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<div class="section" id="decomposition-truncatedsvd">
<span id="svd-doc"></span><h1>decomposition.TruncatedSVD<a class="headerlink" href="#decomposition-truncatedsvd" title="Permalink to this headline">¶</a></h1>
<dl class="class">
<dt id="pai4sk.decomposition.TruncatedSVD">
<em class="property">class </em><code class="descclassname">pai4sk.decomposition.</code><code class="descname">TruncatedSVD</code><span class="sig-paren">(</span><em>n_components=2</em>, <em>algorithm='auto'</em>, <em>n_iter=5</em>, <em>random_state=None</em>, <em>tol=0.0</em>, <em>use_gpu=True</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.decomposition.TruncatedSVD" title="Permalink to this definition">¶</a></dt>
<dd><p>Dimensionality reduction using truncated SVD (aka LSA).</p>
<p>This transformer performs linear dimensionality reduction by means of
truncated singular value decomposition (SVD). Contrary to PCA, this
estimator does not center the data before computing the singular value
decomposition. This means it can work with scipy.sparse matrices
efficiently.</p>
<p>In particular, truncated SVD works on term count/tf-idf matrices as
returned by the vectorizers in pai4sk.feature_extraction.text. In that
context, it is known as latent semantic analysis (LSA).</p>
<p>This estimator supports two algorithms: a fast randomized SVD solver, and
a “naive” algorithm that uses ARPACK as an eigensolver on (X * X.T) or
(X.T * X), whichever is more efficient.</p>
<p>If cuml is installed and if input data is cudf dataframe and if possible, then
the accelerated TruncatedSVD algorithm from cuML will be used. Otherwise,
scikit-learn’s TruncatedSVD algorithm will be used.</p>
<p>cuML in pai4sk is currently supported only
| (a) with python 3.6 and
| (b) without MPI.
| If TruncatedSVD 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>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><em>default = 2</em>) – Desired dimensionality of output data.
Must be strictly less than the number of features.
The default value is useful for visualisation. For LSA, a value of
100 is recommended.</li>
<li><strong>algorithm</strong> (<em>string</em><em>, </em><em>"arpack"</em><em>, </em><em>"randomized"</em><em>, </em><em>"cuml"</em><em>, </em><em>"auto"</em><em>, </em><em>"full"</em><em> or </em><em>"jacobi". default = "auto".</em>) – SVD solver to use. Either “arpack” for the ARPACK wrapper in SciPy
(scipy.sparse.linalg.svds), or “randomized” for the randomized
algorithm due to Halko (2009) if cuml can’t be used.
“auto” will become “full” if cuml is installed and the arguments satisfy
some validations. “auto” will become “randomized” if cuml is not used.
algorithm should be one of “auto”, “cuml”, “full” and “jacobi”.</li>
<li><strong>n_iter</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>optional</em><em> (</em><em>default 5</em><em>)</em>) – Number of iterations for randomized SVD solver. Not used by ARPACK.
The default is larger than the default in <cite>randomized_svd</cite> to handle
sparse matrices that may have large slowly decaying spectrum.</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>) – 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>.</li>
<li><strong>tol</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>, </em><em>optional</em>) – Tolerance for ARPACK. 0 means machine precision. Ignored by randomized
SVD solver.</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>) – </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 object</em>) – The variance of the training samples transformed by a projection to
each component.</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 object</em>) – Percentage of variance explained by each of the selected components.</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 object</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>
</ul>
</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">from</span> <span class="nn">pai4sk.decomposition</span> <span class="k">import</span> <span class="n">TruncatedSVD</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">pai4sk.random_projection</span> <span class="k">import</span> <span class="n">sparse_random_matrix</span>
<span class="gp">>>> </span><span class="n">X</span> <span class="o">=</span> <span class="n">sparse_random_matrix</span><span class="p">(</span><span class="mi">100</span><span class="p">,</span> <span class="mi">100</span><span class="p">,</span> <span class="n">density</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">svd</span> <span class="o">=</span> <span class="n">TruncatedSVD</span><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">n_iter</span><span class="o">=</span><span class="mi">7</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">svd</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: +NORMALIZE_WHITESPACE</span>
<span class="go">TruncatedSVD(algorithm='randomized', n_components=5, n_iter=7,</span>
<span class="go"> random_state=42, tol=0.0)</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">svd</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">[0.0606... 0.0584... 0.0497... 0.0434... 0.0372...]</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">svd</span><span class="o">.</span><span class="n">explained_variance_ratio_</span><span class="o">.</span><span class="n">sum</span><span class="p">())</span> <span class="c1"># doctest: +ELLIPSIS</span>
<span class="go">0.249...</span>
<span class="gp">>>> </span><span class="nb">print</span><span class="p">(</span><span class="n">svd</span><span class="o">.</span><span class="n">singular_values_</span><span class="p">)</span> <span class="c1"># doctest: +ELLIPSIS</span>
<span class="go">[2.5841... 2.5245... 2.3201... 2.1753... 2.0443...]</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<p class="last"><a class="reference internal" href="pcadoc.html#pai4sk.decomposition.PCA" title="pai4sk.decomposition.PCA"><code class="xref py py-class docutils literal notranslate"><span class="pre">PCA</span></code></a></p>
</div>
<p class="rubric">References</p>
<p>Finding structure with randomness: Stochastic algorithms for constructing
approximate matrix decompositions
Halko, et al., 2009 (arXiv:909) https://arxiv.org/pdf/0909.4061.pdf</p>
<p class="rubric">Notes</p>
<p>SVD suffers from a problem called “sign indeterminacy”, which means the
sign of the <code class="docutils literal notranslate"><span class="pre">components_</span></code> and the output from transform depend on the
algorithm and random state. To work around this, fit instances of this
class to data once, then keep the instance around to do transformations.</p>
<dl class="method">
<dt id="pai4sk.decomposition.TruncatedSVD.fit">
<code class="descname">fit</code><span class="sig-paren">(</span><em>X</em>, <em>y=None</em><span class="sig-paren">)</span><a class="headerlink" href="#pai4sk.decomposition.TruncatedSVD.fit" title="Permalink to this definition">¶</a></dt>
<dd><p>Fit LSI model on training data 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</em><em>, </em><em>sparse matrix} of shape</em><em> (</em><em>n_samples</em><em>, </em><em>n_features</em><em>) or </em><em>cudf dataframe</em>) – Training 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>self</strong> – Returns the transformer object.
If TruncatedSVD 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.TruncatedSVD.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.TruncatedSVD.fit_transform" title="Permalink to this definition">¶</a></dt>
<dd><p>Fit LSI model to X and perform 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</em><em>, </em><em>sparse matrix} of shape</em><em> (</em><em>n_samples</em><em>, </em><em>n_features</em><em>) or </em><em>cudf dataframe</em>) – Training data.
If TruncatedSVD 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 API.</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> – Reduced version of X. This will always be a dense array.</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><p class="first last">array of shape (n_samples, n_components) or cudf dataframe</p>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="pai4sk.decomposition.TruncatedSVD.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.TruncatedSVD.inverse_transform" title="Permalink to this definition">¶</a></dt>
<dd><p>Transform X back to its original space.</p>
<p>Returns an array or cudf dataframe 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.</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><strong>X_original</strong> – Note that this is always dense.
If TruncatedSVD from cuML is run, then this method returns 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 of shape (n_samples, n_features) or cudf dataframe</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="pai4sk.decomposition.TruncatedSVD.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.TruncatedSVD.transform" title="Permalink to this definition">¶</a></dt>
<dd><p>Perform 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"><strong>X</strong> (<em>{array-like</em><em>, </em><em>sparse matrix} of shape</em><em> (</em><em>n_samples</em><em>, </em><em>n_features</em><em>) or </em><em>cudf dataframe</em>) – New data.</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><strong>X_new</strong> – Reduced version of X. This will always be dense.
If TruncatedSVD from cuML is run, then this method returns 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 of shape (n_samples, n_components) or cudf dataframe</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
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