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04_pooled.html
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04_pooled.html
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<li><a class="reference internal" href="#Sample-Data">Sample Data</a></li>
<li><a class="reference internal" href="#Default:-Quintiles">Default: Quintiles</a></li>
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<section id="Pooled-Classification">
<h1>Pooled Classification<a class="headerlink" href="#Pooled-Classification" title="Link to this heading">¶</a></h1>
<p>A common workflow with longitudinal spatial data is to apply the same classification scheme to an attribute over different time periods. More specifically, one would like to keep the class breaks the same over each period and examine how the mass of the distribution changes over these classes in the different periods.</p>
<p>The <code class="docutils literal notranslate"><span class="pre">Pooled</span></code> classifier supports this workflow.</p>
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<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>import mapclassify
import numpy
mapclassify.__version__
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'2.4.2+78.gc62d2d7.dirty'
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</div>
<section id="Sample-Data">
<h2>Sample Data<a class="headerlink" href="#Sample-Data" title="Link to this heading">¶</a></h2>
<p>We construct a synthetic dataset composed of 20 cross-sectional units at three time points. Here the mean of the series is increasing over time.</p>
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<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>n = 20
data = numpy.array([numpy.arange(n) + i * n for i in range(1, 4)]).T
data.shape
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(20, 3)
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array([[20, 40, 60],
[21, 41, 61],
[22, 42, 62],
[23, 43, 63],
[24, 44, 64],
[25, 45, 65],
[26, 46, 66],
[27, 47, 67],
[28, 48, 68],
[29, 49, 69],
[30, 50, 70],
[31, 51, 71],
[32, 52, 72],
[33, 53, 73],
[34, 54, 74],
[35, 55, 75],
[36, 56, 76],
[37, 57, 77],
[38, 58, 78],
[39, 59, 79]])
</pre></div></div>
</div>
</section>
<section id="Default:-Quintiles">
<h2>Default: Quintiles<a class="headerlink" href="#Default:-Quintiles" title="Link to this heading">¶</a></h2>
<p>The default is to apply a <a class="reference external" href="https://en.wikipedia.org/wiki/Vectorization_(mathematics)">vec</a> operator to the data matrix and treat the observations as a single collection. Here the quantiles of the pooled data are obtained.</p>
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<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>res = mapclassify.Pooled(data)
res
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Pooled Classifier
Pooled Quantiles
Interval Count
----------------------
[20.00, 31.80] | 12
(31.80, 43.60] | 8
(43.60, 55.40] | 0
(55.40, 67.20] | 0
(67.20, 79.00] | 0
Pooled Quantiles
Interval Count
----------------------
[20.00, 31.80] | 0
(31.80, 43.60] | 4
(43.60, 55.40] | 12
(55.40, 67.20] | 4
(67.20, 79.00] | 0
Pooled Quantiles
Interval Count
----------------------
[20.00, 31.80] | 0
(31.80, 43.60] | 0
(43.60, 55.40] | 0
(55.40, 67.20] | 8
(67.20, 79.00] | 12
</pre></div></div>
</div>
<p>Note that the class definitions are constant across the periods.</p>
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array([15, 5, 0, 0])
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array([ 0, 0, 5, 15])
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array([15, 15, 15, 15])
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</pre></div>
</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>res
</pre></div>
</div>
</div>
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</div>
<div class="output_area docutils container">
<div class="highlight"><pre>
Pooled Classifier
Pooled Quantiles
Interval Count
----------------------
[20.00, 34.75] | 15
(34.75, 49.50] | 5
(49.50, 64.25] | 0
(64.25, 79.00] | 0
Pooled Quantiles
Interval Count
----------------------
[20.00, 34.75] | 0
(34.75, 49.50] | 10
(49.50, 64.25] | 10
(64.25, 79.00] | 0
