2015-10-28-Velocity-Amsterdam/Episode 2 -- Histograms.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Episode 2 -- Histograms\n",
    "\n",
    "* Basic Idea: Use area to compare sample ratios, instead of point counts\n",
    "* Easier to answer questios like: \"How many voters are older than 30, when presented with a histogram, than a table or a rugplot.\"\n",
    "* Both a visualization method and a data-storage format"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Building your own Histogram\n",
    "\n",
    "1. Define value range of histogram `bin_min`, `bin_max`\n",
    "2. Divide range into bins `bin[k], ..., bin[k]`\n",
    "3. The bins may have variying width \n",
    "4. Count the number of samples in each bin `sample_count[k]`\n",
    "5. Draw a rectangle for each bin with height:\n",
    "   - `h[k] = sample_count[k]` -- non normalized \n",
    "   - `h[k] = sample_count[k] / bin_width[k]` -- normalized case\n",
    "   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "X = np.loadtxt(\"DataSets/RequestRates.csv\", delimiter=\",\")[:,1]\n",
    "\n",
    "# Step 1: Represent bins via list of left-edges\n",
    "bin_left = [\n",
    "    500, 700, 800, 900, 1000, 1500, 1800, 2000, 2200\n",
    "]\n",
    "\n",
    "bin_min = bin_left[0]\n",
    "bin_max = bin_left[-1]\n",
    "bins = [ [bin_left[i-1],bin_left[i]] for i in xrange(1, len(bin_left)) ]\n",
    "\n",
    "print \"Bins: \", bins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Counts: [0, 10, 8, 4, 25, 23, 4, 2]\n"
     ]
    }
   ],
   "source": [
    "# Step2: Count number of samples in bins\n",
    "def count(X, bins):\n",
    "    def findBin(x, bins):\n",
    "        for i, bin in enumerate(bins):\n",
    "            left, right = bin\n",
    "            if left <= x and x < right:\n",
    "                return i\n",
    "        return None\n",
    "    \n",
    "    count = [0] * len(bins)\n",
    "    for x in X:\n",
    "        i = findBin(x, bins)\n",
    "        if i != None:\n",
    "            count[i] += 1\n",
    "\n",
    "    return count\n",
    "\n",
    "sample_count = count(X, bins)\n",
    "\n",
    "print \"Counts:\", sample_count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd1453d0a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "# Step3: Plot bar chart\n",
    "def my_hist(X, bins, normed=True, **kwargs):\n",
    "    bin_left = [ l for l, r in bins ]\n",
    "    bin_width = [ r-l  for l,r in bins ]\n",
    "    bin_height = [ \n",
    "        float(c) / w if normed else c \n",
    "        for c,w in zip(count(X, bins), bin_width)\n",
    "    ]\n",
    "    plt.bar(bin_left,width=bin_width,height=bin_height, **kwargs)\n",
    "\n",
    "plt.figure(figsize=(15,5))\n",
    "my_hist(X,bins)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# The choice of bins influences the look of the histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_hist(X,  bin_min, bin_max, bin_width):\n",
    "    plt.figure(figsize=(15,5))\n",
    "    bins =[ [i, i+bin_width] for i in np.arange(bin_min, bin_max, bin_width) ]\n",
    "    my_hist(X,bins)\n",
    "    print \"Histogram with bin_width \", bin_width\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Histogram with bin_width  5\n"
     ]
    },
    {
     "data": {
      "image/png": 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ltdZmzTNvu9FlDtuP1qlttJ00bXT+keeOmX+zdU57fmObR9ttZ9smLWfe/b7T+bdTgyUe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\n/X/GrTTz1IN2xAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd12e504490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bin_min = 600\n",
    "bin_max = 2200\n",
    "plot_hist(X, bin_min, bin_max, 5)\n",
    "\n",
    "#--> Looks almost like the rugplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Histogram with bin_width  50\n"
     ]
    },
    {
     "data": {
      "image/png": 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AgAEJewAAAAMS9gAAAAYk7AEAAAxI2AMAABiQsAcAADAgYQ8AAGBAZy1rUFX7k9yUZFeS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\n/wNmykWZTef9WwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd12e84c190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hist(X, bin_min, bin_max, 50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Histogram with bin_width  500\n"
     ]
    },
    {
     "data": {
      "image/png": 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AYEDCHgAAwICEPQAAgAEJewAAAAMS9gAAAAYk7AEAAAxI2AMAABiQsAcAADAgYQ8AAGBA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\nAAAY0P8H3CTy+9y12uMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd12e688410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hist(X, bin_min, bin_max, 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Histogram with bin_width  2000\n"
     ]
    },
    {
     "data": {
      "image/png": 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AAOAcIgQCAACMiBAIAAAwIkIgAADAiAiBAAAAIyIEAgAAjIgQCAAAMCJCIAAAwIgIgQAA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd12e38bc90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_hist(X, bin_min, bin_max, 2000)\n",
    "# -> Only the total count is displayed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Common bin-width choices\n",
    "\n",
    "Remarks:\n",
    "* Can convert `bin_count` and `bin_width` using relation $$ bin\\_max - bin\\_min = bin\\_count \\cdot bin\\_width.$$\n",
    "\n",
    "* Choices `bin_min=min(X)` and `bin_max=max(X)` are common. But: dependence on input data.\n",
    "\n",
    "Choices for bin-width:\n",
    "\n",
    "* Excel: Let $n$ be the number of samples, then:\n",
    "\n",
