{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "#Automating Binwidth for np.histogram\n", "\n", "When using any kind python visualisation library that uses numpy for it's histogram, the main problem I face is the fact that the number of bins are not dynamically chosen, and in fact default to 10 bins. So whether I have a 50 samples or 5 million samples, by default I have 10 bins. I have to experiment until I get something I like, I don't even get a half decent choice, like in R, nor are different methods avaiable for automatically choosing the binwidths.\n", "\n", "For example" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "from matplotlib import pyplot as plt\n", "%matplotlib inline\n", "plt.style.use('ggplot') #this should be in the matplotlib.__init__.py" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def gen3peaks(numPoints):\n", " numPoints/=3\n", " x1 = np.random.randn(numPoints) * 15 + 100\n", " x2 = np.random.randn(numPoints) * 10 + 60\n", " x3 = np.random.randn(numPoints) * 5+ 140\n", " return np.hstack((x1,x2, x3))\n", "\n", "# using 3 peaks for more features and also avoids \n", "# trap of getting good results with normal data\n", "\n", "xbig = gen3peaks(9000)\n", "xmed = gen3peaks(900)\n", "xsmall = gen3peaks(90)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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kKTc3V11dXero6JAkzZgxI+IV6b7bLFiwQCdPnjTlZAAAAIBYilpc+3w+ZWZm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\nVFTo3LlzysrK0rp165SWlmb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#reverse datasize order to get an idea of what the plot actually should look like\n", "def quickHist(data): \n", " plt.figure(figsize=(12,5))\n", " plt.subplot(121)\n", " plt.hist(data, normed=True, alpha = 0.5)\n", " plt.title(\"10 bins\")\n", " plt.subplot(122)\n", " plt.hist(data, normed=True, alpha = 0.5, bins = 50) # manual increase\n", " plt.title(\"50 bins\")\n", "\n", "# Large data set\n", "quickHist(xbig)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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FNQAAAGCS5Is1aG5u1s6dO+X3+1VSUqKysrJRbXbs2KHm5malpKSooqJCeXl5kqTnn39e\nTU1NSktL04YNGwLta2trtX//fqWlpUmSli1bpjlz5ph1TAAAAEBMRCyu/X6/tm/frnXr1snj8ejx\nxx9XUVGRcnJyAm0aGxvV2dmpTZs26fjx49q2bZuqqqokSYsWLdJtt92mv/3bvw3ar81m05IlS7Rk\nyZIoHBIAAAAQGxGHhbS1tSk7O1tZWVlKTk5WcXGxGhoagto0NDRowYIFkqT8/HwNDg6qr69PkjRr\n1iylpqaG3LdhGGbkBwAAAOJGxDvXPT09ysjICCx7PB61tbVFbJORkaGenh653e6Ib7xnzx4dPnxY\nX//613X33XeHLcIBAAAQn2wD/dKp3tEvDA2NWuUfPiPbx+2j26ZNk+FKNz9cjFx0zPVYjPcu9OLF\ni7V06VJJ0u7du7Vr1y6Vl5ebEQUAAACT5VSvRt6qH7XaPvO60W1Pn9LI+2+PbnvjLdLlUlx7PB51\nd3cHlru7u+XxeMbd5kLp6V+dwJKSEq1fvz5ku5aWFrW0tASWvV6vXC5XxH3HC4fDYZmskrXykjV6\nopH3rMMpnyPF1H1Kkt1ulyPMfpMdTk2Jw/NeW1sb+L6goEAFBQUxTAMAiIaIxfXMmTPV0dGhrq4u\neTwe1dfX68EHHwxqU1RUpL1796q4uFitra1KTU296JCQ3t5eTZs2TZL05ptvKjc3N2S7UL98BgYG\nLnpQ8cDlclkmq2StvGSNnmjktQ0PaWT4jKn7lCSHI0XDYfY7MjykoTg77y6XS16vN9YxAABRFrG4\nttvtWrFihaqqqgJT8eXk5Gjfvn2SpNLSUs2dO1dNTU2qrKyU0+kMGt7x7LPP6tixYxoYGFB5ebm8\nXq8WLVqkl19+We3t7bLZbMrMzNSqVauie5QAAADAJLjomOvCwkIVFhYGrSstLQ1aXrlyZchtH3ro\noZDrV69ePdZ8AAAAgGXwCY0AAACASSiuAQAAAJNQXAMAAAAmobgGAAAATEJxDQAAAJiE4hoAAAAw\nCcU1AAAAYBKKawAAAMAkFNcAAACASSiuAQAAAJNQXAMAAAAmobgGAAAATEJxDQAAAJiE4hoAAAAw\nSXKsAwAAzNPc3KydO3fK7/erpKREZWVlo9rs2LFDzc3NSklJUUVFhfLy8nTy5Elt3rxZ/f39stls\nuvXWW3X77bdLkk6fPq2amhqdPHlSmZmZevjhh5WamjrZhwYAlsCdawBIEH6/X9u3b9fatWtVXV2t\nI0eO6MSJE0FtGhsb1dnZqU2bNmnVqlXatm2bJCk5OVn33HOPqqurVVVVpb179+rjjz+WJNXV1Wn2\n7NnauHGjrr/+etXV1U36sQGAVVBcA0CCaGtrU3Z2trKyspScnKzi4mI1NDQEtWloaNCCBQskSfn5\n+RocHFRfX5/cbrdmzJghSXI6nZo+fbp6enpGbbNw4UIdPXp08g4KACyG4hoAEkRPT48yMjICyx6P\nJ1Agh2uTkZExqk1XV5fa29uVn58vServ75fb7ZYkpaenq7+/P1qHAACWR3ENAJcZwzDCvjY0NKTq\n6motX75cTqdz1Os2my2a0QDA8nigEQAShMfjUXd3d2C5u7tbHo9nzG18Pp82bNig+fPn66abbgq0\nSU9PDwwd6e3tVXp6esj3b2lpUUtLS2DZ6/XK5XKZcmzR5nA4LJNVslZeK2WVrJU3HrKedTjlc6SM\nWp+UPEX2C9bbkmxyhGib7HBqShye89ra2sD3BQUFKigoGNN2FNcAkCBmzpypjo4OdXV1yePxqL6+\nXg8++GBQm6KiIu3du1fFxcVqbW1Vamqq3G63DMPQ1q1bNX36dN1xxx2jtjl48KDKysp06NAhzZs3\nL+T7h/rlMzAwYO5BRonL5bJMVslaea2UVbJW3njIahse0sjwmVHr7b6zo9Y7/YaGQ7QdGR7SUJyd\nc5fLJa/Xe0nbUlwDQIKw2+1asWKFqqqqAlPx5eTkaN++fZKk0tJSzZ07V01NTaqsrJTT6VR5ebkk\n6f3339cbb7yh3NxcPfroo5KkZcuWac6cOSorK1NNTY0OHDgQmIoPABAaxTUAJJDCwkIVFhYGrSst\nLQ1aXrly5ajtrrvuOu3evTvkPqdOnap169aZFxIAEhgPNAIAAAAmobgGAAAATEJxDQAAAJiE4hoA\nAAAwCcU1AAAAYBKKawAAAMAkFNcAAACASSiuAQAAAJNQXAMAAAAm4RMaLc420C+d6p3wfs46nLIN\nD128Ydo0Ga70Cb8fAABAIqK4trpTvRp5q37Cu/E5UjQyfOai7ew33iJRXAMAAITEsBAAAADAJBTX\nAAAAgEkorgEAAACTUFwDAAAAJqG4BgAAAExCcQ0AAACYhOIaAAAAMAnzXAMAACBmbD6f9HH76Bcs\n+sF1FNcAAACIGeP0KY38z3uj1lv1g+sYFgIAAACYhOIaAAAAMAnFNQAAAGASimsAAADAJBTXAAAA\ngEkorgEAAACTUFwDAAAAJqG4BgAAAExCcQ0AAACYhOIaAAAAMAnFNQAAAGASimsAAADAJBTXAAAA\ngEkorgEAAACTUFwDAAAAJqG4BgAAAExCcQ0AAACYhOIaAAAAMEnyxRo0Nzdr586d8vv9KikpUVlZ\n2ag2O3bsUHNzs1JSUlRRUaG8vDxJ0vPPP6+mpialpaVpw4YNgfanT59WTU2NTp48qczMTD388MNK\nTU018bAA4PIVjX67trZW+/fvV1pamiRp2bJlmjNnzuQcEILYBvp19rMO2YaHgl9ImybDlR6bUAAC\nIt659vv92r59u9auXavq6modOXJEJ06cCGrT2Niozs5Obdq0SatWrdK2bdsCry1atEhr164dtd+6\nujrNnj1bGzdu1PXXX6+6ujqTDgcALm/R6rdtNpuWLFmip556Sk899RSFdSyd6pXvrSMaeas+6Eun\nemOdDIAuUly3tbUpOztbWVlZSk5OVnFxsRoaGoLaNDQ0aMGCBZKk/Px8DQ4Oqq+vT5I0a9askHek\nz99m4cKFOnr0qCkHAwCXu2j125JkGEZ0wwNAAohYXPf09CgjIyOw7PF41NPTE7FNRkbGqDYX6u/v\nl9vtliSlp6erv79/3MEBAKNFq9+WpD179mjNmjXasmWLBgcHzQsNAAnkomOux2IidzNsNlvY11pa\nWtTS0hJY9nq9crlcl/xek8nhcExK1rMOp3yOlAnvx263yzGG/SQ7nJoS45/BZJ1bM1gpqxSdvGZd\noxeKdM3Gw3UaSm1tbeD7goICFRQUxCzLePvtxYsXa+nSpZKk3bt3a9euXSovLw9qQ589Oc46nDJC\nXP/xet1b6dxK1sobD1nD9fFJyVNkv2C9LckWst8O1VaK/TV9qX12xOLa4/Gou7s7sNzd3S2PxzPu\nNhdKT09XX1+f3G63ent7lZ4e+gGMUAcyMDAQcd/xwuVyTUpW2/CQRobPTHg/DkeKhsewn5HhIQ3F\n+GcwWefWDFbKKkUnr1nX6IUiXbPxcJ1eyOVyyev1Rv19otlvf6mkpETr168f1YY+e3LYhodkHxkZ\ndf3H43UvWevcStbKGw9Zw/Xxdt/ZUeudfiNkvx2qrRTba3oifXbEYSEzZ85UR0eHurq65PP5VF9f\nr6KioqA2RUVFOnz4sCSptbVVqampgSEf4RQVFengwYOSpEOHDmnevHmXFB4AECxa/XZv71cPy735\n5pvKzc01PzwAJICId67tdrtWrFihqqqqwJROOTk52rdvnySptLRUc+fOVVNTkyorK+V0OoP+TPjs\ns8/q2LFjGhgYUHl5ubxerxYtWqSysjLV1NTowIEDgan4AAATF61+++WXX1Z7e7tsNpsyMzO1atWq\nWB0iAMQ1m2Gxx78/+eSTWEcYk0kbFvJx+7kpmCZorMNC7DfeImP6jAm/30TEw5/BxspKWaUoDQsx\n6Rq9UKRrNh6u0wtdffXVsY4QE/TZ5rN93C7722+Nuv7j8bqXrHVuJWvljYes4fp4+8zrNPI/7wWt\nc37z2xp6/+0xtZVie01PpM/mExoBAAAAk1BcAwAAACahuAYAAABMYso81wAAILZsPp/0cfvoF9Km\nyXCFnvIWGCvbQL90qnf0C0NDkx8mzlFcAwCQAIzTp8I+FCaKa0zUqd6wDy4iGMNCAAAAAJNQXAMA\nAAAmobgGAAAATEJxDQAAAJiEBxoxLmGfRo8mnnQHAAAWQXGNcQn3NHo08aQ7AACwCoprAADiVMi5\nhZlXGIhrFNfABcJOlH8Jzjqcsg1f5Bchw14AhBNibmHmFQbiG8U1cKEwE+VfCp8jRSPDZyK2YdgL\nAACJg9lCAAAAAJNw5xoAAFzWzh8OGDScj2F7uAQU1wAA4PJ23nDA84fzMWwPl4JhIQAAAIBJKK4B\nAAAAk1BcAwAAACahuAYAAABMQnENAAAAmITiGgAAADAJxTUAAABgEoprAAAAwCQU1wAAAIBJKK4B\nAAAAk/Dx5wAAJDCbzyd93B68Mm2aDD7WG4gKimsAABKYcfqURv7nvaB19htvkSiugahgWAgAAABg\nEoprAAAAwCQU1wAAAIBJKK4BAAAAk1BcAwAAACahuAYAAABMQnENAAAAmITiGgAAADAJHyIDAAmk\nublZO3fulN/vV0lJicrKyka12bFjh5qbm5WSkqKKigrl5eVJkp5//nk1NTUpLS1NGzZsCLQ/ffq0\nampqdPLkSWVmZurhhx9WamrqpB0TAFgJd64BIEH4/X5t375da9euVXV1tY4cOaITJ04EtWlsbFRn\nZ6c2bdqkVatWadu2bYHXFi1apLVr147ab11dnWbPnq2NGzfq+uuvV11dXdSPBQCsiuIaABJEW1ub\nsrOzlZWVpeTkZBUXF6uhoSGoTUNDgxYsWCBJys/P1+DgoPr6+iRJs2bNCnlH+vxtFi5cqKNHj0b5\nSC4/toF+2T5uH/WloaFYRwMwTgwLAYAE0dPTo4yMjMCyx+NRW1tbxDYZGRnq6emR2+0Ou9/+/v7A\n6+np6erv7zc5OXSqVyNv1Y9abZ95XQzCAJgI7lwDwGXGMIxL3tZms5mYBAASD3euASBBeDwedXd3\nB5a7u7vl8XjG3eZC6enp6uvrk9vtVm9vr9LT00O2a2lpUUtLS2DZ6/XK5XJdyqFMOofDEdOsZx1O\n+Rwpo9YnJU+R/YL1SclTZLPb5Qix/sK24dYnO5yaMknHG+tzOxbnn3/7eed2Ms/TpZjMczueazTc\neluSbdR1G2kfsT7/tbW1ge8LCgpUUFAwpu0orgEgQcycOVMdHR3q6uqSx+NRfX29HnzwwaA2RUVF\n2rt3r4qLi9Xa2qrU1NSIQ0K+3ObgwYMqKyvToUOHNG/evJDtQv3yGRgYmNhBTRKXyxXTrLbhIY0M\nnxm13u47O2q93XdW9pERDYdYP9Z9jAwPaWgcx2sb6JdO9QavTJsmwxX6P1rni/W5HYvzz7/DkRI4\nt+M9T5NtMs/teK7RcOudfmPUdRtpH7E8/y6XS16v95K2pbgGkHBsPp/0cfvkveEYi4xos9vtWrFi\nhaqqqgJT8eXk5Gjfvn2SpNLSUs2dO1dNTU2qrKyU0+lUeXl5YPtnn31Wx44d08DAgMrLy+X1erVo\n0SKVlZWppqZGBw4cCEzFh8tMiDHh9htvkeLgugfiDcU1EGOXayEYTcbpUxr5n/cm7f3iqcgoLCxU\nYWFh0LrS0tKg5ZUrV4bc9qGHHgq5furUqVq3bp05AQEgwVFcAzF2OReCAAAkGoprAAAQdRMZtw1Y\nCcU1AACIPsZt4zJBcY24d+GY5LMOp2zDUfzUMj4RDQAAXCKKa8S9C8ck+xwpIafsMQufiAYAAC4V\nxTUAAJMo5Nhj/mIGJAyKawAAJlOoscf8xQxIGEmxDgAAAAAkCoprAAAAwCQMCwEAAJLCjAeXGBMO\njAPFNQAAOCfEeHCJMeHAeDAsBAAAADAJxTUAAABgEoaFAACAy8J4x5Rf+AnBkmRzpMgI9UFmadNk\nJMhHuTMX+8RctLhubm7Wzp075ff7VVJSorKyslFtduzYoebmZqWkpKiiokJ5eXkRt62trdX+/fuV\nlpYmSVq2bJnmzJlj5nEBAAAEG+eY8gs/IfjLtheukyT7jbdICVJcMxf7xEQsrv1+v7Zv365169bJ\n4/Ho8cezBaEPAAATlElEQVQfV1FRkXJycgJtGhsb1dnZqU2bNun48ePatm2bqqqqIm5rs9m0ZMkS\nLVmyJOoHCAAAAEyWiGOu29ralJ2draysLCUnJ6u4uFgNDQ1BbRoaGrRgwQJJUn5+vgYHB9XX13fR\nbQ3DiMLhAAAAALET8c51T0+PMjIyAssej0dtbW0R22RkZKinp+ei2+7Zs0eHDx/W17/+dd19991K\nTU2d8MEAAICLCzWWWJIlx9WGHUedQGOgYS2mPNA43rvQixcv1tKlSyVJu3fv1q5du1ReXm5GFAAA\ncBGhxhJLFh1XG24cdSKNgYalRCyuPR6Puru7A8vd3d3yeDxjauPz+cJum57+1cVeUlKi9evXh3z/\nlpYWtbS0BJa9Xq9cLtdYjivmHA7HpGQ963DK50iZ8H7sdrscY9hPUvIU2U14v/G48D3HmtWs95uI\nsWSd7HOa7HBqSphrMxrXrVnX6IUindt4Oqfnq62tDXxfUFCggoKCaMYCAMRAxOJ65syZ6ujoUFdX\nlzwej+rr6/Xggw8GtSkqKtLevXtVXFys1tZWpaamyu12y+Vyhd22t7dX06ZNkyS9+eabys3NDfn+\noX75DAwMXPLBTiaXyzUpWW3DQxoJNSXQODkcKRoew37svrOmvN94XPieY81q1vtNxFiyTvY5HRke\n0lCYazMa161Z1+iFIp3beDqnX3K5XPJ6vZOUCAAQKxGLa7vdrhUrVgRm/ygpKVFOTo727dsnSSot\nLdXcuXPV1NSkyspKOZ3OwPCOcNtK0ssvv6z29nbZbDZlZmZq1apVUT5MAACiI9yY37DzIVtwXHMo\nYcdtx8lY55D54uTcM058bEL+DC1wji465rqwsFCFhYVB60pLS4OWV65cOeZtJWn16tXjyQgAQPyK\nMHdywoxrDiHsuO04Gescbo7quMA48TEJ+TO0wDni488BAAAAk1BcAwAAACahuAYAAABMQnENAAAA\nmITiGgAAADAJxTUAAABgElM+/hxf+XLuyrMOp2zDkzCfZpzM2QkAgFlCzgNtgfmNJyre5w6PB1Y4\nRxTXZvv/uSt9jpRJ+YS4uJmzEwAAs4SYB9oK8xtPVLzPHR4PrHCOGBYCAAAAmITiGgAAADAJxTUA\nAABgEoprAAAAwCQU1wAAAIBJKK4BAAAAkzAVHwAAMM2F8xAHPvdhgp/LEHZ+4zj5vAcrzL+MyUFx\nDQAJprm5WTt37pTf71dJSYnKyspGtdmxY4eam5uVkpKiiooK5eXlRdy2trZW+/fvV1pamiRp2bJl\nmjNnzuQdFCzjwnmIv/zch4l+LkPY+Y3j5PMerDD/MiYHxTUAJBC/36/t27dr3bp18ng8evzxx1VU\nVKScnJxAm8bGRnV2dmrTpk06fvy4tm3bpqqqqojb2mw2LVmyREuWLInh0QFA/GPMNQAkkLa2NmVn\nZysrK0vJyckqLi5WQ0NDUJuGhgYtWLBAkpSfn6/BwUH19fVddFvDMCb1WADAiiiuASCB9PT0KCMj\nI7Ds8XjU09MTsU1GRoZ6enouuu2ePXu0Zs0abdmyRYODg1E8CgCwLoaFAJeZsA/d6LwHj8wUJw8b\nIdh470IvXrxYS5culSTt3r1bu3btUnl5eVCblpYWtbS0BJa9Xq9cLtfEw04Ch8NxyVnPOpzyOVJG\nrU9KniL7GNePt63NbpdjgvsYa9uJ7sP+/1lDtU92ODUlxHkPdU4nK7P9vHNrxrkLdYzjvWbCnaeJ\nXLeRROv825Jso67b8e5jvOdoImprawPfFxQUqKCgYEzbUVwDl5lwD91IXz14ZKZ4edjocuHxeNTd\n3R1Y7u7ulsfjGVMbn88Xdtv09K8eyCopKdH69etHvXeoXz4DAwMTO6BJ4nK5LjmrbXgo5L8bu+/s\nmNePt619ZETDE9zHZGV2OFI0PHwmZPuR4SENhTjvoc7pZGX+Mu9E9nG+UMc43msm3HmayHUbSbTO\nv9NvjLpux7uP8Z6jS+VyueT1ei9pW4aFAEACmTlzpjo6OtTV1SWfz6f6+noVFRUFtSkqKtLhw4cl\nSa2trUpNTZXb7Y64bW9vb2D7N998U7m5uZN3UABgIdy5BoAEYrfbtWLFisDsHyUlJcrJydG+ffsk\nSaWlpZo7d66amppUWVkpp9MZGN4RbltJevnll9Xe3i6bzabMzEytWrUqZscIWEnIoXgMl0toFNcA\nkGAKCwtVWFgYtK60tDRoeeXKlWPeVpJWr15tXkDgMhJqKB7D5RIbw0IAAAAAk1BcAwAAACZhWAgA\nAIDF2Ab6dfazjtHTp6ZNk8HHrccUxTUAAIDVnOqV7+23Rk9Vd+MtEsV1TDEsBAAAADAJxTUAAABg\nEoaFAACAmAg5B7TEPNATEPKcMg57UlFcAwCAmAg1B7TEPNATEXJebcZhTyqGhQAAAAAmobgGAAAA\nTMKwEAAAgDgWchw149LjFsU1AABAHAs5jppx6XGLYSEAAACASSiuAQAAAJMwLAQAgAvYBvqlU72j\nX2C+YCSQsNc547knhOIaAIALnerVyFv1o1YzXzASSrjrnPHcE8KwEAAAAMAkFNcAAACASRgWAgDA\nGDHfMICLobgGAGCMmG8YwMUwLAQAAAAwCcU1AAAAYBKGhQAAACSwkM8KSDwvECUU1wAAAAks1LMC\nEs8LRAvDQgAAAACTUFwDAAAAJmFYCADgsmAb6JdO9QavTJsmg48zB2AiimsAwOXhVK9G3qoPWmW/\n8RaJ4hqAiRgWAgAAAJiE4hoAAAAwCcNCAACXrS/n/z3rcMo2fN6cv8z/C+ASUVwDAC5bX87/63Ok\naGT4TGA98/8CuFQMCwEAAABMkth3rkdGZPu4XfIbk/N+STZJtsl5LwAAAMSdBC+ufRp5t1k67099\nUeVIkX3WDZPzXgAAAAgr5Nz2UtTnt0/s4hoAAACXpxBz20vRn9+eMdcAAACASS5657q5uVk7d+6U\n3+9XSUmJysrKRrXZsWOHmpublZKSooqKCuXl5UXc9vTp06qpqdHJkyeVmZmphx9+WKmpqSYfGgBc\nfqzeZ9u++EIyRoJX2u0yUq6IyvsBgNkiFtd+v1/bt2/XunXr5PF49Pjjj6uoqEg5OTmBNo2Njers\n7NSmTZt0/Phxbdu2TVVVVRG3raur0+zZs3XnnXeqrq5OdXV1+rM/+7OoHywAJLJE6LONlrfk7/w4\naF3SjHypYO6otuHGU9ocKTJCPWvD3NVAwvpyzvogMfo3H3FYSFtbm7Kzs5WVlaXk5GQVFxeroaEh\nqE1DQ4MWLFggScrPz9fg4KD6+voibnv+NgsXLtTRo0ejcWwAcFlJiD7b75dGRoK//P7Qbf9/POWF\nX0bXpyHXa+jz6OUGEFPG6VNx828+YnHd09OjjIyMwLLH41FPT0/ENhkZGerp6Ym4bX9/v9xutyQp\nPT1d/f39Ez8SALjM0WcDQOyZMluIYVz6PNI2WxTnhbYlKSlnxrk7H5PBbpeieTwAYIK47bMl2X4v\nS0kpzqB1SdMyFObeNQDEnYjFtcfjUXd3d2C5u7tbHo9nTG18Pl/YbdPT09XX1ye3263e3l6lp4ee\nDqWlpUUtLS2BZa/Xq6uvvno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x4oQyMzMlSRs2bNDy5cvnJyAASCIk1wCQQgKBgA4ePKi6ujp5PB498sgjKisr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\nPQOA5MY91wCQQjwej/r6+oL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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "quickHist(xsmall)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#Using