.. _fasterpolynomialfeaturesrst:

==========================
Faster Polynomial Features
==========================


.. only:: html

    **Links:** :download:`notebook <faster_polynomial_features.ipynb>`, :downloadlink:`html <faster_polynomial_features2html.html>`, :download:`PDF <faster_polynomial_features.pdf>`, :download:`python <faster_polynomial_features.py>`, :downloadlink:`slides <faster_polynomial_features.slides.html>`, :githublink:`GitHub|_doc/notebooks/sklearn/faster_polynomial_features.ipynb|*`


.. code:: ipython3

    from jyquickhelper import add_notebook_menu
    add_notebook_menu()






.. contents::
    :local:





.. code:: ipython3

    %matplotlib inline

Polynomial Features
-------------------

The current implementation of
`PolynomialFeatures <https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.PolynomialFeatures.html>`__
(0.20.2) implements a term by term product for each pair
:math:`X_i, X_j` of features where :math:`i \leqslant j` which is not
the most efficient way to do it.

.. code:: ipython3

    import numpy.random
    X = numpy.random.random((100, 5))

.. code:: ipython3

    from sklearn.preprocessing import PolynomialFeatures
    poly = PolynomialFeatures(degree=2)
    Xpoly = poly.fit_transform(X)
    poly.get_feature_names()




.. parsed-literal::
    ['1',
     'x0',
     'x1',
     'x2',
     'x3',
     'x4',
     'x0^2',
     'x0 x1',
     'x0 x2',
     'x0 x3',
     'x0 x4',
     'x1^2',
     'x1 x2',
     'x1 x3',
     'x1 x4',
     'x2^2',
     'x2 x3',
     'x2 x4',
     'x3^2',
     'x3 x4',
     'x4^2']



.. code:: ipython3

    %timeit poly.transform(X)


.. parsed-literal::
    114 µs ± 12.4 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)


The class
`ExtendedFeatures <http://www.xavierdupre.fr/app/mlinsights/helpsphinx/mlinsights/mlmodel/extended_features.html>`__
implements a different way to compute the polynomial features as it
tries to reduce the number of calls to numpy by using broacasted vector
multplications.

.. code:: ipython3

    from mlinsights.mlmodel import ExtendedFeatures
    ext = ExtendedFeatures(poly_degree=2)
    Xpoly = ext.fit_transform(X)
    ext.get_feature_names()




.. parsed-literal::
    ['1',
     'x0',
     'x1',
     'x2',
     'x3',
     'x4',
     'x0^2',
     'x0 x1',
     'x0 x2',
     'x0 x3',
     'x0 x4',
     'x1^2',
     'x1 x2',
     'x1 x3',
     'x1 x4',
     'x2^2',
     'x2 x3',
     'x2 x4',
     'x3^2',
     'x3 x4',
     'x4^2']



.. code:: ipython3

    %timeit ext.transform(X)


.. parsed-literal::
    68.7 µs ± 10.6 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)


Comparison with 5 features
--------------------------

.. code:: ipython3

    from cpyquickhelper.numbers import measure_time

.. code:: ipython3

    res = []
    for n in [1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, 2000, 
              5000, 10000, 20000, 50000, 100000, 200000]:
        X = numpy.random.random((n, 5))
        poly.fit(X)
        ext.fit(X)
        r1 = measure_time("poly.transform(X)", context=dict(X=X, poly=poly), repeat=5, number=10, div_by_number=True)
        r2 = measure_time("ext.transform(X)", context=dict(X=X, ext=ext), repeat=5, number=10, div_by_number=True)
        r3 = measure_time("poly.fit_transform(X)", context=dict(X=X, poly=poly), repeat=5, number=10, div_by_number=True)
        r4 = measure_time("ext.fit_transform(X)", context=dict(X=X, ext=ext), repeat=5, number=10, div_by_number=True)
        r1["name"] = "poly"
        r2["name"] = "ext"
        r3["name"] = "poly+fit"
        r4["name"] = "ext+fit"
        r1["size"] = n
        r2["size"] = n
        r3["size"] = n
        r4["size"] = n
        res.append(r1)
        res.append(r2)
        res.append(r3)
        res.append(r4)
        
    import pandas
    df = pandas.DataFrame(res)
    df.tail()






