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<ul>
<li><a class="reference internal" href="#"><code class="docutils literal"><span class="pre">sklearn.cross_decomposition</span></code>.CCA</a><ul>
<li><a class="reference internal" href="#examples-using-sklearn-cross-decomposition-cca">Examples using <code class="docutils literal"><span class="pre">sklearn.cross_decomposition.CCA</span></code></a></li>
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<div class="section" id="sklearn-cross-decomposition-cca">
<h1><a class="reference internal" href="../classes.html#module-sklearn.cross_decomposition" title="sklearn.cross_decomposition"><code class="xref py py-mod docutils literal"><span class="pre">sklearn.cross_decomposition</span></code></a>.CCA<a class="headerlink" href="#sklearn-cross-decomposition-cca" title="Permalink to this headline">¶</a></h1>
<dl class="class">
<dt id="sklearn.cross_decomposition.CCA">
<em class="property">class </em><code class="descclassname">sklearn.cross_decomposition.</code><code class="descname">CCA</code><span class="sig-paren">(</span><em>n_components=2</em>, <em>scale=True</em>, <em>max_iter=500</em>, <em>tol=1e-06</em>, <em>copy=True</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/cross_decomposition/cca_.py#L6"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cross_decomposition.CCA" title="Permalink to this definition">¶</a></dt>
<dd><p>CCA Canonical Correlation Analysis.</p>
<p>CCA inherits from PLS with mode=”B” and deflation_mode=”canonical”.</p>
<p>Read more in the <a class="reference internal" href="../cross_decomposition.html#cross-decomposition"><span>User Guide</span></a>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>n_components</strong> : int, (default 2).</p>
<blockquote>
<div><p>number of components to keep.</p>
</div></blockquote>
<p><strong>scale</strong> : boolean, (default True)</p>
<blockquote>
<div><p>whether to scale the data?</p>
</div></blockquote>
<p><strong>max_iter</strong> : an integer, (default 500)</p>
<blockquote>
<div><p>the maximum number of iterations of the NIPALS inner loop</p>
</div></blockquote>
<p><strong>tol</strong> : non-negative real, default 1e-06.</p>
<blockquote>
<div><p>the tolerance used in the iterative algorithm</p>
</div></blockquote>
<p><strong>copy</strong> : boolean</p>
<blockquote>
<div><p>Whether the deflation be done on a copy. Let the default value
to True unless you don’t care about side effects</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Attributes:</th><td class="field-body"><p class="first"><strong>x_weights_</strong> : array, [p, n_components]</p>
<blockquote>
<div><p>X block weights vectors.</p>
</div></blockquote>
<p><strong>y_weights_</strong> : array, [q, n_components]</p>
<blockquote>
<div><p>Y block weights vectors.</p>
</div></blockquote>
<p><strong>x_loadings_</strong> : array, [p, n_components]</p>
<blockquote>
<div><p>X block loadings vectors.</p>
</div></blockquote>
<p><strong>y_loadings_</strong> : array, [q, n_components]</p>
<blockquote>
<div><p>Y block loadings vectors.</p>
</div></blockquote>
<p><strong>x_scores_</strong> : array, [n_samples, n_components]</p>
<blockquote>
<div><p>X scores.</p>
</div></blockquote>
<p><strong>y_scores_</strong> : array, [n_samples, n_components]</p>
<blockquote>
<div><p>Y scores.</p>
</div></blockquote>
<p><strong>x_rotations_</strong> : array, [p, n_components]</p>
<blockquote>
<div><p>X block to latents rotations.</p>
</div></blockquote>
<p><strong>y_rotations_</strong> : array, [q, n_components]</p>
<blockquote>
<div><p>Y block to latents rotations.</p>
</div></blockquote>
<p><strong>n_iter_</strong> : array-like</p>
<blockquote class="last">
<div><p>Number of iterations of the NIPALS inner loop for each
component.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<p class="last"><a class="reference internal" href="sklearn.cross_decomposition.PLSCanonical.html#sklearn.cross_decomposition.PLSCanonical" title="sklearn.cross_decomposition.PLSCanonical"><code class="xref py py-obj docutils literal"><span class="pre">PLSCanonical</span></code></a>, <a class="reference internal" href="sklearn.cross_decomposition.PLSSVD.html#sklearn.cross_decomposition.PLSSVD" title="sklearn.cross_decomposition.PLSSVD"><code class="xref py py-obj docutils literal"><span class="pre">PLSSVD</span></code></a></p>
</div>
<p class="rubric">Notes</p>
<p>For each component k, find the weights u, v that maximizes
max corr(Xk u, Yk v), such that <code class="docutils literal"><span class="pre">|u|</span> <span class="pre">=</span> <span class="pre">|v|</span> <span class="pre">=</span> <span class="pre">1</span></code></p>
<p>Note that it maximizes only the correlations between the scores.</p>
<p>The residual matrix of X (Xk+1) block is obtained by the deflation on the
current X score: x_score.</p>
<p>The residual matrix of Y (Yk+1) block is obtained by deflation on the