    "  $$ bin\\_count = \\sqrt{n} $$\n",
    "\n",
    "* Scott's normal reference rule\n",
    "\n",
    "  $$ bin\\_width = \\frac{3.5 \\sigma}{n^{1/3}} $$\n",
    "\n",
    "  where $\\sigma$ is the standard deviation (cf. later).\n",
    "  This is optimal for random samples of normally distributed data, in a certain sense.\n",
    "\n",
    "* Freedman–Diaconis rule\n",
    "\n",
    "  $$ bin\\_width = \\frac{2 IQR}{n^{1/3}} $$\n",
    "  \n",
    "  where IQR is the inter-quartile range (cf. later). Like Scott's rule but more robust agains outliers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A pragmatic choice: HDR Histograms\n",
    "\n",
    "Example: A decimal HDR Histogram with precision=2 has bin boundaries:\n",
    "  \n",
    "    .... 1.0,  1.1,  1.2, ... 1.9,  2.0,  2.1, ...., 9.9; --- bin width = 0.1\n",
    "         10.0, 11.0, 12.0 ... 19.0, 20.0, 21.0 ...., 99 ; --- bin width = 1\n",
    "         ...\n",
    "\n",
    "** Properties: **\n",
    "* Captures large part of float range\n",
    "* Bin boundaries do not depend on data! -> Can aggregate counts!\n",
    "* Bin width increase with growing values\n",
    "* Allows compact memory representation\n",
    "* Implementation available at http://hdrhistogram.org/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# To be precise:\n",
    "\n",
    "import math\n",
    "def HDR_bin_width(x):\n",
    "    if x == 0: return 0\n",
    "    sign = x / abs(x)\n",
    "    return sign * 10 ** ( math.floor(math.log10(abs(x)) - 1 ) )\n",
    "\n",
    "def HDR_bin_left(x):\n",
    "    w = bin_width(x)\n",
    "    if w == 0: return 0\n",
    "    return math.floor(x / w) * w\n",
    "\n",
    "def HRD_bin_right(x):\n",
    "    return bin_left(x) + bin_width(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 0.001, 0.01, 0.1, 0.1, 0.1, 0.1, 1.0]"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[ HDR_bin_width(x) for x in 0,0.01,0.1,1,2,9,9.9,10 ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def HDR_hist(X):\n",
    "    count = {}\n",
    "    for x in X:\n",
    "        l = HDR_bin_left(x)\n",
    "        count[l] = count.get(l,0) + 1\n",
    "    bin_left = sorted(count.keys())\n",
    "    bin_width = [ HDR_bin_width(l) for l in bin_left ]\n",
    "    bin_height = [ count[l] / HDR_bin_width(l)\n",
    "        for l in bin_left\n",
    "    ]\n",
    "    plt.figure(figsize=(15,5))\n",
    "    plt.bar(bin_left,width=bin_width,height=bin_height)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fd12968dcd0>"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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DAAAAHSQMAgAAdJAwCAAA0EHCIAAAQAcJgwAAAB3k10QBWBW9Xm9Tkrlpj2MFzU17ACvt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd128a95a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "HDR_hist(X)\n",
    "sns.rugplot(X,height=-0.05, color=\"grey\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example: Heatmaps of HDR Histograms\n",
    "\n",
    "* Can use color coding for bin count\n",
    "* Allows to show many histograms at once\n",
    "* Harder to read off values\n",
    "* Uses HDR Histogram\n",
    "\n",
    "<figure>\n",
    "<center><img src=\"img/Circonus_Histogram.png\"/></center>\n",
    "<figcaption>A histogram metric.</figcaption>\n",
    "</figure>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Traditionally only a single request per sampling period is recorded.\n",
    "<figure>\n",
    "<center><img src=\"img/example_histogram_mean.png\"/></center>\n",
    "<figcaption>Histogram with mean value.</figcaption>\n",
    "</figure>\n",
    "\n",
    "Multimodal and logarithmic structures are not visible."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- share: https://share.circonus.com/shared/graphs/a759d10b-7001-4608-9d6a-283870cb0e84/2FcJcz\n",
    "- graph: https://lethargy.circonus.com/trending/graphs/view/a759d10b-7001-4608-9d6a-283870cb0e84"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Digression: Kernel Density Estimators\n",
    "\n",
    "1. Replace 'rugs\" with little functions (e.g. triangles, rectangles, normal-distributions)\n",
    "2. Sum all functions\n",
    "\n",
    "<center>\n",
    "<img src=\"http://upload.wikimedia.org/wikipedia/en/4/41/Comparison_of_1D_histogram_and_KDE.png\" width='400px'>\n",
    "\n",
    "Source: Wikipdeia, CC BY-SA 3.0, by Drleft <br>\n",
    "http://en.wikipedia.org/wiki/Kernel_density_estimation\n",
    "</center>\n",
    "\n",
    "Remarks:\n",
    "\n",
    "* Smooth version of Histogram\n",
    "* Better approximation for pdf (cf. later)\n",
    "* More expensive to compute\n",
    "* Harder to define\n",
    "* Choices of function and width invloved. Similar to Histogram.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fd1206d6110>"
      ]
     },
     "execution_count": 214,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YtsbyzJr9AXvvsC4nHvSFr/RZpuUroeOqgZq9hvI05v9ufZab7pnO/xw74qNa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\niIhU9f+KbB7kAMkH4gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd115541450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.neighbors import KernelDensity\n",
    "\n",
    "X = np.loadtxt(\"DataSets/RequestRates.csv\", delimiter=\",\")[:,1]\n",
    "\n",
    "KDE=KernelDensity(kernel='epanechnikov', bandwidth=80)\n",
    "KDE.fit(X[:,np.newaxis])\n",
    "grid=np.linspace(min(X)-200, max(X)+200,100)\n",
    "kde =np.exp(KDE.score_samples(grid[:,np.newaxis]))\n",
    "\n",
    "plt.figure(figsize=(15,5))\n",
    "plt.plot(grid, kde)\n",
    "sns.rugplot(X, color='grey', height=-.0001)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}