    ],
 288    "source": [
 289     "ckmeans = Ckmeans.1d.dp(df$intercept_estimate)\n",
 290     "df$cluster = ckmeans$cluster\n",
 291     "ckmeans$centers"
 292    ]
 293   },
 294   {
 295    "cell_type": "markdown",
 296    "metadata": {},
 297    "source": [
 298     "Calculating mean and standard deviation for each cluster. Remove NA rows if necessary"
 299    ]
 300   },
 301   {
 302    "cell_type": "code",
 303    "execution_count": 140,
 304    "metadata": {
 305     "collapsed": true,
 306     "jupyter": {
 307      "outputs_hidden": true
 308     },
 309     "tags": []
 310    },
 311    "outputs": [
 312     {
 313      "data": {
 314       "text/html": [
 315        "<table class=\"dataframe\">\n",
 316        "<caption>A tibble: 8 × 4</caption>\n",
 317        "<thead>\n",
 318        "\t<tr><th scope=col>cluster</th><th scope=col>mean</th><th scope=col>sd</th><th scope=col>count</th></tr>\n",
 319        "\t<tr><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
 320        "</thead>\n",
 321        "<tbody>\n",
 322        "\t<tr><td>1</td><td>1.559763e-07</td><td>4.078012e-09</td><td>2166</td></tr>\n",
 323        "\t<tr><td>2</td><td>1.916024e-07</td><td>1.094938e-08</td><td> 368</td></tr>\n",
 324        "\t<tr><td>3</td><td>2.309763e-07</td><td>1.245767e-08</td><td> 211</td></tr>\n",
 325        "\t<tr><td>4</td><td>2.793051e-07</td><td>2.045145e-08</td><td> 130</td></tr>\n",
 326        "\t<tr><td>5</td><td>4.375881e-07</td><td>1.105646e-08</td><td> 454</td></tr>\n",
 327        "\t<tr><td>6</td><td>5.104603e-07</td><td>2.172848e-08</td><td>  63</td></tr>\n",
 328        "\t<tr><td>7</td><td>5.937901e-07</td><td>2.779261e-08</td><td>  54</td></tr>\n",
 329        "\t<tr><td>8</td><td>7.054843e-07</td><td>4.410606e-08</td><td>  53</td></tr>\n",
 330        "</tbody>\n",
 331        "</table>\n"
 332       ],
 333       "text/latex": [
 334        "A tibble: 8 × 4\n",
 335        "\\begin{tabular}{llll}\n",
 336        " cluster & mean & sd & count\\\\\n",
 337        " <int> & <dbl> & <dbl> & <int>\\\\\n",
 338        "\\hline\n",
 339        "\t 1 & 1.559763e-07 & 4.078012e-09 & 2166\\\\\n",
 340        "\t 2 & 1.916024e-07 & 1.094938e-08 &  368\\\\\n",
 341        "\t 3 & 2.309763e-07 & 1.245767e-08 &  211\\\\\n",
 342        "\t 4 & 2.793051e-07 & 2.045145e-08 &  130\\\\\n",
 343        "\t 5 & 4.375881e-07 & 1.105646e-08 &  454\\\\\n",
 344        "\t 6 & 5.104603e-07 & 2.172848e-08 &   63\\\\\n",
 345        "\t 7 & 5.937901e-07 & 2.779261e-08 &   54\\\\\n",
 346        "\t 8 & 7.054843e-07 & 4.410606e-08 &   53\\\\\n",
 347        "\\end{tabular}\n"
 348       ],
 349       "text/markdown": [
 350        "\n",
 351        "A tibble: 8 × 4\n",
 352        "\n",
 353        "| cluster &lt;int&gt; | mean &lt;dbl&gt; | sd &lt;dbl&gt; | count &lt;int&gt; |\n",
 354        "|---|---|---|---|\n",
 355        "| 1 | 1.559763e-07 | 4.078012e-09 | 2166 |\n",
 356        "| 2 | 1.916024e-07 | 1.094938e-08 |  368 |\n",
 357        "| 3 | 2.309763e-07 | 1.245767e-08 |  211 |\n",
 358        "| 4 | 2.793051e-07 | 2.045145e-08 |  130 |\n",
 359        "| 5 | 4.375881e-07 | 1.105646e-08 |  454 |\n",