R in notebook, these next 3 cells will not operate without rpy2 installed\n", "%load_ext rpy2.ipython" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%R -i xbig,xsmall,xmed" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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PESN0NQE75M97Dnjv3r3qJLZQc8DGZSDe4HkZiDcN93y3Q/7cQ4s5TSsBkwLG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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%R\n", "par(mfrow=c(2,3))\n", "hist(xbig);\n", "hist(xmed);\n", "hist(xsmall);\n", "#second row is using the scott estimation\n", "hist(xbig, 'scott');\n", "hist(xmed, 'scott');\n", "hist(xsmall, 'scott');\n", "#sorry about the shit plot - fig size control is iffy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is obvious that R is clearly adapting to the amount and the type of data being passed in (even giving options for the automatic bin selection). It should be noted that R has a `pretty` method that interferes a little bit, making the sections start on whole numbers, with preference given to multiples of 2 and 5 and some freedom to increase or decrease the number of bins. Either way, the hist method that R provides gives us better functionality out of the box." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#Solution\n", "\n", "Provide some kind of similar functionality for hist, taking inspiration from R's methods. Pretty can be implemented at a later stage if necessary. The focus here is to provide at least some kind of adaptability for the hist method.\n", "\n", "* n = size of data\n", "* h = binwidth\n", "* Number of bins $\\propto 1/h$\n", "* The $\\left\\lceil f(x) \\right\\rceil$ mean the ceiling of the function\n", "\n", "It is a known fact that the asymptotically optimal number of bins is proportional to $n^{1/3}$, which is the motivating reason behind the $n^{1/3}$ in the expressions below (binwidth ~ $n^{-1/3}$). This project been motivated by my study of non-parametrics at university.\n", "\n", "We implement 5 methods here:\n", "\n", "1. Sturges - default method in R\n", " * Number of Bins = $\\left\\lceil \\log _{2}n+1 \\right\\rceil$\n", " * O(1) estimation\n", " * This method is considered to be too conservative for large datasets (the log grows too slowly), and is designed with the assumption of normality, which is commonly violated.\n", "2. Rice - Sturges alternative\n", " * Number of Bins = $\\left\\lceil 2n^{-1/3} \\right\\rceil$\n", " * O(1) estimation\n", " * This method follows the asymptotic normality idea, but the constant 2 means it tends to make no allowance for data variability.