Pooled Quantiles
Interval Count
----------------------
[20.00, 34.75] | 0
(34.75, 49.50] | 0
(49.50, 64.25] | 5
(64.25, 79.00] | 15
</pre></div></div>
</div>
<p>Extract the pooled classification objects for each column.</p>
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</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>c0, c1, c2 = res.col_classifiers
c0
</pre></div>
</div>
</div>
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</div>
<div class="output_area docutils container">
<div class="highlight"><pre>
Pooled Quantiles
Interval Count
----------------------
[20.00, 34.75] | 15
(34.75, 49.50] | 5
(49.50, 64.25] | 0
(64.25, 79.00] | 0
</pre></div></div>
</div>
<p>Compare to the unrestricted classifier for the first column…</p>
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<div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[11]:
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</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>mapclassify.Quantiles(c0.y, k=4)
</pre></div>
</div>
</div>
<div class="nboutput nblast docutils container">
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</div>
<div class="output_area docutils container">
<div class="highlight"><pre>
Quantiles
Interval Count
----------------------
[20.00, 24.75] | 5
(24.75, 29.50] | 5
(29.50, 34.25] | 5
(34.25, 39.00] | 5
</pre></div></div>
</div>
<p>… and the last column comparisions.</p>
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</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>c2
</pre></div>
</div>
</div>
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</div>
<div class="output_area docutils container">
<div class="highlight"><pre>
Pooled Quantiles
Interval Count
----------------------
[20.00, 34.75] | 0
(34.75, 49.50] | 0
(49.50, 64.25] | 5
(64.25, 79.00] | 15
</pre></div></div>
</div>
<div class="nbinput docutils container">
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</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>mapclassify.Quantiles(c2.y, k=4)
</pre></div>
</div>
</div>
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</div>
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<div class="highlight"><pre>
Quantiles
Interval Count
----------------------
[60.00, 64.75] | 5
(64.75, 69.50] | 5
(69.50, 74.25] | 5
(74.25, 79.00] | 5
</pre></div></div>
</div>
</section>
<section id="Non-default-classifier:-BoxPlot">
<h2>Non-default classifier: BoxPlot<a class="headerlink" href="#Non-default-classifier:-BoxPlot" title="Link to this heading">¶</a></h2>
<div class="nbinput docutils container">
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</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>res = mapclassify.Pooled(data, classifier="BoxPlot", hinge=1.5)
res
</pre></div>
</div>
</div>
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</pre></div>
</div>
<div class="output_area docutils container">
<div class="highlight"><pre>
Pooled Classifier
Pooled BoxPlot
Interval Count
------------------------
( -inf, -9.50] | 0
( -9.50, 34.75] | 15
( 34.75, 49.50] | 5
( 49.50, 64.25] | 0
( 64.25, 108.50] | 0
Pooled BoxPlot
Interval Count
------------------------
( -inf, -9.50] | 0
( -9.50, 34.75] | 0
( 34.75, 49.50] | 10
( 49.50, 64.25] | 10
( 64.25, 108.50] | 0
Pooled BoxPlot
Interval Count
------------------------
( -inf, -9.50] | 0
( -9.50, 34.75] | 0
( 34.75, 49.50] | 0
( 49.50, 64.25] | 5
( 64.25, 108.50] | 15
</pre></div></div>
</div>
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</pre></div>
</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>res.col_classifiers[0].bins
</pre></div>
</div>
</div>
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</pre></div>
</div>
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<div class="highlight"><pre>
array([ -9.5 , 34.75, 49.5 , 64.25, 108.5 ])
</pre></div></div>
</div>
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</pre></div>
</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>c0, c1, c2 = res.col_classifiers
</pre></div>
</div>
</div>
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</pre></div>
</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>c0.yb
</pre></div>
</div>
