8_chemometrics-GCMS.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Chemometrics\n",
    "<br>\n",
    "**Julien Wist / 2017 / Universidad del Valle**\n",
    "<br>\n",
    "**Andrés Bernal / 2017 / ???**\n",
    "\n",
    "An up-to-date version of this notebook can be found here: https://github.com/jwist/chemometrics/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "options(repr.plot.width=4, repr.plot.height=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# we load a few packages\n",
    "library(ggplot2)\n",
    "library(corrplot)\n",
    "library(reshape2)\n",
    "library(caret)\n",
    "library(MASS) # for LDA\n",
    "library(klaR) # for pls\n",
    "library(pls)\n",
    "library(e1071)# for pls\n",
    "library(pROC) # for pls\n",
    "library(vegan)\n",
    "require(scales)\n",
    "require(gridExtra);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## let's look at GC-MS data\n",
    "\n",
    "we load data of 7 compounds:\n",
    "- caffein\n",
    "- vitamin E\n",
    "- sitosterol\n",
    "- hexadecanoic acid\n",
    "- furanmethanol\n",
    "- tocopherol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "rm(list=ls(all=TRUE))\n",
    "\n",
    "load(url('https://github.com/jwist/chemometrics/raw/master/datasets/coffeeMulti.rda'))\n",
    "d <- coffeeMulti$gc                       # select GCMS data\n",
    "#d <- data.frame(\"x\"=coffeeMulti$gc[5:11],\"country\"=coffeeMulti$gc$country) \n",
    "\n",
    "#par(mfrow=c(3,3))\n",
    "# first we have a look to the data... this is rule number one!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
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     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "d <- data.frame(\"x\"=coffeeMulti$gc$caffeine,\"country\"=coffeeMulti$gc$country) #31.87\n",
    "boxplot(tapply(d$x,d$country,function(x) x))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.width=8, repr.plot.height=8)\n",
    "par(mfrow=c(3,3))\n",
    "d <- data.frame(\"x\"=coffeeMulti$gc$vitE,\"country\"=coffeeMulti$gc$country) #6.14 alias a-tocopherol\n",
    "boxplot(tapply(d$x,d$country,function(x) x))\n",
    "d <- data.frame(\"x\"=coffeeMulti$gc$stigmasterol,\"country\"=coffeeMulti$gc$country) #1.21\n",
    "boxplot(tapply(d$x,d$country,function(x) x))\n",
    "d <- data.frame(\"x\"=coffeeMulti$gc$sitosterol,\"country\"=coffeeMulti$gc$country) #0.93\n",
    "boxplot(tapply(d$x,d$country,function(x) x))\n",
    "d <- data.frame(\"x\"=coffeeMulti$gc$hexadecanoicAcid,\"country\"=coffeeMulti$gc$country) #0.584\n",
    "boxplot(tapply(d$x,d$country,function(x) x))\n",
    "d <- data.frame(\"x\"=coffeeMulti$gc$furanmethanol,\"country\"=coffeeMulti$gc$country) #4.76\n",
    "boxplot(tapply(d$x,d$country,function(x) x))\n",
    "d <- data.frame(\"x\"=coffeeMulti$gc$tocoferol,\"country\"=coffeeMulti$gc$country) #1.14\n",
    "boxplot(tapply(d$x,d$country,function(x) x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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       "  <use xlink:href=\"#glyph0-27\" x=\"112.870605\" y=\"81.339844\"/>\n",
       "  <use xlink:href=\"#glyph0-16\" x=\"119.82251\" y=\"81.339844\"/>\n",
       "  <use xlink:href=\"#glyph0-12\" x=\"122.599609\" y=\"81.339844\"/>\n",
       "</g>\n",
       "<g style=\"fill:rgb(0%,0%,0%);fill-opacity:1;\">\n",
       "  <use xlink:href=\"#glyph0-28\" x=\"76.75\" y=\"87.367188\"/>\n",
       "  <use xlink:href=\"#glyph0-29\" x=\"85.087402\" y=\"87.367188\"/>\n",
       "  <use xlink:href=\"#glyph0-21\" x=\"92.039307\" y=\"87.367188\"/>\n",
       "  <use xlink:href=\"#glyph0-30\" x=\"96.201904\" y=\"87.367188\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "Plot with title \"density.default(x = x[1][[1]])\""
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.width=4, repr.plot.height=4)\n",
    "# here we plot the distribution for each class\n",
    "d <- data.frame(\"x\"=coffeeMulti$gc$caffeine,\"country\"=coffeeMulti$gc$country) #31.87\n",
    "x <- tapply(d$x,d$country,function(x) x)\n",
    "xlims <- range(unlist(tapply(d$x,d$country,function(x) unlist(range(density(x)$x)))))\n",
    "ylims <- range(unlist(tapply(d$x,d$country,function(x) unlist(range(density(x)$y)))))\n",
    "plot(density(x[1][[1]]),type='l', xlim=xlims, ylim=ylims, col=2)\n",
    "lines(density(x[2][[1]]), col=3)\n",
    "lines(density(x[3][[1]]), col=4)\n",
    "legend(min(xlims),max(ylims),levels(d$country), col=2:4, pch=\"*\")\n"
   ]
  },
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   "source": []
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   "execution_count": null,
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   "source": []
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