\n", "3. Sturges Rice Average\n", " * Number of Bins = mean(Sturges, Rice)\n", " * I've chosen the geometric mean, but arithmetic mean works since the number of bins is usually quite small\n", " * O(1) estimation\n", " * Provides decent results for smaller data\n", "4. Scott - provided method in R\n", " * Binwidth = $\\frac{3.5\\sigma}{n^{-1/3}}$ \n", " * if the binwidth is estimated to be 0, then return 1 as the number of bins\n", " * O(n) estimation\n", " * Uses the standard deviation of the data to account for data variabilty when choosing the number of bins.\n", " * The cube root factor means this method provides decent results for large amounts of data.\n", "5. Freedman Diaconis - provided method in R\n", " * Binwidth = $2 \\frac{IQR}{n^{-1/3}}$ \n", " * If Inter Quartile Range (IQR) is 0, then use the Median Absolute Deviation instead as IQR. If it too is 0, return 1\n", " * O(n) estimation (percentile may be $O(log_2 n)$ but the range is O(n)\n", " * The IQR is a more robust estimator of variance than the standard deviation of the Scott estimator, which is more vulnerable to outliers.\n", "\n", "\n", "\n", "## Further Reading/ Resources\n", "* [This fairly thorough summary](http://www.stat.rice.edu/~scottdw/stat550/HW/hw3/c03.pdf) of histogram methods and some analysis from Rice's stats department.\n", "* [R page](https://stat.ethz.ch/R-manual/R-devel/library/grDevices/html/nclass.html) on the included methods for automatic bin numbers. Note, that opening up an R console and typing nclass.Sturges (or scott, FD) will output the code. The publication references are provided in this page.\n", "* [R page](https://stat.ethz.ch/R-manual/R-devel/library/graphics/html/hist.html) on histograms\n", "* [Wikipedia](http://en.wikipedia.org/wiki/Histogram#Number_of_bins_and_width) for an overview of the methods and a simple argument for the optimality of $n^{1/3}$ for number of bins" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def min8decorator(func):\n", " \"\"\"\"\n", " Decorate the estimators in case we need to provide a lower bound\n", " \n", " @min8decorator\n", " def func():\n", " ...\n", " \"\"\"\n", " def inner(*args, **kwargs):\n", " return max(func(*args, **kwargs), 8)\n", " return inner\n", "\n", "def minNdecorator(N):\n", " \"\"\"\"\n", " Decorate the estimators in case we need to provide a lower bound\n", " The minimum value can be defined as so\n", " @minNdecorator(10)\n", " def func():\n", " ...\n", " \"\"\"\n", " def decorator(func):\n", " def inner(*args, **kwargs):\n", " return max(func(*args, **kwargs), N)\n", " return inner\n", " return decorator\n", "\n", "def sturges(x):\n", " \"\"\"\n", " Using Sturges estimator\n", " Very simplistic based on logarithms, however \n", " poorer performance for large datasets and non-normal data\n", " \"\"\"\n", " return np.ceil(np.log2(x.size)) + 1\n", "\n", "def rice(x):\n", " \"\"\"\n", " A similar version of sturges with another simple estimator. \n", " Better performance for larger datasets\n", " The number of bins is proportional to the cube root of data size\n", " \"\"\"\n", " return np.ceil(2 * len(x) ** (1.0/3))\n", "\n", "\n", "def SturgesRice(x, geom= True):\n", " \"\"\"\n", " An average or the Rice and Sturges - works surprisingly well in practice\n", " \"\"\"\n", " if geom:\n", " #geometric