 360        "| 6 | 5.104603e-07 | 2.172848e-08 |   63 |\n",
 361        "| 7 | 5.937901e-07 | 2.779261e-08 |   54 |\n",
 362        "| 8 | 7.054843e-07 | 4.410606e-08 |   53 |\n",
 363        "\n"
 364       ],
 365       "text/plain": [
 366        "  cluster mean         sd           count\n",
 367        "1 1       1.559763e-07 4.078012e-09 2166 \n",
 368        "2 2       1.916024e-07 1.094938e-08  368 \n",
 369        "3 3       2.309763e-07 1.245767e-08  211 \n",
 370        "4 4       2.793051e-07 2.045145e-08  130 \n",
 371        "5 5       4.375881e-07 1.105646e-08  454 \n",
 372        "6 6       5.104603e-07 2.172848e-08   63 \n",
 373        "7 7       5.937901e-07 2.779261e-08   54 \n",
 374        "8 8       7.054843e-07 4.410606e-08   53 "
 375       ]
 376      },
 377      "metadata": {},
 378      "output_type": "display_data"
 379     }
 380    ],
 381    "source": [
 382     "library(dplyr)\n",
 383     "\n",
 384     "df_normal = df %>% group_by(cluster) %>% summarize(mean = mean(intercept_estimate), sd = sd(intercept_estimate), count = n())\n",
 385     "df_normal = na.omit(df_normal)\n",
 386     "df_normal"
 387    ]
 388   },
 389   {
 390    "cell_type": "markdown",
 391    "metadata": {},
 392    "source": [
 393     "Calculating probability and adding the quantile regression"
 394    ]
 395   },
 396   {
 397    "cell_type": "code",
 398    "execution_count": 143,
 399    "metadata": {},
 400    "outputs": [
 401     {
 402      "data": {
 403       "text/html": [
 404        "<table class=\"dataframe\">\n",
 405        "<caption>A tibble: 8 × 6</caption>\n",
 406        "<thead>\n",
 407        "\t<tr><th scope=col>cluster</th><th scope=col>mean</th><th scope=col>sd</th><th scope=col>count</th><th scope=col>coefficient</th><th scope=col>prob</th></tr>\n",
 408        "\t<tr><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
 409        "</thead>\n",
 410        "<tbody>\n",
 411        "\t<tr><td>1</td><td>1.559763e-07</td><td>4.078012e-09</td><td>2166</td><td>3.333333e-10</td><td>0.61903401</td></tr>\n",
 412        "\t<tr><td>2</td><td>1.916024e-07</td><td>1.094938e-08</td><td> 368</td><td>3.333333e-10</td><td>0.10517291</td></tr>\n",
 413        "\t<tr><td>3</td><td>2.309763e-07</td><td>1.245767e-08</td><td> 211</td><td>3.333333e-10</td><td>0.06030294</td></tr>\n",
 414        "\t<tr><td>4</td><td>2.793051e-07</td><td>2.045145e-08</td><td> 130</td><td>3.333333e-10</td><td>0.03715347</td></tr>\n",
 415        "\t<tr><td>5</td><td>4.375881e-07</td><td>1.105646e-08</td><td> 454</td><td>3.333333e-10</td><td>0.12975136</td></tr>\n",
 416        "\t<tr><td>6</td><td>5.104603e-07</td><td>2.172848e-08</td><td>  63</td><td>3.333333e-10</td><td>0.01800514</td></tr>\n",
 417        "\t<tr><td>7</td><td>5.937901e-07</td><td>2.779261e-08</td><td>  54</td><td>3.333333e-10</td><td>0.01543298</td></tr>\n",
 418        "\t<tr><td>8</td><td>7.054843e-07</td><td>4.410606e-08</td><td>  53</td><td>3.333333e-10</td><td>0.01514718</td></tr>\n",
 419        "</tbody>\n",
 420        "</table>\n"
 421       ],
 422       "text/latex": [
 423        "A tibble: 8 × 6\n",
