{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Centrography of Point Patterns\n", "\n", "**Authors: Serge Rey and Wei Kang **\n", "\n", "## Introduction\n", "\n", "Centrography refers to a set of descriptive statistics that provide summary descriptions of point patterns.\n", "\n", "This notebook introduces three types of centrography analysis for point patterns in pysal.\n", "* [Central Tendency](#Central-Tendency)\n", "* [Dispersion and Orientation](#Dispersion-and-Orientation)\n", "* [Shape Analysis](#Shape-Analysis)\n", "\n", "We also illustrate centrography analysis using two simulated datasets. See [Another Example](#Another-Example)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The python file **centrography.py** contains several functions with which we can conduct centrography analysis.\n", "* Central Tendency\n", " 1. mean_center: calculate the mean center of the unmarked point pattern.\n", " 2. weighted_mean_center: calculate the weighted mean center of the marked point pattern.\n", " 3. manhattan_median: calculate the manhattan median\n", " 4. euclidean_median: calculate the Euclidean median\n", "* Dispersion and Orientation\n", " 1. std_distance: calculate the standard distance\n", "* Shape Analysis\n", " 1. hull: calculate the convex hull of the point pattern\n", " 2. mbr: calculate the minimum bounding box (rectangle)\n", " \n", "All of the above functions operate on a series of coordinate pairs. That is, the data type of the first argument should be $(n,2)$ array_like. In case that you have a point pattern (PointPattern instance), you need to pass its attribute \"points\" instead of itself to these functions." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " x y\n", "0 66.22 32.54\n", "1 22.52 22.39\n", "2 31.01 81.21\n", "3 9.47 31.02\n", "4 30.78 60.10\n", "5 75.21 58.93\n", "6 79.26 7.68\n", "7 8.23 39.93\n", "8 98.73 77.17\n", "9 89.78 42.53\n", "10 65.19 92.08\n", "11 54.46 8.48" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "from pointpats import PointPattern\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "points = [[66.22, 32.54], [22.52, 22.39], [31.01, 81.21],\n", " [9.47, 31.02], [30.78, 60.10], [75.21, 58.93],\n", " [79.26, 7.68], [8.23, 39.93], [98.73, 77.17],\n", " [89.78, 42.53], [65.19, 92.08], [54.46, 8.48]]\n", "pp = PointPattern(points) #create a point pattern \"pp\" from list\n", "pp.points " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "pandas.core.frame.DataFrame" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(pp.points)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use PointPattern class method **plot** to visualize **pp**." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pp.plot()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "#import centragraphy analysis functions \n", "from pointpats.centrography import hull, mbr, mean_center, weighted_mean_center, manhattan_median, std_distance,euclidean_median,ellipse" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Central Tendency\n", "\n", "Central Tendency concerns about the center point of the two-dimensional distribution. It is similar to the first moment of a one-dimensional distribution. There are several ways to measure central tendency, each having pros and cons. We need to carefully select the appropriate measure according to our objective and data status.\n", "\n", "### Mean Center $(x_{mc},y_{mc})$\n", "\n", "$$x_{mc}=\\frac{1}{n} \\sum^n_{i=1}x_i$$\n", "$$y_{mc}=\\frac{1}{n} \\sum^n_{i=1}y_i$$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([52.57166667, 46.17166667])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mc = mean_center(pp.points)\n", "mc" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pp.plot()\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Weighted Mean Center $(x_{wmc},y_{wmc})$\n", "\n", "$$x_{wmc}=\\sum^n_{i=1} \\frac{w_i x_i}{\\sum^n_{i=1}w_i}$$\n", "$$y_{wmc}=\\sum^n_{i=1} \\frac{w_i y_i}{\\sum^n_{i=1}w_i}$$\n", "\n", "Weighted mean center is meant for marked point patterns. Aside from the first argument which is a seris of $(x,y)$ coordinates in **weighted_mean_center** function, we need to specify its second argument which is the weight for each event point." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "weights = np.arange(12)\n", "weights" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([60.51681818, 47.76848485])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wmc = weighted_mean_center(pp.points, weights)\n", "wmc" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pp.plot() #use class method \"plot\" to visualize point pattern\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center') \n", "plt.plot(wmc[0], wmc[1], 'gd', label='Weighted Mean Center')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Manhattan Median $(x_{mm},y_{mm})$\n", "\n", "$$min f(x_{mm},y_{mm})= \\sum^n_{i=1}(|x_i-x_{mm}|+|y_i-y_{mm}|)$$\n", "\n", "The Manhattan median is the location which minimizes the absolute distance to all the event points. It is an extension of the median measure in one-dimensional space to two-dimensional space. Since in one-dimensional space, a median is the number separating the higher half of a dataset from the lower half, we define the Manhattan median as a tuple whose first element is the median of $x$ coordinates and second element is the median of $y$ coordinates.\n", "\n", "Though Manhattan median can be found very quickly, it is not unique if you have even number of points. In this case, pysal handles the Manhattan median the same way as numpy.median: return the average of the two middle values." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "12" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#get the number of points in point pattern \"pp\"\n", "pp.n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/serge/Dropbox/p/pysal/src/subpackages/pointpats/pointpats/centrography.py:151: UserWarning: Manhattan Median is not unique for even point patterns.\n", " warnings.warn(s)\n" ] }, { "data": { "text/plain": [ "array([59.825, 41.23 ])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Manhattan Median is not unique for \"pp\"\n", "mm = manhattan_median(pp.points)\n", "mm" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pp.plot()\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center')\n", "plt.plot(wmc[0], wmc[1], 'gd', label='Weighted Mean Center')\n", "plt.plot(mm[0], mm[1], 'rv', label='Manhattan Median')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Euclidean Median $(x_{em},y_{em})$\n", "\n", "$$min f(x_{em},y_{em})= \\sum^n_{i=1} \\sqrt{(x_i-x_{em})^2+(y_i-y_{em})^2}$$\n", "\n", "The Euclidean Median is the location from which the sum of the Euclidean distances to all points in a distribution is a minimum. It is an optimization problem and very important for more general location allocation problems. There is no closed form solution. We can use first iterative algorithm (Kuhn and Kuenne, 1962) to approximate Euclidean Median. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below, we define a function named median_center with the first argument **points** a series of $(x,y)$ coordinates and the second argument **crit** the convergence criterion." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "def median_center(points, crit=0.0001):\n", " points = np.asarray(points)\n", " x0, y0 = points.mean(axis=0)\n", " dx = np.inf\n", " dy = np.inf\n", " iteration = 0\n", " while np.abs(dx) > crit or np.abs(dy) > crit:\n", " xd = points[:, 0] - x0\n", " yd = points[:, 1] - y0\n", " d = np.sqrt(xd*xd + yd*yd)\n", " w = 1./d\n", " w = w / w.sum()\n", " x1 = w * points[:, 0]\n", " x1 = x1.sum()\n", " y1 = w * points[:, 1]\n", " y1 = y1.sum()\n", " dx = x1 - x0\n", " dy = y1 - y0\n", " iteration +=1 \n", " print(x0, x1, dx, dy, d.sum(), iteration)\n", " x0 = x1\n", " y0 = y1\n", " \n", " return x1, y1" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "52.57166666666668 53.178128280602785 0.606461613936105 -0.9290354286335258 466.24479074356606 1\n", "53.178128280602785 53.56643624463614 0.388307964033352 -0.4199402653980684 465.9311160558993 2\n", "53.56643624463614 53.80720376806838 0.24076752343224683 -0.1974862190386233 465.84555867343346 3\n", "53.80720376806838 53.95348076207835 0.1462769940099662 -0.09642613786996179 465.8197750145871 4\n", "53.95348076207835 54.04117257066307 0.08769180858472225 -0.04872250646902643 465.8115372002813 5\n", "54.04117257066307 54.09327726928146 0.05210469861838618 -0.025370793047137852 465.80882301324334 6\n", "54.09327726928146 54.12405125525861 0.030773985977148755 -0.013552246205456697 465.8079149010591 7\n", "54.12405125525861 54.14215248769505 0.018101232436443127 -0.00739190209046825 465.8076087750224 8\n", "54.14215248769505 54.15276956049696 0.010617072801906602 -0.0040992658298719675 465.8075052025632 9\n", "54.15276956049696 54.15898467957115 0.0062151190741914775 -0.0023026998071102867 465.80747009858044 10\n", "54.15898467957115 54.16261796248172 0.0036332829105703013 -0.0013061853179365812 465.80745819050844 11\n", "54.16261796248172 54.16473989468326 0.002121932201539778 -0.0007463404183738476 465.80745414933307 