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<span id="sphx-glr-auto-examples-classification-plot-lda-py"></span><h1>Normal and Shrinkage Linear Discriminant Analysis for classification<a class="headerlink" href="#normal-and-shrinkage-linear-discriminant-analysis-for-classification" title="Permalink to this headline">¶</a></h1>
<p>Shows how shrinkage improves classification.</p>
<img alt="../../_images/sphx_glr_plot_lda_001.png" class="sphx-glr-single-img" src="../../_images/sphx_glr_plot_lda_001.png" />
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">division</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.datasets.make_blobs.html#sklearn.datasets.make_blobs" title="View documentation for sklearn.datasets.make_blobs"><span class="n">make_blobs</span></a>
<span class="kn">from</span> <span class="nn">sklearn.discriminant_analysis</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html#sklearn.discriminant_analysis.LinearDiscriminantAnalysis" title="View documentation for sklearn.discriminant_analysis.LinearDiscriminantAnalysis"><span class="n">LinearDiscriminantAnalysis</span></a>
<span class="n">n_train</span> <span class="o">=</span> <span class="mi">20</span> <span class="c1"># samples for training</span>
<span class="n">n_test</span> <span class="o">=</span> <span class="mi">200</span> <span class="c1"># samples for testing</span>
<span class="n">n_averages</span> <span class="o">=</span> <span class="mi">50</span> <span class="c1"># how often to repeat classification</span>
<span class="n">n_features_max</span> <span class="o">=</span> <span class="mi">75</span> <span class="c1"># maximum number of features</span>
<span class="n">step</span> <span class="o">=</span> <span class="mi">4</span> <span class="c1"># step size for the calculation</span>
<span class="k">def</span> <span class="nf">generate_data</span><span class="p">(</span><span class="n">n_samples</span><span class="p">,</span> <span class="n">n_features</span><span class="p">):</span>
<span class="sd">"""Generate random blob-ish data with noisy features.</span>
<span class="sd"> This returns an array of input data with shape `(n_samples, n_features)`</span>
<span class="sd"> and an array of `n_samples` target labels.</span>
<span class="sd"> Only one feature contains discriminative information, the other features</span>
<span class="sd"> contain only noise.</span>
<span class="sd"> """</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.make_blobs.html#sklearn.datasets.make_blobs" title="View documentation for sklearn.datasets.make_blobs"><span class="n">make_blobs</span></a><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="n">n_samples</span><span class="p">,</span> <span class="n">n_features</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">centers</span><span class="o">=</span><span class="p">[[</span><span class="o">-</span><span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">]])</span>
<span class="c1"># add non-discriminative features</span>
<span class="k">if</span> <span class="n">n_features</span> <span class="o">></span> <span class="mi">1</span><span class="p">:</span>
<span class="n">X</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.hstack.html#numpy.hstack" title="View documentation for numpy.hstack"><span class="n">np</span><span class="o">.</span><span class="n">hstack</span></a><span class="p">([</span><span class="n">X</span><span class="p">,</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.randn.html#numpy.random.randn" title="View documentation for numpy.random.randn"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span></a><span class="p">(</span><span class="n">n_samples</span><span class="p">,</span> <span class="n">n_features</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)])</span>
<span class="k">return</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span>
<span class="n">acc_clf1</span><span class="p">,</span> <span class="n">acc_clf2</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[]</span>
<span class="n">n_features_range</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n_features_max</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">step</span><span class="p">)</span>
<span class="k">for</span> <span class="n">n_features</span> <span class="ow">in</span> <span class="n">n_features_range</span><span class="p">:</span>
<span class="n">score_clf1</span><span class="p">,</span> <span class="n">score_clf2</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_averages</span><span class="p">):</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">generate_data</span><span class="p">(</span><span class="n">n_train</span><span class="p">,</span> <span class="n">n_features</span><span class="p">)</span>
<span class="n">clf1</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html#sklearn.discriminant_analysis.LinearDiscriminantAnalysis" title="View documentation for sklearn.discriminant_analysis.LinearDiscriminantAnalysis"><span class="n">LinearDiscriminantAnalysis</span></a><span class="p">(</span><span class="n">solver</span><span class="o">=</span><span class="s1">'lsqr'</span><span class="p">,</span> <span class="n">shrinkage</span><span class="o">=</span><span class="s1">'auto'</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">clf2</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html#sklearn.discriminant_analysis.LinearDiscriminantAnalysis" title="View documentation for sklearn.discriminant_analysis.LinearDiscriminantAnalysis"><span class="n">LinearDiscriminantAnalysis</span></a><span class="p">(</span><span class="n">solver</span><span class="o">=</span><span class="s1">'lsqr'</span><span class="p">,</span> <span class="n">shrinkage</span><span class="o">=</span><span class="bp">None</span><span class="p">)</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">generate_data</span><span class="p">(</span><span class="n">n_test</span><span class="p">,</span> <span class="n">n_features</span><span class="p">)</span>
<span class="n">score_clf1</span> <span class="o">+=</span> <span class="n">clf1</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">score_clf2</span> <span class="o">+=</span> <span class="n">clf2</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="n">acc_clf1</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">score_clf1</span> <span class="o">/</span> <span class="n">n_averages</span><span class="p">)</span>
<span class="n">acc_clf2</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">score_clf2</span> <span class="o">/</span> <span class="n">n_averages</span><span class="p">)</span>
<span class="n">features_samples_ratio</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.array.html#numpy.array" title="View documentation for numpy.array"><span class="n">np</span><span class="o">.</span><span class="n">array</span></a><span class="p">(</span><span class="n">n_features_range</span><span class="p">)</span> <span class="o">/</span> <span class="n">n_train</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">features_samples_ratio</span><span class="p">,</span> <span class="n">acc_clf1</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s2">"Linear Discriminant Analysis with shrinkage"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'navy'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.plot.html#matplotlib.pyplot.plot" title="View documentation for matplotlib.pyplot.plot"><span class="n">plt</span><span class="o">.</span><span class="n">plot</span></a><span class="p">(</span><span class="n">features_samples_ratio</span><span class="p">,</span> <span class="n">acc_clf2</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
<span class="n">label</span><span class="o">=</span><span class="s2">"Linear Discriminant Analysis"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'gold'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.xlabel.html#matplotlib.pyplot.xlabel" title="View documentation for matplotlib.pyplot.xlabel"><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span></a><span class="p">(</span><span class="s1">'n_features / n_samples'</span><span class="p">)</span>
<a href="https://matplotlib.org/api/_as_gen/matplotlib.pyplot.ylabel.html#matplotlib.pyplot.ylabel" title="View documentation for matplotlib.pyplot.ylabel"><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span></a><span class="p">(</span><span class="s1">'Classification accuracy'</span><span class="p">)</span>
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