</div>
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<div class="highlight"><pre>
array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2])
</pre></div></div>
</div>
<div class="nbinput nblast docutils container">
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</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>c00 = mapclassify.BoxPlot(c0.y, hinge=3)
</pre></div>
</div>
</div>
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</pre></div>
</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>c00.yb
</pre></div>
</div>
</div>
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<div class="highlight"><pre>
array([1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4])
</pre></div></div>
</div>
<div class="nbinput docutils container">
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</pre></div>
</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>c00
</pre></div>
</div>
</div>
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</div>
<div class="output_area docutils container">
<div class="highlight"><pre>
BoxPlot
Interval Count
----------------------
( -inf, -3.75] | 0
(-3.75, 24.75] | 5
(24.75, 29.50] | 5
(29.50, 34.25] | 5
(34.25, 62.75] | 5
</pre></div></div>
</div>
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</pre></div>
</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>c0
</pre></div>
</div>
</div>
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</pre></div>
</div>
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<div class="highlight"><pre>
Pooled BoxPlot
Interval Count
------------------------
( -inf, -9.50] | 0
( -9.50, 34.75] | 15
( 34.75, 49.50] | 5
( 49.50, 64.25] | 0
( 64.25, 108.50] | 0
</pre></div></div>
</div>
</section>
<section id="Non-default-classifier:-FisherJenks">
<h2>Non-default classifier: FisherJenks<a class="headerlink" href="#Non-default-classifier:-FisherJenks" title="Link to this heading">¶</a></h2>
<div class="nbinput docutils container">
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</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>res = mapclassify.Pooled(data, classifier="FisherJenks", k=5)
res
</pre></div>
</div>
</div>
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Pooled Classifier
Pooled FisherJenks
Interval Count
----------------------
[20.00, 31.00] | 12
(31.00, 43.00] | 8
(43.00, 55.00] | 0
(55.00, 67.00] | 0
(67.00, 79.00] | 0
Pooled FisherJenks
Interval Count
----------------------
[20.00, 31.00] | 0
(31.00, 43.00] | 4
(43.00, 55.00] | 12
(55.00, 67.00] | 4
(67.00, 79.00] | 0
Pooled FisherJenks
Interval Count
----------------------
[20.00, 31.00] | 0
(31.00, 43.00] | 0
(43.00, 55.00] | 0
(55.00, 67.00] | 8
(67.00, 79.00] | 12
</pre></div></div>
</div>
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</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>c0, c1, c2 = res.col_classifiers
mapclassify.FisherJenks(c0.y, k=5)
</pre></div>
</div>
</div>
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FisherJenks
Interval Count
----------------------
[20.00, 23.00] | 4
(23.00, 27.00] | 4
(27.00, 31.00] | 4
(31.00, 35.00] | 4
(35.00, 39.00] | 4
</pre></div></div>
</div>
</section>
<section id="Non-default-classifier:-MaximumBreaks">
<h2>Non-default classifier: MaximumBreaks<a class="headerlink" href="#Non-default-classifier:-MaximumBreaks" title="Link to this heading">¶</a></h2>
<div class="nbinput docutils container">
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</pre></div>
</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>data[1, 0] = 10
data[1, 1] = 10
data[1, 2] = 10
data[9, 2] = 10
data
</pre></div>
</div>
</div>
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array([[20, 40, 60],
[10, 10, 10],
[22, 42, 62],
[23, 43, 63],
[24, 44, 64],
[25, 45, 65],
[26, 46, 66],
[27, 47, 67],
[28, 48, 68],
[29, 49, 10],
[30, 50, 70],
[31, 51, 71],
[32, 52, 72],
[33, 53, 73],
[34, 54, 74],
[35, 55, 75],
[36, 56, 76],
[37, 57, 77],
[38, 58, 78],
[39, 59, 79]])
</pre></div></div>
</div>
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</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>res = mapclassify.Pooled(data, classifier="MaximumBreaks", k=5)
res
</pre></div>
</div>
</div>