.. raw:: html

    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

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        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>average</th>
          <th>deviation</th>
          <th>min_exec</th>
          <th>max_exec</th>
          <th>repeat</th>
          <th>number</th>
          <th>context_size</th>
          <th>name</th>
          <th>size</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <td>63</td>
          <td>0.037830</td>
          <td>0.005577</td>
          <td>0.031248</td>
          <td>0.044832</td>
          <td>5</td>
          <td>10</td>
          <td>240</td>
          <td>ext+fit</td>
          <td>100000</td>
        </tr>
        <tr>
          <td>64</td>
          <td>0.072671</td>
          <td>0.005360</td>
          <td>0.067559</td>
          <td>0.082539</td>
          <td>5</td>
          <td>10</td>
          <td>240</td>
          <td>poly</td>
          <td>200000</td>
        </tr>
        <tr>
          <td>65</td>
          <td>0.075712</td>
          <td>0.018271</td>
          <td>0.060476</td>
          <td>0.100143</td>
          <td>5</td>
          <td>10</td>
          <td>240</td>
          <td>ext</td>
          <td>200000</td>
        </tr>
        <tr>
          <td>66</td>
          <td>0.106755</td>
          <td>0.019861</td>
          <td>0.079880</td>
          <td>0.139184</td>
          <td>5</td>
          <td>10</td>
          <td>240</td>
          <td>poly+fit</td>
          <td>200000</td>
        </tr>
        <tr>
          <td>67</td>
          <td>0.074090</td>
          <td>0.009142</td>
          <td>0.063925</td>
          <td>0.085899</td>
          <td>5</td>
          <td>10</td>
          <td>240</td>
          <td>ext+fit</td>
          <td>200000</td>
        </tr>
      </tbody>
    </table>
    </div>



.. code:: ipython3

    piv = df.pivot("size", "name", "average")
    piv[:5]






.. raw:: html

    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
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        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th>name</th>
          <th>ext</th>
          <th>ext+fit</th>
          <th>poly</th>
          <th>poly+fit</th>
        </tr>
        <tr>
          <th>size</th>
          <th></th>
          <th></th>
          <th></th>
          <th></th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <td>1</td>
          <td>0.000068</td>
          <td>0.000402</td>
          <td>0.000238</td>
          <td>0.000275</td>
        </tr>
        <tr>
          <td>2</td>
          <td>0.000066</td>
          <td>0.000156</td>
          <td>0.000166</td>
          <td>0.000213</td>
        </tr>
        <tr>
          <td>5</td>
          <td>0.000031</td>
          <td>0.000427</td>
          <td>0.000165</td>
          <td>0.000196</td>
        </tr>
        <tr>
          <td>10</td>
          <td>0.000048</td>
          <td>0.000237</td>
          <td>0.000134</td>
          <td>0.000306</td>
        </tr>
        <tr>
          <td>20</td>
          <td>0.000070</td>
          <td>0.000188</td>
          <td>0.000109</td>
          <td>0.000153</td>
        </tr>
      </tbody>
    </table>
    </div>



.. code:: ipython3

    ax = piv.plot(logy=True, logx=True)
    ax.set_title("Polynomial Features for 5 features\ndegree=2")
    ax.set_ylabel("seconds")
    ax.set_xlabel("number of observations");



.. image:: faster_polynomial_features_14_0.png


The gain is mostly visible for small dimensions.

Comparison with 1000 observations
---------------------------------

In this experiment, the number of observations is fixed to 1000 but the
number of features varies.