 424        "\\begin{tabular}{llllll}\n",
 425        " cluster & mean & sd & count & coefficient & prob\\\\\n",
 426        " <int> & <dbl> & <dbl> & <int> & <dbl> & <dbl>\\\\\n",
 427        "\\hline\n",
 428        "\t 1 & 1.559763e-07 & 4.078012e-09 & 2166 & 3.333333e-10 & 0.61903401\\\\\n",
 429        "\t 2 & 1.916024e-07 & 1.094938e-08 &  368 & 3.333333e-10 & 0.10517291\\\\\n",
 430        "\t 3 & 2.309763e-07 & 1.245767e-08 &  211 & 3.333333e-10 & 0.06030294\\\\\n",
 431        "\t 4 & 2.793051e-07 & 2.045145e-08 &  130 & 3.333333e-10 & 0.03715347\\\\\n",
 432        "\t 5 & 4.375881e-07 & 1.105646e-08 &  454 & 3.333333e-10 & 0.12975136\\\\\n",
 433        "\t 6 & 5.104603e-07 & 2.172848e-08 &   63 & 3.333333e-10 & 0.01800514\\\\\n",
 434        "\t 7 & 5.937901e-07 & 2.779261e-08 &   54 & 3.333333e-10 & 0.01543298\\\\\n",
 435        "\t 8 & 7.054843e-07 & 4.410606e-08 &   53 & 3.333333e-10 & 0.01514718\\\\\n",
 436        "\\end{tabular}\n"
 437       ],
 438       "text/markdown": [
 439        "\n",
 440        "A tibble: 8 × 6\n",
 441        "\n",
 442        "| cluster &lt;int&gt; | mean &lt;dbl&gt; | sd &lt;dbl&gt; | count &lt;int&gt; | coefficient &lt;dbl&gt; | prob &lt;dbl&gt; |\n",
 443        "|---|---|---|---|---|---|\n",
 444        "| 1 | 1.559763e-07 | 4.078012e-09 | 2166 | 3.333333e-10 | 0.61903401 |\n",
 445        "| 2 | 1.916024e-07 | 1.094938e-08 |  368 | 3.333333e-10 | 0.10517291 |\n",
 446        "| 3 | 2.309763e-07 | 1.245767e-08 |  211 | 3.333333e-10 | 0.06030294 |\n",
 447        "| 4 | 2.793051e-07 | 2.045145e-08 |  130 | 3.333333e-10 | 0.03715347 |\n",
 448        "| 5 | 4.375881e-07 | 1.105646e-08 |  454 | 3.333333e-10 | 0.12975136 |\n",
 449        "| 6 | 5.104603e-07 | 2.172848e-08 |   63 | 3.333333e-10 | 0.01800514 |\n",
 450        "| 7 | 5.937901e-07 | 2.779261e-08 |   54 | 3.333333e-10 | 0.01543298 |\n",
 451        "| 8 | 7.054843e-07 | 4.410606e-08 |   53 | 3.333333e-10 | 0.01514718 |\n",
 452        "\n"
 453       ],
 454       "text/plain": [
 455        "  cluster mean         sd           count coefficient  prob      \n",
 456        "1 1       1.559763e-07 4.078012e-09 2166  3.333333e-10 0.61903401\n",
 457        "2 2       1.916024e-07 1.094938e-08  368  3.333333e-10 0.10517291\n",
 458        "3 3       2.309763e-07 1.245767e-08  211  3.333333e-10 0.06030294\n",
 459        "4 4       2.793051e-07 2.045145e-08  130  3.333333e-10 0.03715347\n",
 460        "5 5       4.375881e-07 1.105646e-08  454  3.333333e-10 0.12975136\n",
 461        "6 6       5.104603e-07 2.172848e-08   63  3.333333e-10 0.01800514\n",
 462        "7 7       5.937901e-07 2.779261e-08   54  3.333333e-10 0.01543298\n",
 463        "8 8       7.054843e-07 4.410606e-08   53  3.333333e-10 0.01514718"
 464       ]
 465      },
 466      "metadata": {},
 467      "output_type": "display_data"
 468     }
 469    ],
 470    "source": [
 471     "df_normal$coefficient = coef(rqResult)[coeff_col_name]\n",
 472     "df_normal$prob = df_normal$count/sum(df_normal$count)"
 473    ]
 474   },
 475   {
 476    "cell_type": "markdown",
 477    "metadata": {},
 478    "source": [
 479     "Saving result to a csv file."