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Pooled Classifier
Pooled MaximumBreaks
Interval Count
----------------------
[10.00, 15.00] | 1
(15.00, 21.00] | 1
(21.00, 41.00] | 18
(41.00, 61.00] | 0
(61.00, 79.00] | 0
Pooled MaximumBreaks
Interval Count
----------------------
[10.00, 15.00] | 1
(15.00, 21.00] | 0
(21.00, 41.00] | 1
(41.00, 61.00] | 18
(61.00, 79.00] | 0
Pooled MaximumBreaks
Interval Count
----------------------
[10.00, 15.00] | 2
(15.00, 21.00] | 0
(21.00, 41.00] | 0
(41.00, 61.00] | 1
(61.00, 79.00] | 17
</pre></div></div>
</div>
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</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>c0, c1, c2 = res.col_classifiers
c0
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</div>
</div>
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Pooled MaximumBreaks
Interval Count
----------------------
[10.00, 15.00] | 1
(15.00, 21.00] | 1
(21.00, 41.00] | 18
(41.00, 61.00] | 0
(61.00, 79.00] | 0
</pre></div></div>
</div>
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</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>c0.y
</pre></div>
</div>
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array([20, 10, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36,
37, 38, 39])
</pre></div></div>
</div>
<div class="nbinput nblast docutils container">
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</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>import warnings
</pre></div>
</div>
</div>
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</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>with warnings.catch_warnings():
warnings.filterwarnings("error")
try:
mapclassify.MaximumBreaks(c0.y, k=5)
except UserWarning as e:
print(e)
with warnings.catch_warnings():
warnings.filterwarnings("ignore")
mapclassify.MaximumBreaks(c0.y, k=5)
</pre></div>
</div>
</div>
<div class="nboutput nblast docutils container">
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Insufficient number of unique diffs. Breaks are random.
</pre></div></div>
</div>
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</pre></div>
</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>res = mapclassify.Pooled(
data, classifier="UserDefined", bins=mapclassify.Quantiles(data[:, -1]).bins
)
res
</pre></div>
</div>
</div>
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Pooled Classifier
Pooled UserDefined
Interval Count
----------------------
[10.00, 62.80] | 20
(62.80, 66.60] | 0
(66.60, 71.40] | 0
(71.40, 75.20] | 0
(75.20, 79.00] | 0
Pooled UserDefined
Interval Count
----------------------
[10.00, 62.80] | 20
(62.80, 66.60] | 0
(66.60, 71.40] | 0
(71.40, 75.20] | 0
(75.20, 79.00] | 0
Pooled UserDefined
Interval Count
----------------------
[10.00, 62.80] | 4
(62.80, 66.60] | 4
(66.60, 71.40] | 4
(71.40, 75.20] | 4
(75.20, 79.00] | 4
</pre></div></div>
</div>
<div class="nbinput docutils container">
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</pre></div>
</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>mapclassify.Quantiles(data[:, -1])
</pre></div>
</div>
</div>
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Quantiles
Interval Count
----------------------
[10.00, 62.80] | 4
(62.80, 66.60] | 4
(66.60, 71.40] | 4
(71.40, 75.20] | 4
(75.20, 79.00] | 4
</pre></div></div>
</div>
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</pre></div>
</div>
<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>data[:, -1]
</pre></div>
</div>
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array([60, 10, 62, 63, 64, 65, 66, 67, 68, 10, 70, 71, 72, 73, 74, 75, 76,
77, 78, 79])
</pre></div></div>
</div>
</section>
<section id="Pinning-the-pooling">
<h2>Pinning the pooling<a class="headerlink" href="#Pinning-the-pooling" title="Link to this heading">¶</a></h2>
<p>Another option is to specify a specific subperiod as the definition for the classes in the pooling.</p>
<section id="Pinning-to-the-last-period">
<h3>Pinning to the last period<a class="headerlink" href="#Pinning-to-the-last-period" title="Link to this heading">¶</a></h3>
<p>As an example, we can use the quintles from the third period to defined the pooled classifier:</p>