.. code:: ipython3

    poly = PolynomialFeatures(degree=2)
    ext = ExtendedFeatures(poly_degree=2)
    # implementation of PolynomialFeatures in 0.20.2
    extslow = ExtendedFeatures(poly_degree=2, kind="poly-slow") 
    
    
    res = []
    for n in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 40, 50]:
        X = numpy.random.random((1000, n))
        poly.fit(X)
        ext.fit(X)
        extslow.fit(X)
        r1 = measure_time("poly.transform(X)", context=dict(X=X, poly=poly), repeat=5, number=30, div_by_number=True)
        r2 = measure_time("ext.transform(X)", context=dict(X=X, ext=ext), repeat=5, number=30, div_by_number=True)
        r3 = measure_time("extslow.transform(X)", context=dict(X=X, extslow=extslow), repeat=5, number=30, div_by_number=True)
        r1["name"] = "poly"
        r2["name"] = "ext"
        r3["name"] = "extslow"
        r1["nfeat"] = n
        r2["nfeat"] = n
        r3["nfeat"] = n
        x1 = poly.transform(X)
        x2 = ext.transform(X)
        x3 = extslow.transform(X)
        r1["numf"] = x1.shape[1]
        r2["numf"] = x2.shape[1]
        r3["numf"] = x3.shape[1]
        res.append(r1)
        res.append(r2)
        res.append(r3)
        
    import pandas
    df = pandas.DataFrame(res)
    df.tail()






.. raw:: html

    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
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        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>average</th>
          <th>deviation</th>
          <th>min_exec</th>
          <th>max_exec</th>
          <th>repeat</th>
          <th>number</th>
          <th>context_size</th>
          <th>name</th>
          <th>nfeat</th>
          <th>numf</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <td>37</td>
          <td>0.009331</td>
          <td>0.001603</td>
          <td>0.008280</td>
          <td>0.012519</td>
          <td>5</td>
          <td>30</td>
          <td>240</td>
          <td>ext</td>
          <td>40</td>
          <td>861</td>
        </tr>
        <tr>
          <td>38</td>
          <td>0.022619</td>
          <td>0.002868</td>
          <td>0.018793</td>
          <td>0.026324</td>
          <td>5</td>
          <td>30</td>
          <td>240</td>
          <td>extslow</td>
          <td>40</td>
          <td>861</td>
        </tr>
        <tr>
          <td>39</td>
          <td>0.013188</td>
          <td>0.000370</td>
          <td>0.012828</td>
          <td>0.013888</td>
          <td>5</td>
          <td>30</td>
          <td>240</td>
          <td>poly</td>
          <td>50</td>
          <td>1326</td>
        </tr>
        <tr>
          <td>40</td>
          <td>0.012817</td>
          <td>0.000102</td>
          <td>0.012700</td>
          <td>0.012951</td>
          <td>5</td>
          <td>30</td>
          <td>240</td>
          <td>ext</td>
          <td>50</td>
          <td>1326</td>
        </tr>
        <tr>
          <td>41</td>
          <td>0.030384</td>
          <td>0.000717</td>
          <td>0.029955</td>
          <td>0.031813</td>
          <td>5</td>
          <td>30</td>
          <td>240</td>
          <td>extslow</td>
          <td>50</td>
          <td>1326</td>
        </tr>
      </tbody>
    </table>
    </div>



.. code:: ipython3

    piv = df.pivot("nfeat", "name", "average")
    piv[:5]






.. raw:: html

    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th>name</th>
          <th>ext</th>
          <th>extslow</th>
          <th>poly</th>
        </tr>
        <tr>
          <th>nfeat</th>
          <th></th>
          <th></th>
          <th></th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <td>1</td>
          <td>0.000026</td>
          <td>0.000059</td>
          <td>0.000152</td>
        </tr>
        <tr>
          <td>2</td>
          <td>0.000055</td>
          <td>0.000100</td>
          <td>0.000113</td>
        </tr>
        <tr>
          <td>3</td>
          <td>0.000161</td>
          <td>0.000381</td>
          <td>0.000237</td>
        </tr>
        <tr>
          <td>4</td>
          <td>0.000148</td>
          <td>0.000221</td>
          <td>0.000219</td>
        </tr>
        <tr>
          <td>5</td>
          <td>0.000185</td>
          <td>0.000340</td>
          <td>0.000236</td>
        </tr>
      </tbody>
    </table>
    </div>



