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<div class="section" id="decomposition-pca">
<span id="pca-doc"></span><h1>decomposition.PCA<a class="headerlink" href="#decomposition-pca" title="Permalink to this headline">¶</a></h1>
<dl class="class">
<dt id="pai4sk.decomposition.PCA">
<em class="property">class </em><code class="descclassname">pai4sk.decomposition.</code><code class="descname">PCA</code><span class="sig-paren">(</span><em>n_components=None</em>, <em>copy=True</em>, <em>whiten=False</em>, <em>svd_solver='auto'</em>, <em>tol=0.0</em>, <em>iterated_power='auto'</em>, <em>random_state=None</em>, <em>use_gpu=True</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.decomposition.PCA" title="Permalink to this definition">¶</a></dt>
<dd><p>Principal component analysis (PCA)</p>
<p>Linear dimensionality reduction using Singular Value Decomposition of the
data to project it to a lower dimensional space.</p>
<p>It uses the LAPACK implementation of the full SVD or a randomized truncated
SVD by the method of Halko et al. 2009, depending on the shape of the input
data and the number of components to extract.</p>
<p>It can also use the scipy.sparse.linalg ARPACK implementation of the
truncated SVD.</p>
<p>If cuml is installed and input data is cudf dataframe, then pai4sk will try
to use the accelerated PCA algorithm from cuML. Otherwise, scikit-learn’s
PCA algorithm will be used.</p>
<p>cuML in pai4sk is currently supported only
| (a) with python 3.6 and
| (b) without MPI.
| If PCA from cuML is run, then the return values from the APIs will be
cudf dataframe and cudf Series objects instead of the return types of
scikit-learn API.</p>
<p>Notice that this class does not support sparse input. See
<a class="reference internal" href="svddoc.html#pai4sk.decomposition.TruncatedSVD" title="pai4sk.decomposition.TruncatedSVD"><code class="xref py py-class docutils literal notranslate"><span class="pre">TruncatedSVD</span></code></a> for an alternative with sparse data.</p>
<p>Read more in the <span class="xref std std-ref">User Guide</span>.</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"><ul class="first simple">
<li><strong>n_components</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em>, </em><a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.7)"><em>None</em></a><em> or </em><em>string</em>) – <p>Number of components to keep.
if n_components is not set all components are kept:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">n_components</span> <span class="o">==</span> <span class="nb">min</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>
</pre></div>
</div>
<p>If <code class="docutils literal notranslate"><span class="pre">n_components</span> <span class="pre">==</span> <span class="pre">'mle'</span></code> and <code class="docutils literal notranslate"><span class="pre">svd_solver</span> <span class="pre">==</span> <span class="pre">'full'</span></code>, Minka’s
MLE is used to guess the dimension. Use of <code class="docutils literal notranslate"><span class="pre">n_components</span> <span class="pre">==</span> <span class="pre">'mle'</span></code>
will interpret <code class="docutils literal notranslate"><span class="pre">svd_solver</span> <span class="pre">==</span> <span class="pre">'auto'</span></code> as <code class="docutils literal notranslate"><span class="pre">svd_solver</span> <span class="pre">==</span> <span class="pre">'full'</span></code>.</p>
<p>If <code class="docutils literal notranslate"><span class="pre">0</span> <span class="pre"><</span> <span class="pre">n_components</span> <span class="pre"><</span> <span class="pre">1</span></code> and <code class="docutils literal notranslate"><span class="pre">svd_solver</span> <span class="pre">==</span> <span class="pre">'full'</span></code>, select the
number of components such that the amount of variance that needs to be
explained is greater than the percentage specified by n_components.</p>
<p>If <code class="docutils literal notranslate"><span class="pre">svd_solver</span> <span class="pre">==</span> <span class="pre">'arpack'</span></code>, the number of components must be
strictly less than the minimum of n_features and n_samples.</p>
<p>Hence, the None case results in:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">n_components</span> <span class="o">==</span> <span class="nb">min</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="o">-</span> <span class="mi">1</span>
</pre></div>
</div>
</li>
<li><strong>copy</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><em>bool</em></a><em> (</em><em>default True</em><em>)</em>) – If False, data passed to fit are overwritten and running
fit(X).transform(X) will not yield the expected results,
use fit_transform(X) instead.</li>
<li><strong>whiten</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#bool" title="(in Python v3.7)"><em>bool</em></a><em>, </em><em>optional</em><em> (</em><em>default False</em><em>)</em>) – <p>When True (False by default) the <cite>components_</cite> vectors are multiplied
