{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n", "\n", "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*\n", "\n", "*No changes were made to the contents of this notebook from the original.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [Density and Contour Plots](04.04-Density-and-Contour-Plots.ipynb) | [Contents](Index.ipynb) | [Customizing Plot Legends](04.06-Customizing-Legends.ipynb) >" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Histograms, Binnings, and Density" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A simple histogram can be a great first step in understanding a dataset.\n", "Earlier, we saw a preview of Matplotlib's histogram function (see [Comparisons, Masks, and Boolean Logic](02.06-Boolean-Arrays-and-Masks.ipynb)), which creates a basic histogram in one line, once the normal boiler-plate imports are done:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "plt.style.use('seaborn-white')\n", "\n", "data = np.random.randn(1000)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(data);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The hist() function has many options to tune both the calculation and the display; \n", "here's an example of a more customized histogram:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(data, bins=30, normed=True, alpha=0.5,\n", " histtype='stepfilled', color='steelblue',\n", " edgecolor='none');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plt.hist docstring has more information on other customization options available.\n", "I find this combination of histtype='stepfilled' along with some transparency alpha to be very useful when comparing histograms of several distributions:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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TIr1goKc5r9eL/9d+DooMeLxR5OdN3g7M330aZa4rMKmcFXXLMkaqV0EUJ37N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\nOhGRTjDQiYh04v8DF2mFWN13xe4AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x1 = np.random.normal(0, 0.8, 1000)\n", "x2 = np.random.normal(-2, 1, 1000)\n", "x3 = np.random.normal(3, 2, 1000)\n", "\n", "kwargs = dict(histtype='stepfilled', alpha=0.3, normed=True, bins=40)\n", "\n", "plt.hist(x1, **kwargs)\n", "plt.hist(x2, **kwargs)\n", "plt.hist(x3, **kwargs);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you would like to simply compute the histogram (that is, count the number of points in a given bin) and not display it, the np.histogram() function is available:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 12 190 468 301 29]\n" ] } ], "source": [ "counts, bin_edges = np.histogram(data, bins=5)\n", "print(counts)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Two-Dimensional Histograms and Binnings\n", "\n", "Just as we create histograms in one dimension by dividing the number-line into bins, we can also create histograms in two-dimensions by dividing points among two-dimensional bins.\n", "We'll take a brief look at several ways to do this here.\n", "We'll start by defining some data—an x and y array drawn from a multivariate Gaussian distribution:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "mean = [0, 0]\n", "cov = [[1, 1], [1, 2]]\n", "x, y = np.random.multivariate_normal(mean, cov, 10000).T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### plt.hist2d: Two-dimensional histogram\n", "\n", "One straightforward way to plot a two-dimensional histogram is to use Matplotlib's plt.hist2d function:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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DjRs3+uqtAGCCJiIzUSQfZ6GqKoqKivDwww/j+uuvP6VvjMViQUtLS8/FfgZc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\nAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist2d(x, y, bins=30, cmap='Blues')\n", "cb = plt.colorbar()\n", "cb.set_label('counts in bin')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just as with plt.hist, plt.hist2d has a number of extra options to fine-tune the plot and the binning, which are nicely outlined in the function docstring.\n", "Further, just as plt.hist has a counterpart in np.histogram, plt.hist2d has a counterpart in np.histogram2d, which can be used as follows:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "counts, xedges, yedges = np.histogram2d(x, y, bins=30)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the generalization of this histogram binning in dimensions higher than two, see the np.histogramdd function." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### plt.hexbin: Hexagonal binnings\n", "\n", "The two-dimensional histogram creates a tesselation of squares across the axes.\n", "Another natural shape for such a tesselation is the regular hexagon.\n", "For this purpose, Matplotlib provides the plt.hexbin routine, which will represents a two-dimensional dataset binned within a grid of hexagons:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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IoOWyrphAUUB8CZ3HZaWPaGWTYEk1JTKm7jD88mgdMy0nJIRfHmvgV7MNnDpW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\nPDSEAOCXr3JY1A1PVmiZLliYLFg41nYghMCET8z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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hexbin(x, y, gridsize=30, cmap='Blues')\n", "cb = plt.colorbar(label='count in bin')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "plt.hexbin has a number of interesting options, including the ability to specify weights for each point, and to change the output in each bin to any NumPy aggregate (mean of weights, standard deviation of weights, etc.)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Kernel density estimation\n", "\n", "Another common method of evaluating densities in multiple dimensions is *kernel density estimation* (KDE).\n", "This will be discussed more fully in [In-Depth: Kernel Density Estimation](05.13-Kernel-Density-Estimation.ipynb), but for now we'll simply mention that KDE can be thought of as a way to \"smear out\" the points in space and add up the result to obtain a smooth function.\n", "One extremely quick and simple KDE implementation exists in the scipy.stats package.\n", "Here is a quick example of using the KDE on this data:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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nEZKeR6tsfaiyLBRazz2brV/6AWBXYsecTjEZD/yxxx7DeeedBwBYuHAhhoeH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\nsOV2xtx6dJ36zz74fbvDydeOgLvMLoFetpcZXIdZKgEwIwV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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.stats import gaussian_kde\n", "\n", "# fit an array of size [Ndim, Nsamples]\n", "data = np.vstack([x, y])\n", "kde = gaussian_kde(data)\n", "\n", "# evaluate on a regular grid\n", "xgrid = np.linspace(-3.5, 3.5, 40)\n", "ygrid = np.linspace(-6, 6, 40)\n", "Xgrid, Ygrid = np.meshgrid(xgrid, ygrid)\n", "Z = kde.evaluate(np.vstack([Xgrid.ravel(), Ygrid.ravel()]))\n", "\n", "# Plot the result as an image\n", "plt.imshow(Z.reshape(Xgrid.shape),\n", " origin='lower', aspect='auto',\n", " extent=[-3.5, 3.5, -6, 6],\n", " cmap='Blues')\n", "cb = plt.colorbar()\n", "cb.set_label(\"density\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "KDE has a smoothing length that effectively slides the knob between detail and smoothness (one example of the ubiquitous bias–variance trade-off).\n", "The literature on choosing an appropriate smoothing length is vast: gaussian_kde uses a rule-of-thumb to attempt to find a nearly optimal smoothing length for the input data.\n", "\n", "Other KDE implementations are available within the SciPy ecosystem, each with its own strengths and weaknesses; see, for example, sklearn.neighbors.KernelDensity and statsmodels.nonparametric.kernel_density.KDEMultivariate.\n", "For visualizations based on KDE, using Matplotlib tends to be overly verbose.\n", "The Seaborn library, discussed in [Visualization With Seaborn](04.14-Visualization-With-Seaborn.ipynb), provides a much more terse API for creating KDE-based visualizations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [Density and Contour Plots](04.04-Density-and-Contour-Plots.ipynb) | [Contents](Index.ipynb) | [Customizing Plot Legends](04.06-Customizing-Legends.ipynb) >" ] } ], "metadata": { "anaconda-cloud": {}, "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 }