.. code:: ipython3

    ax = piv.plot(logy=True, logx=True)
    ax.set_title("Polynomial Features for 1000 observations\ndegree=2")
    ax.set_ylabel("seconds")
    ax.set_xlabel("number of features");



.. image:: faster_polynomial_features_19_0.png


It is twice faster.

Comparison for different degrees
--------------------------------

In this experiment, the number of observations and features is fixed,
the degree increases.

.. code:: ipython3

    res = []
    for n in [2, 3, 4, 5, 6, 7, 8]:
        X = numpy.random.random((1000, 4))
        poly = PolynomialFeatures(degree=n)
        ext = ExtendedFeatures(poly_degree=n)
        poly.fit(X)
        ext.fit(X)
        r1 = measure_time("poly.transform(X)", context=dict(X=X, poly=poly), repeat=5, number=30, div_by_number=True)
        r2 = measure_time("ext.transform(X)", context=dict(X=X, ext=ext), repeat=5, number=30, div_by_number=True)
        r1["name"] = "poly"
        r2["name"] = "ext"
        r1["degree"] = n
        r2["degree"] = n
        x1 = poly.transform(X)
        x2 = ext.transform(X)
        r1["numf"] = x1.shape[1]
        r2["numf"] = x2.shape[1]
        res.append(r1)
        res.append(r2)
        
    import pandas
    df = pandas.DataFrame(res)
    df.tail()






.. raw:: html

    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>average</th>
          <th>deviation</th>
          <th>min_exec</th>
          <th>max_exec</th>
          <th>repeat</th>
          <th>number</th>
          <th>context_size</th>
          <th>name</th>
          <th>degree</th>
          <th>numf</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <td>9</td>
          <td>0.001960</td>
          <td>0.000067</td>
          <td>0.001915</td>
          <td>0.002094</td>
          <td>5</td>
          <td>30</td>
          <td>240</td>
          <td>ext</td>
          <td>6</td>
          <td>210</td>
        </tr>
        <tr>
          <td>10</td>
          <td>0.003131</td>
          <td>0.000118</td>
          <td>0.003009</td>
          <td>0.003327</td>
          <td>5</td>
          <td>30</td>
          <td>240</td>
          <td>poly</td>
          <td>7</td>
          <td>330</td>
        </tr>
        <tr>
          <td>11</td>
          <td>0.003076</td>
          <td>0.000233</td>
          <td>0.002845</td>
          <td>0.003393</td>
          <td>5</td>
          <td>30</td>
          <td>240</td>
          <td>ext</td>
          <td>7</td>
          <td>330</td>
        </tr>
        <tr>
          <td>12</td>
          <td>0.004299</td>
          <td>0.000046</td>
          <td>0.004243</td>
          <td>0.004367</td>
          <td>5</td>
          <td>30</td>
          <td>240</td>
          <td>poly</td>
          <td>8</td>
          <td>495</td>
        </tr>
        <tr>
          <td>13</td>
          <td>0.004157</td>
          <td>0.000035</td>
          <td>0.004114</td>
          <td>0.004217</td>
          <td>5</td>
          <td>30</td>
          <td>240</td>
          <td>ext</td>
          <td>8</td>
          <td>495</td>
        </tr>
      </tbody>
    </table>
    </div>



.. code:: ipython3

    piv = df.pivot("degree", "name", "average")
    piv[:5]






.. raw:: html

    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th>name</th>
          <th>ext</th>
          <th>poly</th>
        </tr>
        <tr>
          <th>degree</th>
          <th></th>
          <th></th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <td>2</td>
          <td>0.000140</td>
          <td>0.000312</td>
        </tr>
        <tr>
          <td>3</td>
          <td>0.000304</td>
          <td>0.000363</td>
        </tr>
        <tr>
          <td>4</td>
          <td>0.000506</td>
          <td>0.000579</td>
        </tr>
        <tr>
          <td>5</td>
          <td>0.000715</td>
          <td>0.000789</td>
        </tr>
        <tr>
          <td>6</td>
          <td>0.001960</td>
          <td>0.002032</td>
        </tr>
      </tbody>
    </table>
    </div>



.. code:: ipython3

    ax = piv.plot(logy=True, logx=True)
    ax.set_title("Polynomial Features for 1000 observations\nnumber of features is 4")
    ax.set_ylabel("seconds")
    ax.set_xlabel("degree");



.. image:: faster_polynomial_features_24_0.png


It is worth transposing.

Same experiment with interaction_only=True
------------------------------------------

.. code:: ipython3

    res = []
    for n in [1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, 2000, 
              5000, 10000, 20000, 50000, 100000, 200000]:
        poly = PolynomialFeatures(degree=2, interaction_only=True)
        ext = ExtendedFeatures(poly_degree=2, poly_interaction_only=True)
        X = numpy.random.random((n, 5))
        poly.fit(X)
        ext.fit(X)
        r1 = measure_time("poly.transform(X)", context=dict(X=X, poly=poly), repeat=2, number=30, div_by_number=True)
        r2 = measure_time("ext.transform(X)", context=dict(X=X, ext=ext), repeat=2, number=30, div_by_number=True)
        r1["name"] = "poly"
        r2["name"] = "ext"
        r1["size"] = n
        r2["size"] = n
        res.append(r1)
        res.append(r2)
        
    import pandas
    df = pandas.DataFrame(res)
    df.tail()






.. raw:: html

    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>average</th>
          <th>deviation</th>
          <th>min_exec</th>
          <th>max_exec</th>
          <th>repeat</th>
          <th>number</th>
          <th>context_size</th>
          <th>name</th>
          <th>size</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <td>29</td>
          <td>0.010691</td>
          <td>0.000073</td>
          <td>0.010618</td>
          <td>0.010764</td>
          <td>2</td>
          <td>30</td>
          <td>240</td>
          <td>ext</td>
          <td>50000</td>
        </tr>
        <tr>
          <td>30</td>
          <td>0.026612</td>
          <td>0.000794</td>
          <td>0.025817</td>
          <td>0.027406</td>
          <td>2</td>
          <td>30</td>
          <td>240</td>
          <td>poly</td>
          <td>100000</td>
        </tr>
        <tr>
          <td>31</td>
          <td>0.025052</td>
          <td>0.001583</td>
          <td>0.023469</td>
          <td>0.026635</td>
          <td>2</td>
          <td>30</td>
          <td>240</td>
          <td>ext</td>
          <td>100000</td>
        </tr>
        <tr>
          <td>32</td>
          <td>0.058772</td>
          <td>0.001345</td>
          <td>0.057427</td>
          <td>0.060118</td>
          <td>2</td>
          <td>30</td>
          <td>240</td>
          <td>poly</td>
          <td>200000</td>
        </tr>
        <tr>
          <td>33</td>
          <td>0.054771</td>
          <td>0.004555</td>
          <td>0.050216</td>
          <td>0.059327</td>
          <td>2</td>
          <td>30</td>
          <td>240</td>
          <td>ext</td>
          <td>200000</td>
        </tr>
      </tbody>
    </table>
    </div>



.. code:: ipython3

    piv = df.pivot("size", "name", "average")
    piv[:5]