mean\n", " return np.ceil(np.sqrt(rice(x) * sturges(x)))\n", " else:\n", " #arithmetic Mean\n", " return np.ceil((rice(x) + sturges(x))/2)\n", "\n", "def scott(x):\n", " \"\"\"\n", " The binwidth is proprtional to the standard deviation of the data and \n", " inversely proportional to the cube root of data size\n", " \n", " \"\"\"\n", " h = 3.5 * x.std() * x.size **(-1.0/3)\n", " if h>0:\n", " return np.ceil(x.ptp()/h)\n", " return 1\n", "\n", "def mad(data, axis=None):\n", " \"\"\"\n", " Mean Absolute Deviation - simple well defined function\n", " Simplest implementation, even length case left to default behaviour\n", " \"\"\"\n", " return np.median(np.absolute(data - np.median(data, axis)), axis)\n", "\n", "def FD(x):\n", " \"\"\"\n", " Freedman Diaconis rule using IQR for binwidth\n", " Considered a variation of the Scott rule with more robustness as the Interquartile range\n", " is less affected by outliers than the standard deviation.\n", " \n", " If the IQR is 0, we return the median absolute deviation as defined above, else 1\n", " \"\"\"\n", " iqr = np.subtract(*np.percentile(x, [75, 25]))\n", " \n", " \n", " if iqr ==0: #unlikely\n", " iqr = mad(x) # replace with something useful\n", " \n", " h = (2 * iqr * x.size**(-1.0/3)) # binwidth\n", " \n", " if iqr > 0:\n", " return np.ceil(x.ptp()/h)\n", "\n", " return 1 #all else fails\n", " \n", "autoMethods = [sturges, rice, SturgesRice, scott, FD]" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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R47BxQUREZENVTVXYf3G/2TLTw6ezcUFEbom3RRERERERkU2wcUFERERERDbB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\nt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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def methodDisplay(x, manual = 10):\n", " \"\"\"\n", " Let's have a look at how our methods fare?\n", " \"\"\"\n", "\n", " num_bins = [manual] + map(lambda method: method(x), autoMethods)\n", " bindesc = [\"manual\"] + map(lambda method: method.__name__, autoMethods[:-2]) + [\"scott\", \"FD\"] \n", " # Using decorators means this trick doesn't work anymore\n", "\n", " plt.figure(tight_layout=True, figsize=(11,7))\n", "\n", "\n", " for i in range(len(bindesc)):\n", " binChoice = num_bins[i]\n", " desc = bindesc[i]\n", " plt.subplot(2,3,i+1)\n", " # the histogram of the data\n", " n, bins, patches = plt.hist(x, binChoice, normed=1, facecolor = 'green', alpha=0.5)\n", " plt.xlabel('X axis')\n", " plt.ylabel('Probability')\n", " plt.title(r'method = {1}, nbins = {0}'.format(binChoice, desc))\n", "\n", " # Tweak spacing to prevent clipping of ylabel\n", " plt.subplots_adjust(left=0.15)\n", " plt.show()\n", " \n", "methodDisplay(xbig)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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iV8DOBREREfUaJpMJ6enpWL16NXQ6HVauXInIyEgEBQVJZfLz81FeXo7Nmzfj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\n0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REBAAZ2dnREVFITU11WCe1NRUDBs2DAAQGhqK0tJSFBUVQa1Wo0uXLgAAlUqF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\nHqqoqHCrVXAAxiZbYlP//v3x7bffIjs7GyEhIXjllVfwi1/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HIEhj/fLF7TFuuL7eGjec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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "methodDisplay(xsmall)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Conclusion\n", "\n", "As