 480    ]
 481   },
 482   {
 483    "cell_type": "code",
 484    "execution_count": null,
 485    "metadata": {},
 486    "outputs": [],
 487    "source": [
 488     "df_normal %>% select(mean, sd, prob, coefficient) %>% write.csv(output_file)"
 489    ]
 490   },
 491   {
 492    "cell_type": "markdown",
 493    "metadata": {},
 494    "source": [
 495     "## Visualizing"
 496    ]
 497   },
 498   {
 499    "cell_type": "markdown",
 500    "metadata": {},
 501    "source": [
 502     "Histogram with vertical lines at the mean of each cluster."
 503    ]
 504   },
 505   {
 506    "cell_type": "code",
 507    "execution_count": 47,
 508    "metadata": {},
 509    "outputs": [
 510     {
 511      "data": {
 512       "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAC2VBMVEUAAAABAQECAgIDAwME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\nWRsSklkbEpJZGxKSWRv6f1W5kuzZlztBAAAAAElFTkSuQmCC",
 513       "text/plain": [
 514        "plot without title"
 515       ]
 516      },
 517      "metadata": {
 518       "image/png": {
 519        "height": 420,
 520        "width": 420
 521       }
 522      },
 523      "output_type": "display_data"
 524     }
 525    ],
 526    "source": [
 527     "library(ggplot2)\n",
 528     "\n",
 529     "ggplot(df, aes(x=intercept_estimate)) + geom_histogram(bins=100) +\n",
 530     "    geom_vline(data=df_normal, aes(xintercept=mean)) + \n",
 531     "    theme_bw()"
 532    ]
 533   },
 534   {
 535    "cell_type": "markdown",
 536    "metadata": {},
 537    "source": [
 538     "Same but in log scale"
 539    ]
 540   },
 541   {
 542    "cell_type": "code",
 543    "execution_count": 48,
 544    "metadata": {},
 545    "outputs": [
 546     {
 547      "name": "stderr",
 548      "output_type": "stream",
 549      "text": [
 550       "Warning message:\n",
 551       "“Transformation introduced infinite values in continuous y-axis”\n",
 552       "Warning message:\n",
 553       "“Removed 62 rows containing missing values (geom_bar).”\n"
 554      ]
 555     },
 556     {
 557      "data": {
 558 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QaD0jxgCQCUmg8IMUDkghIofGAFA9IIiCFxgNSPCCJgBQaD0jx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\nJKIKAhJRBQGJqIL+P2Mv2HhIa/nDAAAAAElFTkSuQmCC",
 559       "text/plain": [
 560        "plot without title"
 561       ]
 562      },
 563      "metadata": {
 564       "image/png": {
 565        "height": 420,
 566        "width": 420
 567       }
 568      },
 569      "output_type": "display_data"
 570     }
 571    ],
 572    "source": [
 573     "ggplot(df, aes(x=intercept_estimate)) + geom_histogram(bins=100) +\n",
 574     "    geom_vline(data=df_normal, aes(xintercept=mean)) + \n",
 575     "    scale_x_log10() + scale_y_log10() +\n",
 576     "    theme_bw()"
 577    ]
 578   },
 579   {
 580    "cell_type": "markdown",
 581    "metadata": {},
 582    "source": [
 583     "Plot original data with colors.\n",
 584     "\n",
 585     "Each color represents a group found by ckmeans. The line is the mean value for each group.\n",
 586     "\n",
 587     "Also plot an extra line with the result of the quantile regression."