by the square root of n_samples and then divided by the singular values
to ensure uncorrelated outputs with unit component-wise variances.</p>
<p>Whitening will remove some information from the transformed signal
(the relative variance scales of the components) but can sometime
improve the predictive accuracy of the downstream estimators by
making their data respect some hard-wired assumptions.</p>
</li>
<li><strong>svd_solver</strong> (<em>string {'auto'</em><em>, </em><em>'full'</em><em>, </em><em>'arpack'</em><em>, </em><em>'randomized'</em><em>, </em><em>'cuml'</em><em>, </em><em>'jacobi'}</em>) – <dl class="docutils">
<dt>auto :</dt>
<dd>when cuml is not used, the solver is selected by a default policy based
on <cite>X.shape</cite> and <cite>n_components</cite>: if the input data is larger than 500x500 and the
number of components to extract is lower than 80% of the smallest
dimension of the data, then the more efficient ‘randomized’
method is enabled. Otherwise the exact full SVD is computed and
optionally truncated afterwards. If cuml is used, then the default
algorithm ‘full’ will be used when the svd_solver is ‘auto’ or ‘cuml’.</dd>
<dt>full :</dt>
<dd>run exact full SVD calling the standard LAPACK solver via
<cite>scipy.linalg.svd</cite> and select the components by postprocessing</dd>
<dt>arpack :</dt>
<dd>run SVD truncated to n_components calling ARPACK solver via
<cite>scipy.sparse.linalg.svds</cite>. It requires strictly
0 < n_components < min(X.shape)</dd>
<dt>randomized :</dt>
<dd>run randomized SVD by the method of Halko et al.</dd>
</dl>
<div class="versionadded">
<p><span class="versionmodified">New in version 0.18.0.</span></p>
</div>
</li>
<li><strong>tol</strong> (<em>float >= 0</em><em>, </em><em>optional</em><em> (</em><em>default .0</em><em>)</em>) – <p>Tolerance for singular values computed by svd_solver == ‘arpack’.</p>
<div class="versionadded">
<p><span class="versionmodified">New in version 0.18.0.</span></p>
</div>
</li>
<li><strong>iterated_power</strong> (<em>int >= 0</em><em>, or </em><em>'auto'</em><em>, </em><em>(</em><em>default 'auto'</em><em>)</em>) – <p>Number of iterations for the power method computed by
svd_solver == ‘randomized’.
Note : cuML for pai4sk only supports integer values for this parameter.</p>
<div class="versionadded">
<p><span class="versionmodified">New in version 0.18.0.</span></p>
</div>
</li>
<li><strong>random_state</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a><em>, </em><em>RandomState instance</em><em> or </em><a class="reference external" href="https://docs.python.org/3/library/constants.html#None" title="(in Python v3.7)"><em>None</em></a><em>, </em><em>optional</em><em> (</em><em>default None</em><em>)</em>) – <p>If int, random_state is the seed used by the random number generator;
If RandomState instance, random_state is the random number generator;
If None, the random number generator is the RandomState instance used
by <cite>np.random</cite>. Used when <code class="docutils literal notranslate"><span class="pre">svd_solver</span></code> == ‘arpack’ or ‘randomized’.</p>
<div class="versionadded">
<p><span class="versionmodified">New in version 0.18.0.</span></p>
</div>
</li>
<li><strong>use_gpu</strong> (<em>boolean</em><em>, </em><em>Default is True</em>) – If True, cuML will use GPU 0. Applicable only for cuML.</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Variables:</th><td class="field-body"><ul class="first last simple">
<li><strong>components</strong> (<em>array of shape</em><em> (</em><em>n_components</em><em>, </em><em>n_features</em><em>) or </em><em>cudf dataframe</em>) – Principal axes in feature space, representing the directions of
maximum variance in the data. The components are sorted by
<code class="docutils literal notranslate"><span class="pre">explained_variance_</span></code>.</li>
<li><strong>explained_variance</strong> (<em>array of shape</em><em> (</em><em>n_components</em><em>,</em><em>) or </em><em>cudf Series</em>) – <p>The amount of variance explained by each of the selected components.</p>
<p>Equal to n_components largest eigenvalues
of the covariance matrix of X.</p>
<div class="versionadded">
<p><span class="versionmodified">New in version 0.18.</span></p>
</div>
</li>
<li><strong>explained_variance_ratio</strong> (<em>array of shape</em><em> (</em><em>n_components</em><em>,</em><em>) or </em><em>cudf Series</em>) – <p>Percentage of variance explained by each of the selected components.</p>
<p>If <code class="docutils literal notranslate"><span class="pre">n_components</span></code> is not set then all components are stored and the
sum of the ratios is equal to 1.0.</p>
</li>
<li><strong>singular_values</strong> (<em>array of shape</em><em> (</em><em>n_components</em><em>,</em><em>) or </em><em>cudf Series</em>) – The singular values corresponding to each of the selected components.
