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LISA cluster maps with `PySAL`
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "source": [ | |
| "# LISA cluster maps with `PySAL`" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "* Dani Arribas-Bel ([@darribas](http://twitter.com/darribas))\n", | |
| "\n", | |
| "This notebook is available as a [gist](https://gist.github.com/darribas/657e0568df7a63362762), or viewable online as [static html](http://nbviewer.ipython.org/urls/gist.githubusercontent.com/darribas/657e0568df7a63362762/raw/pysal_lisa_maps.ipynb).\n", | |
| "\n", | |
| "----\n", | |
| "\n", | |
| "[Local Indicators of Spatial Association](https://en.wikipedia.org/wiki/Indicators_of_spatial_association) (LISAs, [Anselin, 1995](http://onlinelibrary.wiley.com/doi/10.1111/j.1538-4632.1995.tb00338.x/abstract)) are a common tool to explore spatial heterogeneity, identify spatial concentration of (dis)similar values and test for the probability such agglomerations originate from a random process.\n", | |
| "\n", | |
| "[`PySAL`](http://pysal.org) has had functionality to run LISAs since its very beginning. However, the output of such computation is not very useful just by itself as, being a local statistic, LISAs imply running a test for every single observation. The usual approach has been to visualize significant clusters on a map using a simple color coding for each class (High-High, HH; Low-Low, LL; High-Low, HL; Low-High, LH). Such visualiations have been available for a long time in packages such as [GeoDa](https://geodacenter.asu.edu/projects/opengeoda), but this would imply breaking the workflow to switch between Python and GeoDa, plus with the annoyance that the workflow cannot thus be automated, a convenient feature for [reproducible science](https://en.wikipedia.org/wiki/Reproducibility).\n", | |
| "\n", | |
| "In this notebook, we show how to leverage the visualization layer that is being built in `PySAL` to create generic and custom LISA cluster maps." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Set up " | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "For this example, we will use the `NAT` dataset, included in `PySAL` by default, exploring the variable `HR90`, homicide rates in 1990 at the county level. \n", | |
| "\n", | |
| "Let's start by importing the required code. This is all code that will be made available in the upcoming release of `PySAL` in July 2015 (if you're reading this afterwards, it's all in there by default!)." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Reading from /Users/dani/code/pysal_darribas/pysal/examples/nat/NAT.shp\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%matplotlib inline\n", | |
| "\n", | |
| "import pysal as ps\n", | |
| "import numpy as np\n", | |
| "from pysal.contrib.viz import mapping as maps\n", | |
| "\n", | |
| "shp_link = ps.examples.get_path('NAT.shp')\n", | |
| "print 'Reading from ', shp_link\n", | |
| "\n", | |
| "hr90 = np.array(ps.open(shp_link.replace('.shp', '.dbf')).by_col('HR90'))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Before any further analysis, it is always good practice to visualize the distribution of values. We can now conveniently do that in `PySAL`:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 15, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
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| ], | |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x10b0f4e90>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "_ = maps.plot_choropleth(shp_link, hr90, 'quantiles', cmap='Greens', figsize=(9, 6))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Before we can plot a map, we need to run a LISA. In the spirit of flexibility and modularity envisioned in `PySAL`, the two operations (computation, visualization) are decoupled. We will use a simple contiguity matrix for this." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 45, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "w = ps.queen_from_shapefile(shp_link)\n", | |
| "lisa = ps.Moran_Local(hr90, w, permutations=9999)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## LISA maps in one line of code" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "The simplest way to obtain a quick visualization of LISA results is with the \"one-liner\" `plot_lisa_cluster`:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 46, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
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| ], | |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x10b9a53d0>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "_ = maps.plot_lisa_cluster(shp_link, lisa, figsize=(9, 6))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## (Prettier) LISA maps using `cartopy`" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "The previous map is a very quick, painless way to obtain a visualization of LISA results. This is incredibly useful for interactive work where one wants to quickly iterate to get a sense of the data. However, once the researcher settles on a particular visualiation, there's some \"eye-candy\" that can be applied that improves notably the final result.\n", | |
| "\n", | |
| "In this section, we use the fantastic library [`cartopy`](http://scitools.org.uk/cartopy/) to produce a publication-ready LISA plot. This, in part, uses some of the internal machinery in `pysal.contrib.viz`, combined with plain `matplotlib` functionality.\n", | |
| "\n", | |
| "**NOTE**: besides `PySAL`, you will need `cartopy` installed in your system to reproduce this example." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 24, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "import matplotlib.pyplot as plt\n", | |
| "import cartopy.crs as ccrs" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 47, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
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| ], | |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x10c7d3510>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "orig_crs = ccrs.PlateCarree()\n", | |
| "projection = ccrs.LambertConformal()\n", | |
| "p_thres = 0.01\n", | |
| "\n", | |
| "shp = ps.open(shp_link)\n", | |
| "polys = maps.map_poly_shp(shp)\n", | |
| "polys = maps.base_lisa_cluster(polys, lisa, p_thres=p_thres)\n", | |
| "polys.set_edgecolor('1')\n", | |
| "polys.set_linewidth(0.2)\n", | |
| "polys.set_transform(orig_crs)\n", | |
| "\n", | |
| "f = plt.figure(figsize=(12, 8))\n", | |
| "\n", | |
| "ax = plt.axes(projection=projection)\n", | |
| "extent = [shp.bbox[0], shp.bbox[2], shp.bbox[1], shp.bbox[3]]\n", | |
| "ax.set_extent(extent, crs=ccrs.PlateCarree())\n", | |
| "ax.add_collection(polys)\n", | |
| "ax.outline_patch.set_visible(False)\n", | |
| "\n", | |
| "boxes, labels = maps.lisa_legend_components(lisa, p_thres=p_thres)\n", | |
| "plt.legend(boxes, labels, loc='lower left', fancybox=True)\n", | |
| "\n", | |
| "plt.title('HR90 | LISA clusters | P-value = %.2f'%p_thres)\n", | |
| "\n", | |
| "plt.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Having this kind of maps produced in an automated way is handy because it is very straightforward then to plot a series of them. As an example, we will plot a different map for solutions that consider different significance thresholds." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 48, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
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