.. raw:: html

    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th>name</th>
          <th>ext</th>
          <th>poly</th>
        </tr>
        <tr>
          <th>size</th>
          <th></th>
          <th></th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <td>1</td>
          <td>0.000042</td>
          <td>0.000086</td>
        </tr>
        <tr>
          <td>2</td>
          <td>0.000034</td>
          <td>0.000104</td>
        </tr>
        <tr>
          <td>5</td>
          <td>0.000068</td>
          <td>0.000089</td>
        </tr>
        <tr>
          <td>10</td>
          <td>0.000032</td>
          <td>0.000092</td>
        </tr>
        <tr>
          <td>20</td>
          <td>0.000040</td>
          <td>0.000103</td>
        </tr>
      </tbody>
    </table>
    </div>



.. code:: ipython3

    ax = piv.plot(logy=True, logx=True)
    ax.set_title("Polynomial Features for 5 features\ndegree is 2 + interaction_only=True")
    ax.set_ylabel("seconds")
    ax.set_xlabel("N obs");



.. image:: faster_polynomial_features_29_0.png


Memory profiler
---------------

.. code:: ipython3

    from memory_profiler import memory_usage
    poly = PolynomialFeatures(degree=2, interaction_only=True)
    poly.fit(X)
    memory_usage((poly.transform, (X,)), interval=0.1, max_usage=True)




.. parsed-literal::
    258.02734375



.. code:: ipython3

    def pick_value(v):
        try:
            return v[0]
        except TypeError:
            return v
    
    res = []
    for n in [10000, 50000, 100000, 200000]:
        X = numpy.random.random((n, 50))
        print(n)
        poly = PolynomialFeatures(degree=2, interaction_only=True)
        ext = ExtendedFeatures(poly_degree=2, poly_interaction_only=True)
        poly.fit(X)
        ext.fit(X)
        r1 = memory_usage((poly.transform, (X,)), interval=0.1, max_usage=True)
        r2 = memory_usage((ext.transform, (X,)), interval=0.1, max_usage=True)
        r1 = {"memory": pick_value(r1)}
        r2 = {"memory": pick_value(r2)}
        r1["name"] = "poly"
        r2["name"] = "ext"
        r1["size"] = n
        r2["size"] = n
        res.append(r1)
        res.append(r2)
        
    import pandas
    df = pandas.DataFrame(res)
    df.tail()


.. parsed-literal::
    10000
    50000
    100000
    200000






.. raw:: html

    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>memory</th>
          <th>name</th>
          <th>size</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <td>3</td>
          <td>699.679688</td>
          <td>ext</td>
          <td>50000</td>
        </tr>
        <tr>
          <td>4</td>
          <td>1243.664062</td>
          <td>poly</td>
          <td>100000</td>
        </tr>
        <tr>
          <td>5</td>
          <td>1205.515625</td>
          <td>ext</td>
          <td>100000</td>
        </tr>
        <tr>
          <td>6</td>
          <td>1952.316406</td>
          <td>poly</td>
          <td>200000</td>
        </tr>
        <tr>
          <td>7</td>
          <td>2029.765625</td>
          <td>ext</td>
          <td>200000</td>
        </tr>
      </tbody>
    </table>
    </div>



.. code:: ipython3

    piv = df.pivot("size", "name", "memory")
    piv[:5]






.. raw:: html

    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th>name</th>
          <th>ext</th>
          <th>poly</th>
        </tr>
        <tr>
          <th>size</th>
          <th></th>
          <th></th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <td>10000</td>
          <td>392.445312</td>
          <td>396.347656</td>
        </tr>
        <tr>
          <td>50000</td>
          <td>699.679688</td>
          <td>718.839844</td>
        </tr>
        <tr>
          <td>100000</td>
          <td>1205.515625</td>
          <td>1243.664062</td>
        </tr>
        <tr>
          <td>200000</td>
          <td>2029.765625</td>
          <td>1952.316406</td>
        </tr>
      </tbody>
    </table>
    </div>



.. code:: ipython3

    ax = piv.plot(logy=True, logx=True)
    ax.set_title("Polynomial Features for 50 features\ndegree is 2 - memory")
    ax.set_ylabel("Mb")
    ax.set_xlabel("N obs");



.. image:: faster_polynomial_features_34_0.png