12\n", "54.16473989468326 54.165978319450346 0.00123842476708802 -0.00042875101595285514 465.80745277762423 13\n", "54.165978319450346 54.166700756153695 0.0007224367033487056 -0.00024727631074483725 465.80745231197506 14\n", "54.166700756153695 54.16712204754273 0.0004212913890384584 -0.00014302182778891392 465.8074521538953 15\n", "54.16712204754273 54.16736766581608 0.00024561827334679265 -8.289363293556562e-05 465.8074521002288 16\n", "54.16736766581608 54.167510839857464 0.0001431740413835314 -4.8115880247223686e-05 465.80745208200943 17\n", "54.167510839857464 54.167594287646125 8.344778866131719e-05 -2.7959041396741213e-05 465.807452075824 18\n" ] }, { "data": { "text/plain": [ "(54.167594287646125, 44.42430865883205)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "median_center(pp.points, crit=.0001)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After 18 iterations, the convergence criterion is reached. The Euclidean Median is $(54.167594287646125,44.424308658832047)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also call the function **euclidean_median** in pysal to calculate the Euclidean Median." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([54.16770671, 44.4242589 ])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "em = euclidean_median(pp.points)\n", "em" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The two results we get from **euclidean_median** function in pysal and the **median_center** function we define here are very much the same." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pp.plot()\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center')\n", "plt.plot(wmc[0], wmc[1], 'gd', label='Weighted Mean Center')\n", "plt.plot(mm[0], mm[1], 'rv', label='Manhattan Median')\n", "plt.plot(em[0], em[1], 'm+', label='Euclidean Median')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Dispersion and Orientation\n", "\n", "### Standard Distance & Standard Distance Circle\n", "\n", "$$SD = \\displaystyle \\sqrt{\\frac{\\sum^n_{i=1}(x_i-x_{m})^2}{n} + \\frac{\\sum^n_{i=1}(y_i-y_{m})^2}{n}}$$\n", "\n", "The Standard distance is closely related to the usual definition of the standard deviation of a data set, and it provides a measure of how dispersed the events are around their mean center $(x_m,y_m)$. Taken together, these measurements can be used to plot a summary circle (standard distance circle) for the point pattern, centered at $(x_m,y_m)$ with radius $SD$, as shown below." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "40.14980648908671" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stdd = std_distance(pp.points)\n", "stdd" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot mean center as well as the standard distance circle." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "circle1=plt.Circle((mc[0], mc[1]),stdd,color='r')\n", "ax = pp.plot(get_ax=True, title='Standard Distance Circle')\n", "ax.add_artist(circle1)\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center')\n", "ax.set_aspect('equal')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the above figure, we can observe that there are five points outside the standard distance circle which are potential outliers." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Standard Deviational Ellipse\n", "\n", "Compared with standard distance circle which measures dispersion using a single parameter $SD$, standard deviational ellipse measures dispersion and trend in two dimensions through angle of rotation $\\theta$, dispersion along major axis $s_x$ and dispersion along minor axis $s_y$:\n", "\n", "* Major axis defines the direction of maximum spread in the distribution. $s_x$ is the semi-major axis (half the length of the major axis):\n", "\n", "$$ s_x = \\displaystyle \\sqrt{\\frac{2(\\sum_{i=1}^n (x_i-\\bar{x})\\cos(\\theta) - \\sum_{i=1}^n (y_i-\\bar{y})\\sin(\\theta))^2}{n-2}}$$\n", "\n", "* Minor axis defines the direction of minimum spread and is orthogonal to major axis. $s_y$ is the semi-minor axis (half the length of the minor axis):\n", "\n", "$$ s_y = \\displaystyle \\sqrt{\\frac{2(\\sum_{i=1}^n (x_i-\\bar{x})\\sin(\\theta) - \\sum_{i=1}^n (y_i-\\bar{y})\\cos(\\theta))^2}{n-2}}$$\n", "\n", "* The ellipse is rotated clockwise through an angle $\\theta$:\n", "\n", "$$\\theta = \\displaystyle \\arctan{\\{ (\\sum_i(x_i-\\bar{x})^2-\\sum_i(y_i-\\bar{y})^2) + \\frac{[(\\sum_i(x_i-\\bar{x})^2-\\sum_i(y_i-\\bar{y})^2)^2 + 4(\\sum_i(x-\\bar{x})(y_i-\\bar{y}))^2]^\\frac{1}{2}}{2\\sum_i(x-\\bar{x})(y_i-\\bar{y})}\\}}$$\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(39.62386788646298, 42.753818949026815, 1.1039268428650906)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sx, sy, theta = ellipse(pp.points)\n", "sx, sy, theta" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "63.250348987371304" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "theta_degree = np.degrees(theta) #need degree of rotation to plot the ellipse\n", "theta_degree" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Standard Deviational Ellipse for the point pattern is rotated clockwise by $63.25^{\\circ}$." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib.patches import Ellipse\n", "from pylab import figure, show,rand\n", "fig = figure()\n", "#ax = fig.add_subplot(111, aspect='equal')\n", "e = Ellipse(xy=mean_center(pp.points), width=sx*2, height=sy*2, angle=-theta_degree) #angle is rotation in degrees (anti-clockwise)\n", "ax = pp.plot(get_ax=True, title='Standard Deviational Ellipse')\n", "ax.add_artist(e)\n", "e.set_clip_box(ax.bbox)\n", "e.set_facecolor([0.8,0,0])\n", "e.set_edgecolor([1,0,0])\n", "ax.set_xlim(0,100)\n", "ax.set_ylim(0,100)\n", "ax.set_aspect('equal')\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center')\n", "plt.legend(numpoints=1)\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Shape Analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### [Convex Hull](https://en.wikipedia.org/wiki/Convex_hull)\n", "\n", "The convex hull of a point pattern *pp* is the smallest convex set that contains *pp*. We can call function **hull** to caculate the convex hull." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[31.01, 81.21],\n", " [ 8.23, 39.93],\n", " [ 9.47, 31.02],\n", " [22.52, 22.39],\n", " [54.46, 8.48],\n", " [79.26, 7.68],\n", " [89.78, 42.53],\n", " [98.73, 77.17],\n", " [65.19, 92.08]])" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hull(pp.points)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By specifying \"hull\" argument **True** in PointPattern class method **plot**, we can easily plot convex hull of the point pattern." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pp.plot(title='Centers', hull=True ) #plot point pattern \"pp\" as well as its convex hull\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center')\n", "plt.plot(wmc[0], wmc[1], 'gd', label='Weighted Mean Center')\n", "plt.plot(mm[0], mm[1], 'rv', label='Manhattan Median')\n", "plt.plot(em[0], em[1], 'm+', label='Euclidean Median')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### [Minimum Bounding Rectangle](https://en.wikipedia.org/wiki/Minimum_bounding_rectangle)\n", "\n", "Minimum Bounding Rectangle (Box) is the same as the minimum bounding Rectangle of its convex hull. Thus, it is almost always bigger than convex hull.\n", "\n", "We can call **mbr** function to calculate the leftmost, downmost, rightmost, and upmost value of the vertices of minimum bounding rectangle." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(8.23, 7.68, 98.73, 92.08)" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mbr(pp.points)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thus, four vertices of the minimum bounding rectangle is $(8.23,7.68),(98.73,7.68),(98.73,92.08),(8.23,92.08)$." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pp.plot(title='Centers', window=True ) #plot point pattern \"pp\" as well as its Minimum Bounding Rectangle\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center')\n", "plt.plot(wmc[0], wmc[1], 'gd', label='Weighted Mean Center')\n", "plt.plot(mm[0], mm[1], 'rv', label='Manhattan Median')\n", "plt.plot(em[0], em[1], 'm+', label='Euclidean Median')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pp.plot(title='Centers', hull=True , window=True )#plot point pattern \"pp\", convex hull, and Minimum Bounding Rectangle\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center')\n", "plt.plot(wmc[0], wmc[1], 'gd', label='Weighted Mean Center')\n", "plt.plot(mm[0], mm[1], 'rv', label='Manhattan Median')\n", "plt.plot(em[0], em[1], 'm+', label='Euclidean Median')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot Standard Distance Circle and Convex Hull." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "circle1=plt.Circle((mc[0], mc[1]),stdd,color='r',alpha=0.2)\n", "ax = pp.plot(get_ax=True, title='Standard Distance Circle', hull=True)\n", "ax.add_artist(circle1)\n", "plt.plot(mc[0], mc[1], 'b^', label='Mean Center')\n", "ax.set_aspect('equal')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Another Example\n", "\n", "We apply the centrography statistics and visualization to 2 simulated random datasets." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "#from pysal.contrib import shapely_ext\n", "from libpysal.cg import shapely_ext\n", "from pointpats import PoissonPointProcess as csr\n", "import libpysal as ps\n", "from pointpats import as_window\n", "#import pysal_examples\n", "\n", "# open \"vautm17n\" polygon shapefile\n", "va = ps.io.open(ps.examples.get_path(\"vautm17n.shp\"))\n", "\n", "# Create the exterior polygons for VA from the union of the county shapes\n", "polys = [shp for shp in va]\n", "state = shapely_ext.cascaded_union(polys)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Simulate a 100-point dataset within VA state border from a CSR (complete spatial randomness) process." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pp = csr(as_window(state), 100, 1, asPP=True).realizations[0]\n", "pp.plot(window=True)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mc = mean_center(pp.points)\n", "mm = manhattan_median(pp.points)\n", "em = euclidean_median(pp.points)\n", "pp.plot(title='Centers', hull=True , window=True )#plot point pattern \"pp\", convex hull, and Minimum Bounding Rectangle\n", "plt.plot(mc[0], mc[1], 'c^', label='Mean Center')\n", "plt.plot(mm[0], mm[1], 'rv', label='Manhattan Median')\n", "plt.plot(em[0], em[1], 'm+', label='Euclidean Median')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot Standard Distance Circle of the simulated point pattern." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sx, sy, theta = ellipse(pp.points)\n", "sx, sy, theta\n", "theta_degree = np.degrees(theta) #need degree of rotation to plot the ellipse\n", "from matplotlib.patches import Ellipse\n", "from pylab import figure, show,rand\n", "fig = figure()\n", "#ax = fig.add_subplot(111, aspect='equal')\n", "e = Ellipse(xy=mean_center(pp.points), width=sx*2, height=sy*2, angle=-theta_degree)\n", "ax = pp.plot(get_ax=True, title='Standard Deviational Ellipse')\n", "ax.add_artist(e)\n", "e.set_clip_box(ax.bbox)\n", "e.set_facecolor([0.8,0,0])\n", "e.set_edgecolor([1,0,0])\n", "ax.set_xlim(300000,1000000)\n", "ax.set_ylim(4050000,4350000)\n", "#ax.set_aspect('equal')\n", "plt.plot(mc[0], mc[1], 'c^', label='Mean Center')\n", "plt.legend(numpoints=1)\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Simulate a 500-point dataset within VA state border from a CSR (complete spatial randomness) process." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pp = csr(as_window(state), 500, 1, asPP=True).realizations[0]\n", "pp.plot(window=True)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mc = mean_center(pp.points)\n", "mm = manhattan_median(pp.points)\n", "em = euclidean_median(pp.points)\n", "pp.plot(title='Centers', hull=True , window=True )#plot point pattern \"pp\", convex hull, and Minimum Bounding Rectangle\n", "plt.plot(mc[0], mc[1], 'c^', label='Mean Center')\n", "plt.plot(mm[0], mm[1], 'rv', label='Manhattan Median')\n", "plt.plot(em[0], em[1], 'm+', label='Euclidean Median')\n", "plt.legend(numpoints=1)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sx, sy, theta = ellipse(pp.points)\n", "sx, sy, theta\n", "theta_degree = np.degrees(theta) #need degree of rotation to plot the ellipse\n", "from matplotlib.patches import Ellipse\n", "from pylab import figure, show,rand\n", "fig = figure()\n", "#ax = fig.add_subplot(111, aspect='equal')\n", "e = Ellipse(xy=mean_center(pp.points), width=sx*2, height=sy*2, angle=-theta_degree)\n", "ax = pp.plot(get_ax=True, title='Standard Deviational Ellipse')\n", "ax.add_artist(e)\n", "e.set_clip_box(ax.bbox)\n", "e.set_facecolor([0.8,0,0])\n", "e.set_edgecolor([1,0,0])\n", "ax.set_xlim(300000,1000000)\n", "ax.set_ylim(4050000,4350000)\n", "#ax.set_aspect('equal')\n", "plt.plot(mc[0], mc[1], 'c^', label='Mean Center')\n", "plt.legend(numpoints=1)\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we calculate the Euclidean distances between every event point and Mean Center (Euclidean Median), and sum them up, we can see that Euclidean Median is the optimal point in iterms of minimizing the Euclidean distances to all the event points." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "73007071.24620631\n", "72780262.40401942\n", "True\n" ] } ], "source": [ "from pointpats import dtot\n", "print(dtot(mc, pp.points))\n", "print(dtot(em, pp.points))\n", "print(dtot(mc, pp.points) > dtot(em, pp.points))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "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": "3.7.3" }, "widgets": { "state": {}, "version": "1.1.2" } }, "nbformat": 4, "nbformat_minor": 1 }