The singular values are equal to the 2-norms of the <code class="docutils literal notranslate"><span class="pre">n_components</span></code>
variables in the lower-dimensional space.</li>
<li><strong>mean</strong> (<em>array</em><em>, </em><em>shape</em><em> (</em><em>n_features</em><em>,</em><em>)</em>) – <p>Per-feature empirical mean, estimated from the training set.</p>
<p>Equal to <cite>X.mean(axis=0)</cite>.</p>
</li>
<li><strong>n_components</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#int" title="(in Python v3.7)"><em>int</em></a>) – The estimated number of components. When n_components is set
to ‘mle’ or a number between 0 and 1 (with svd_solver == ‘full’) this
number is estimated from input data. Otherwise it equals the parameter
n_components, or the lesser value of n_features and n_samples
if n_components is None.</li>
<li><strong>noise_variance</strong> (<a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)"><em>float</em></a><em> or </em><em>cudf Series</em>) – <p>The estimated noise covariance following the Probabilistic PCA model
from Tipping and Bishop 1999. See “Pattern Recognition and
Machine Learning” by C. Bishop, 12.2.1 p. 574 or
<a class="reference external" href="http://www.miketipping.com/papers/met-mppca.pdf">http://www.miketipping.com/papers/met-mppca.pdf</a>. It is required to
compute the estimated data covariance and score samples.</p>
<p>Equal to the average of (min(n_features, n_samples) - n_components)
smallest eigenvalues of the covariance matrix of X.</p>
</li>
</ul>
</td>
</tr>
</tbody>
</table>
<p class="rubric">References</p>
<p>For n_components == ‘mle’, this class uses the method of <cite>Minka, T. P.
“Automatic choice of dimensionality for PCA”. In NIPS, pp. 598-604</cite></p>
<p>Implements the probabilistic PCA model from:
<a href="#id1"><span class="problematic" id="id2">`</span></a>Tipping, M. E., and Bishop, C. M. (1999). “Probabilistic principal
component analysis”. Journal of the Royal Statistical Society:
Series B (Statistical Methodology), 61(3), 611-622.
via the score and score_samples methods.
See <a class="reference external" href="http://www.miketipping.com/papers/met-mppca.pdf">http://www.miketipping.com/papers/met-mppca.pdf</a></p>
<p>For svd_solver == ‘arpack’, refer to <cite>scipy.sparse.linalg.svds</cite>.</p>
<p>For svd_solver == ‘randomized’, see:
<cite>Halko, N., Martinsson, P. G., and Tropp, J. A. (2011).
“Finding structure with randomness: Probabilistic algorithms for
constructing approximate matrix decompositions”.
SIAM review, 53(2), 217-288.</cite> and also
<cite>Martinsson, P. G., Rokhlin, V., and Tygert, M. (2011).
“A randomized algorithm for the decomposition of matrices”.