current Y score.</p>
<p class="rubric">References</p>
<p>Jacob A. Wegelin. A survey of Partial Least Squares (PLS) methods, with
emphasis on the two-block case. Technical Report 371, Department of
Statistics, University of Washington, Seattle, 2000.</p>
<p>In french but still a reference:
Tenenhaus, M. (1998). La regression PLS: theorie et pratique. Paris:
Editions Technic.</p>
<p class="rubric">Examples</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">sklearn.cross_decomposition</span> <span class="kn">import</span> <span class="n">CCA</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">],</span> <span class="p">[</span><span class="mf">1.</span><span class="p">,</span><span class="mf">0.</span><span class="p">,</span><span class="mf">0.</span><span class="p">],</span> <span class="p">[</span><span class="mf">2.</span><span class="p">,</span><span class="mf">2.</span><span class="p">,</span><span class="mf">2.</span><span class="p">],</span> <span class="p">[</span><span class="mf">3.</span><span class="p">,</span><span class="mf">5.</span><span class="p">,</span><span class="mf">4.</span><span class="p">]]</span>
<span class="gp">>>> </span><span class="n">Y</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">0.1</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.2</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.9</span><span class="p">,</span> <span class="mf">1.1</span><span class="p">],</span> <span class="p">[</span><span class="mf">6.2</span><span class="p">,</span> <span class="mf">5.9</span><span class="p">],</span> <span class="p">[</span><span class="mf">11.9</span><span class="p">,</span> <span class="mf">12.3</span><span class="p">]]</span>
<span class="gp">>>> </span><span class="n">cca</span> <span class="o">=</span> <span class="n">CCA</span><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">cca</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="gp">... </span>
<span class="go">CCA(copy=True, max_iter=500, n_components=1, scale=True, tol=1e-06)</span>
<span class="gp">>>> </span><span class="n">X_c</span><span class="p">,</span> <span class="n">Y_c</span> <span class="o">=</span> <span class="n">cca</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">)</span>
</pre></div>
</div>
<p class="rubric">Methods</p>
<table border="1" class="longtable docutils">
<colgroup>
<col width="10%" />
<col width="90%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td><a class="reference internal" href="#sklearn.cross_decomposition.CCA.fit" title="sklearn.cross_decomposition.CCA.fit"><code class="xref py py-obj docutils literal"><span class="pre">fit</span></code></a>(X, Y)</td>
<td>Fit model to data.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#sklearn.cross_decomposition.CCA.fit_transform" title="sklearn.cross_decomposition.CCA.fit_transform"><code class="xref py py-obj docutils literal"><span class="pre">fit_transform</span></code></a>(X[, y])</td>
<td>Learn and apply the dimension reduction on the train data.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#sklearn.cross_decomposition.CCA.get_params" title="sklearn.cross_decomposition.CCA.get_params"><code class="xref py py-obj docutils literal"><span class="pre">get_params</span></code></a>([deep])</td>
<td>Get parameters for this estimator.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#sklearn.cross_decomposition.CCA.predict" title="sklearn.cross_decomposition.CCA.predict"><code class="xref py py-obj docutils literal"><span class="pre">predict</span></code></a>(X[, copy])</td>
<td>Apply the dimension reduction learned on the train data.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#sklearn.cross_decomposition.CCA.score" title="sklearn.cross_decomposition.CCA.score"><code class="xref py py-obj docutils literal"><span class="pre">score</span></code></a>(X, y[, sample_weight])</td>
<td>Returns the coefficient of determination R^2 of the prediction.</td>
</tr>
<tr class="row-even"><td><a class="reference internal" href="#sklearn.cross_decomposition.CCA.set_params" title="sklearn.cross_decomposition.CCA.set_params"><code class="xref py py-obj docutils literal"><span class="pre">set_params</span></code></a>(**params)</td>
<td>Set the parameters of this estimator.</td>
</tr>
<tr class="row-odd"><td><a class="reference internal" href="#sklearn.cross_decomposition.CCA.transform" title="sklearn.cross_decomposition.CCA.transform"><code class="xref py py-obj docutils literal"><span class="pre">transform</span></code></a>(X[, Y, copy])</td>
<td>Apply the dimension reduction learned on the train data.</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="sklearn.cross_decomposition.CCA.__init__">
<code class="descname">__init__</code><span class="sig-paren">(</span><em>n_components=2</em>, <em>scale=True</em>, <em>max_iter=500</em>, <em>tol=1e-06</em>, <em>copy=True</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/cross_decomposition/cca_.py#L102"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cross_decomposition.CCA.__init__" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="sklearn.cross_decomposition.CCA.fit">
<code class="descname">fit</code><span class="sig-paren">(</span><em>X</em>, <em>Y</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/cross_decomposition/pls_.py#L233"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cross_decomposition.CCA.fit" title="Permalink to this definition">¶</a></dt>
<dd><p>Fit model to data.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>X</strong> : array-like, shape = [n_samples, n_features]</p>
<blockquote>
<div><p>Training vectors, where n_samples in the number of samples and
n_features is the number of predictors.</p>
</div></blockquote>
<p><strong>Y</strong> : array-like of response, shape = [n_samples, n_targets]</p>
<blockquote class="last">
<div><p>Target vectors, where n_samples in the number of samples and
n_targets is the number of response variables.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.cross_decomposition.CCA.fit_transform">
<code class="descname">fit_transform</code><span class="sig-paren">(</span><em>X</em>, <em>y=None</em>, <em>**fit_params</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/cross_decomposition/pls_.py#L437"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cross_decomposition.CCA.fit_transform" title="Permalink to this definition">¶</a></dt>
<dd><p>Learn and apply the dimension reduction on the train data.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>X</strong> : array-like of predictors, shape = [n_samples, p]</p>
<blockquote>
<div><p>Training vectors, where n_samples in the number of samples and
p is the number of predictors.</p>
</div></blockquote>
<p><strong>Y</strong> : array-like of response, shape = [n_samples, q], optional</p>
<blockquote>
<div><p>Training vectors, where n_samples in the number of samples and
q is the number of response variables.</p>
</div></blockquote>
<p><strong>copy</strong> : boolean, default True</p>
<blockquote>
<div><p>Whether to copy X and Y, or perform in-place normalization.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last"><strong>x_scores if Y is not given, (x_scores, y_scores) otherwise.</strong> :</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.cross_decomposition.CCA.get_params">
<code class="descname">get_params</code><span class="sig-paren">(</span><em>deep=True</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/base.py#L199"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cross_decomposition.CCA.get_params" title="Permalink to this definition">¶</a></dt>
<dd><p>Get parameters for this estimator.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>deep: boolean, optional</strong> :</p>
<blockquote>
<div><p>If True, will return the parameters for this estimator and
contained subobjects that are estimators.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>params</strong> : mapping of string to any</p>
<blockquote class="last">
<div><p>Parameter names mapped to their values.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.cross_decomposition.CCA.predict">
<code class="descname">predict</code><span class="sig-paren">(</span><em>X</em>, <em>copy=True</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/cross_decomposition/pls_.py#L412"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cross_decomposition.CCA.predict" title="Permalink to this definition">¶</a></dt>
<dd><p>Apply the dimension reduction learned on the train data.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>X</strong> : array-like of predictors, shape = [n_samples, p]</p>
<blockquote>
<div><p>Training vectors, where n_samples in the number of samples and
p is the number of predictors.</p>
</div></blockquote>
<p><strong>copy</strong> : boolean, default True</p>
<blockquote class="last">
<div><p>Whether to copy X and Y, or perform in-place normalization.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Notes</p>
<p>This call requires the estimation of a p x q matrix, which may
be an issue in high dimensional space.</p>
</dd></dl>
<dl class="method">
<dt id="sklearn.cross_decomposition.CCA.score">
<code class="descname">score</code><span class="sig-paren">(</span><em>X</em>, <em>y</em>, <em>sample_weight=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/base.py#L318"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cross_decomposition.CCA.score" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the coefficient of determination R^2 of the prediction.</p>
<p>The coefficient R^2 is defined as (1 - u/v), where u is the regression
sum of squares ((y_true - y_pred) ** 2).sum() and v is the residual
sum of squares ((y_true - y_true.mean()) ** 2).sum().