 588    ]
 589   },
 590   {
 591    "cell_type": "code",
 592    "execution_count": 130,
 593    "metadata": {},
 594    "outputs": [
 595     {
 596      "name": "stderr",
 597      "output_type": "stream",
 598      "text": [
 599       "Joining, by = \"cluster\"\n",
 600       "\n",
 601       "Warning message:\n",
 602       "“Removed 1 row(s) containing missing values (geom_path).”\n"
 603      ]
 604     },
 605     {
 606      "data": {
 607 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eLgqowUQ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\nEREREdmEy+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 608       "text/plain": [
 609        "plot without title"
 610       ]
 611      },
 612      "metadata": {
 613       "image/png": {
 614        "height": 420,
 615        "width": 420
 616       }
 617      },
 618      "output_type": "display_data"
 619     }
 620    ],
 621    "source": [
 622     "# new dataframe where duration(y) is equal to estimated values by group\n",
 623     "tmp = data.frame(cluster=df$cluster, x=df[[coeff_col_name]], y=df[[coeff_col_name]]*coef(rqResult)[coeff_col_name])\n",
 624     "tmp = tmp %>% left_join(df_normal) %>% mutate(y = y + mean) %>% select(cluster, x, y)#sum by estimated intercept\n",
 625     "# add quantile regression to it\n",
 626     "tmp = rbind(tmp, data.frame(cluster=\"quantile\", x=df[[coeff_col_name]], y=df[[coeff_col_name]]*coef(rqResult)[coeff_col_name] + coef(rqResult)['(Intercept)']))\n",
 627     "\n",
 628     "ggplot(df, aes_string(x=coeff_col_name, y=metric, color=as.factor(df$cluster))) + geom_point() +\n",
 629     "    geom_line(data=tmp, aes(x=x, y=y, color=cluster)) +\n",
 630     "    theme_bw()"
 631    ]
 632   },
 633   {
 634    "cell_type": "markdown",
 635    "metadata": {},
 636    "source": [
 637     "Same in log scale in y-axis."
 638    ]
 639   },
 640   {
 641    "cell_type": "code",
 642    "execution_count": 131,
 643    "metadata": {},
 644    "outputs": [
 645     {
 646      "name": "stderr",
 647      "output_type": "stream",
 648      "text": [
 649       "Warning message:\n",
 650       "“Removed 1 row(s) containing missing values (geom_path).”\n"
 651      ]
 652     },
 653     {
 654      "data": {
 655 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szmqNR1e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\nQCX+DzAMKgPipULUAAAAAElFTkSuQmCC",
 656       "text/plain": [
 657        "plot without title"
 658       ]
 659      },
 660      "metadata": {
 661       "image/png": {
 662        "height": 420,
 663        "width": 420
 664       }
 665      },
 666      "output_type": "display_data"
 667     }
 668    ],
 669    "source": [
 670     "ggplot(df, aes_string(x=coeff_col_name, y=metric, color=as.factor(df$cluster))) + geom_point() +\n",
 671     "    geom_line(data=tmp, aes(x=x, y=y, color=as.factor(cluster))) +\n",
 672     "    scale_y_log10() +\n",
 673     "    theme_bw()\n",
 674     "ggsave(paste0('plot_ckmeans_', unique(df$op), '.png'))"
 675    ]
 676   }
 677  ],
 678  "metadata": {
 679   "kernelspec": {
 680    "display_name": "R",
 681    "language": "R",
 682    "name": "ir"
 683   },
 684   "language_info": {
 685    "codemirror_mode": "r",
 686    "file_extension": ".r",
 687    "mimetype": "text/x-r-source",
 688    "name": "R",
 689    "pygments_lexer": "r",
 690    "version": "4.0.4"
 691   }
 692  },
 693  "nbformat": 4,
 694  "nbformat_minor": 4
 695 }