Applied and Computational Harmonic Analysis, 30(1), 47-68.</cite></p>
<p class="rubric">Examples</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">pai4sk.decomposition</span> <span class="k">import</span> <span class="n">PCA</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">3</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">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">pca</span> <span class="o">=</span> <span class="n">PCA</span><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">pca</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="go">PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,</span>
<span class="go"> svd_solver='auto', tol=0.0, whiten=False)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">pca</span><span class="o">.</span><span class="n">explained_variance_ratio_</span><span class="p">)</span> <span class="c1"># doctest: +ELLIPSIS</span>
<span class="go">[0.9924... 0.0075...]</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">pca</span><span class="o">.</span><span class="n">singular_values_</span><span class="p">)</span> <span class="c1"># doctest: +ELLIPSIS</span>
<span class="go">[6.30061... 0.54980...]</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">pca</span> <span class="o">=</span> <span class="n">PCA</span><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">svd_solver</span><span class="o">=</span><span class="s1">'full'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">pca</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="c1"># doctest: +ELLIPSIS +NORMALIZE_WHITESPACE</span>
<span class="go">PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,</span>
<span class="go"> svd_solver='full', tol=0.0, whiten=False)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">pca</span><span class="o">.</span><span class="n">explained_variance_ratio_</span><span class="p">)</span> <span class="c1"># doctest: +ELLIPSIS</span>
<span class="go">[0.9924... 0.00755...]</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">pca</span><span class="o">.</span><span class="n">singular_values_</span><span class="p">)</span> <span class="c1"># doctest: +ELLIPSIS</span>
<span class="go">[6.30061... 0.54980...]</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">pca</span> <span class="o">=</span> <span class="n">PCA</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="n">svd_solver</span><span class="o">=</span><span class="s1">'arpack'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">pca</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="go">PCA(copy=True, iterated_power='auto', n_components=1, random_state=None,</span>
<span class="go"> svd_solver='arpack', tol=0.0, whiten=False)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">pca</span><span class="o">.</span><span class="n">explained_variance_ratio_</span><span class="p">)</span> <span class="c1"># doctest: +ELLIPSIS</span>
<span class="go">[0.99244...]</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">pca</span><span class="o">.</span><span class="n">singular_values_</span><span class="p">)</span> <span class="c1"># doctest: +ELLIPSIS</span>
<span class="go">[6.30061...]</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<p class="last"><code class="xref py py-class docutils literal notranslate"><span class="pre">KernelPCA</span></code>, <code class="xref py py-class docutils literal notranslate"><span class="pre">SparsePCA</span></code>, <a class="reference internal" href="svddoc.html#pai4sk.decomposition.TruncatedSVD" title="pai4sk.decomposition.TruncatedSVD"><code class="xref py py-class docutils literal notranslate"><span class="pre">TruncatedSVD</span></code></a>, <code class="xref py py-class docutils literal notranslate"><span class="pre">IncrementalPCA</span></code></p>
</div>
<dl class="method">
<dt id="pai4sk.decomposition.PCA.fit">
<code class="descname">fit</code><span class="sig-paren">(</span><em>X</em>, <em>y=None</em>, <em>_transform=True</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.decomposition.PCA.fit" title="Permalink to this definition">¶</a></dt>
<dd><p>Fit the model with X.</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"><ul class="first simple">
<li><strong>X</strong> (<em>array-like of shape</em><em> (</em><em>n_samples</em><em>, </em><em>n_features</em><em>) or </em><em>cudf dataframe</em>) – Training data, where n_samples is the number of samples
and n_features is the number of features.</li>
<li><strong>y</strong> (<em>Ignored</em>) – </li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>self</strong> – Returns the instance itself.
If PCA from cuML is run, then this fit method saves the computed
values as cudf dataframes and cudf Series objects instead of the
results’ types seen from scikit-learn’s fit method.</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last"><a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.7)">object</a></p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="pai4sk.decomposition.PCA.fit_transform">
<code class="descname">fit_transform</code><span class="sig-paren">(</span><em>X</em>, <em>y=None</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.decomposition.PCA.fit_transform" title="Permalink to this definition">¶</a></dt>
<dd><p>Fit the model with X and apply the dimensionality reduction on X.</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"><ul class="first simple">
<li><strong>X</strong> (<em>array-like of shape</em><em> (</em><em>n_samples</em><em>, </em><em>n_features</em><em>) or </em><em>cudf dataframe</em>) – Training data, where n_samples is the number of samples
and n_features is the number of features.</li>
<li><strong>y</strong> (<em>Ignored</em>) – </li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>X_new</strong> – If PCA from cuML is run, then this method saves the computed
values as cudf dataframes and cudf Series objects instead of the
results’ types seen from scikit-learn’s fit_transform method.</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">array-like of shape (n_samples, n_components) or cudf dataframe</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="pai4sk.decomposition.PCA.inverse_transform">
<code class="descname">inverse_transform</code><span class="sig-paren">(</span><em>X</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.decomposition.PCA.inverse_transform" title="Permalink to this definition">¶</a></dt>
<dd><p>Transform data back to its original space.</p>
<p>In other words, return an input X_original whose transform would be X.</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"><strong>X</strong> (<em>array-like of shape</em><em> (</em><em>n_samples</em><em>, </em><em>n_components</em><em>) or </em><em>cudf dataframe</em>) – New data, where n_samples is the number of samples
and n_components is the number of components.</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><strong>X_original</strong> – If PCA from cuML is run, then this method returns cudf dataframe
instead of the results’ types seen from scikit-learn’s
inverse_transform method.</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body">array-like of shape (n_samples, n_features) or cudf dataframe</td>
</tr>
</tbody>
</table>
<p class="rubric">Notes</p>
<p>If whitening is enabled, inverse_transform will compute the
exact inverse operation, which includes reversing whitening.</p>
</dd></dl>
<dl class="method">
<dt id="pai4sk.decomposition.PCA.score">
<code class="descname">score</code><span class="sig-paren">(</span><em>X</em>, <em>y=None</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.decomposition.PCA.score" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the average log-likelihood of all samples.</p>
<p>See. “Pattern Recognition and Machine Learning”
by C. Bishop, 12.2.1 p. 574
or <a class="reference external" href="http://www.miketipping.com/papers/met-mppca.pdf">http://www.miketipping.com/papers/met-mppca.pdf</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"><ul class="first simple">
<li><strong>X</strong> (<em>array</em><em>, </em><em>shape</em><em>(</em><em>n_samples</em><em>, </em><em>n_features</em><em>)</em>) – The data.</li>
<li><strong>y</strong> (<em>Ignored</em>) – </li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>ll</strong> – Average log-likelihood of the samples under the current model</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last"><a class="reference external" href="https://docs.python.org/3/library/functions.html#float" title="(in Python v3.7)">float</a></p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="pai4sk.decomposition.PCA.transform">
<code class="descname">transform</code><span class="sig-paren">(</span><em>X</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.decomposition.PCA.transform" title="Permalink to this definition">¶</a></dt>
<dd><p>Apply dimensionality reduction to X.</p>
<p>X is projected on the first principal components previously extracted
from a training set.</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"><strong>X</strong> (<em>array-like of shape</em><em> (</em><em>n_samples</em><em>, </em><em>n_features</em><em>) or </em><em>cudf dataframe</em>) – New data, where n_samples is the number of samples
and n_features is the number of features.</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><strong>X_new</strong> – If PCA from cuML is run, then this method saves the computed
values as cudf dataframe instead of the results’ types seen from
scikit-learn’s transform method.</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body">array-like of shape (n_samples, n_components) or cudf dataframe</td>
</tr>
</tbody>
</table>
<p class="rubric">Examples</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">pai4sk.decomposition</span> <span class="k">import</span> <span class="n">IncrementalPCA</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mi">3</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">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">]])</span>
<span class="gp">>>> </span><span class="n">ipca</span> <span class="o">=</span> <span class="n">IncrementalPCA</span><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">batch_size</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">ipca</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="go">IncrementalPCA(batch_size=3, copy=True, n_components=2, whiten=False)</span>
<span class="gp">>>> </span><span class="n">ipca</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="c1"># doctest: +SKIP</span>
</pre></div>
</div>
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