Best possible score is 1.0 and it can be negative (because the
model can be arbitrarily worse). A constant model that always
predicts the expected value of y, disregarding the input features,
would get a R^2 score of 0.0.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>X</strong> : array-like, shape = (n_samples, n_features)</p>
<blockquote>
<div><p>Test samples.</p>
</div></blockquote>
<p><strong>y</strong> : array-like, shape = (n_samples) or (n_samples, n_outputs)</p>
<blockquote>
<div><p>True values for X.</p>
</div></blockquote>
<p><strong>sample_weight</strong> : array-like, shape = [n_samples], optional</p>
<blockquote>
<div><p>Sample weights.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>score</strong> : float</p>
<blockquote class="last">
<div><p>R^2 of self.predict(X) wrt. y.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.cross_decomposition.CCA.set_params">
<code class="descname">set_params</code><span class="sig-paren">(</span><em>**params</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/base.py#L236"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cross_decomposition.CCA.set_params" title="Permalink to this definition">¶</a></dt>
<dd><p>Set the parameters of this estimator.</p>
<p>The method works on simple estimators as well as on nested objects
(such as pipelines). The former have parameters of the form
<code class="docutils literal"><span class="pre"><component>__<parameter></span></code> so that it’s possible to update each
component of a nested object.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body"><strong>self</strong> :</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="sklearn.cross_decomposition.CCA.transform">
<code class="descname">transform</code><span class="sig-paren">(</span><em>X</em>, <em>Y=None</em>, <em>copy=True</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/cross_decomposition/pls_.py#L374"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.cross_decomposition.CCA.transform" title="Permalink to this definition">¶</a></dt>
<dd><p>Apply the dimension reduction learned on the train data.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><p class="first"><strong>X</strong> : array-like of predictors, shape = [n_samples, p]</p>
<blockquote>
<div><p>Training vectors, where n_samples in the number of samples and
p is the number of predictors.</p>
</div></blockquote>
<p><strong>Y</strong> : array-like of response, shape = [n_samples, q], optional</p>
<blockquote>
<div><p>Training vectors, where n_samples in the number of samples and
q is the number of response variables.</p>
</div></blockquote>
<p><strong>copy</strong> : boolean, default True</p>
<blockquote>
<div><p>Whether to copy X and Y, or perform in-place normalization.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first last"><strong>x_scores if Y is not given, (x_scores, y_scores) otherwise.</strong> :</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<div class="section" id="examples-using-sklearn-cross-decomposition-cca">
<h2>Examples using <code class="docutils literal"><span class="pre">sklearn.cross_decomposition.CCA</span></code><a class="headerlink" href="#examples-using-sklearn-cross-decomposition-cca" title="Permalink to this headline">¶</a></h2>
<div class="thumbnailContainer" tooltip="This example simulates a multi-label document classification problem. The dataset is generated ..."><div class="figure" id="id1">
<a class="reference external image-reference" href="./../../auto_examples/./plot_multilabel.html"><img alt="../../_images/plot_multilabel1.png" src="../../_images/plot_multilabel1.png" /></a>
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/plot_multilabel.html#example-plot-multilabel-py"><span>Multilabel classification</span></a></span></p>
</div>
</div><div class="thumbnailContainer" tooltip="Simple usage of various cross decomposition algorithms: - PLSCanonical - PLSRegression, with mu..."><div class="figure" id="id2">
<a class="reference external image-reference" href="./../../auto_examples/cross_decomposition/plot_compare_cross_decomposition.html"><img alt="../../_images/plot_compare_cross_decomposition1.png" src="../../_images/plot_compare_cross_decomposition1.png" /></a>
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/cross_decomposition/plot_compare_cross_decomposition.html#example-cross-decomposition-plot-compare-cross-decomposition-py"><span>Compare cross decomposition methods</span></a></span></p>
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