a conclusion, I hope it's been quite obvious that the default 10 bins gives us a subpar solution for visualising the data. It provides decent results for data < 1000 samples, and makes no allowance for data variability. The other methods as discussed in literature and in R show much better performance, for larger datasets, and in fact anything over a 1000 datapoints will consistently use more than 10 bins to reveal the true nature of the data (play around with the sizes of xsmall, xmed and xbig to see).\n", "\n", "Furthermore it is also noted\n", "* Sturges' method is too conservative, especially for larger datasizes. \n", "* Rice's method is a bit too loose on it's estimation, showing significant noise in its bins.\n", "* Sturges' and Rice's mean provides practically decent results for small datasets. \n", "* FD and scott also appear to very effective, but for small datasets tend to have very few bins chosen which may be less informative/optimal\n", "\n", "\n", "# Recommendations\n", "##Signature Change\n", "I propose histogram's signature changes to\n", "\n", "```python\n", "def histogam(a, bins='optimal', ... )\n", "\"\"\"\n", "bins: integer, string, or array_like, optional\n", "\"\"\"\n", "```\n", "* Default behaviour is to use the SturgesRice estimator for number of bins for x.size < 1000, else the Freeman Diaconis estimator. These functions attempt to estimate the optimal number of bins for the given data.\n", "* You may use any of ['sturges', 'rice', 'SturgesRice', 'scott', 'FD'] as value of bins to choose between the different methods\n", "* An integer ...\n", "* An array like ...\n", "\n", "This would allow all the visualisation libraries out there that depend on np.histogram to be able to get a somewhat optimal histogram as simply as passing 'FD' as the argument to bins.\n", "\n", "There is also reason to pass a function for the bins argument, which automatically calculates the number of bins for the given data, however I'm unconvinced of it's necessity.\n", "\n", "## Default\n", "I would recommend providing a default method `'default'` of `max(Sturges(data), FD(data))` for visualisation libraries, as the FD tends to have subpar performance for small datasets, as the asymptotic optimality conditions haven't kicked in. The Sturges estimator provides an good enough value for small datasets, and the FD provides a good value that is bigger than the Sturges estimator for most cases where n>1000. \n", "\n", "From a statistics point of view, it would be great to have a good automatic bin choice when using a histogram function instead of manually playing around with the bins until we get a decent result. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }