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<section id="module-torchdr">
<span id="id1"></span><span id="api-and-modules"></span><h1>API and Modules<a class="headerlink" href="#module-torchdr" title="Link to this heading">#</a></h1>
<section id="dimensionality-reduction-sklearn-compatible-estimators">
<h2>Dimensionality Reduction <code class="docutils literal notranslate"><span class="pre">sklearn</span></code> Compatible Estimators<a class="headerlink" href="#dimensionality-reduction-sklearn-compatible-estimators" title="Link to this heading">#</a></h2>
<p>TorchDR provides a set of classes that are compatible with the <code class="docutils literal notranslate"><span class="pre">sklearn</span></code> API.
For example, running <a class="reference internal" href="gen_modules/torchdr.TSNE.html#torchdr.TSNE" title="torchdr.TSNE"><code class="xref py py-class docutils literal notranslate"><span class="pre">TSNE</span></code></a> can be done in the exact same way as running
<code class="xref py py-class docutils literal notranslate"><span class="pre">sklearn.manifold.TSNE</span></code> with the same parameters.
Note that the TorchDR classes work seamlessly with both Numpy and PyTorch tensors.</p>
<p>For all methods, TorchDR provides the ability to use GPU acceleration using
<code class="docutils literal notranslate"><span class="pre">device='cuda'</span></code> as well as LazyTensor objects that allows to fit large scale models
directly on the GPU memory without overflows using <code class="docutils literal notranslate"><span class="pre">keops=True</span></code>.</p>
<p>TorchDR supports a variety of dimensionality reduction methods. They are presented in the following sections.</p>
<section id="spectral-embedding">
<h3>Spectral Embedding<a class="headerlink" href="#spectral-embedding" title="Link to this heading">#</a></h3>
<p>Those classes are used to perform classical spectral embedding from a
<a class="reference internal" href="stubs/torchdr.Affinity.html#torchdr.Affinity" title="torchdr.Affinity"><code class="xref py py-class docutils literal notranslate"><span class="pre">torchdr.Affinity</span></code></a> object defined on the input data.
They give the same output as using <a class="reference internal" href="stubs/torchdr.AffinityMatcher.html#torchdr.AffinityMatcher" title="torchdr.AffinityMatcher"><code class="xref py py-class docutils literal notranslate"><span class="pre">torchdr.AffinityMatcher</span></code></a> with this same
<a class="reference internal" href="stubs/torchdr.Affinity.html#torchdr.Affinity" title="torchdr.Affinity"><code class="xref py py-class docutils literal notranslate"><span class="pre">torchdr.Affinity</span></code></a> in input space and a <a class="reference internal" href="gen_modules/torchdr.ScalarProductAffinity.html#torchdr.ScalarProductAffinity" title="torchdr.ScalarProductAffinity"><code class="xref py py-class docutils literal notranslate"><span class="pre">torchdr.ScalarProductAffinity</span></code></a> in
the embedding space. However, <a class="reference internal" href="stubs/torchdr.AffinityMatcher.html#torchdr.AffinityMatcher" title="torchdr.AffinityMatcher"><code class="xref py py-class docutils literal notranslate"><span class="pre">torchdr.AffinityMatcher</span></code></a> relies on a
gradient-based solver while the spectral embedding classes rely on the
eigendecomposition of the affinity matrix.</p>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="gen_modules/torchdr.PCA.html#torchdr.PCA" title="torchdr.PCA"><code class="xref py py-obj docutils literal notranslate"><span class="pre">PCA</span></code></a>([n_components, device, verbose, ...])</p></td>
<td><p>Principal Component Analysis module.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="gen_modules/torchdr.KernelPCA.html#torchdr.KernelPCA" title="torchdr.KernelPCA"><code class="xref py py-obj docutils literal notranslate"><span class="pre">KernelPCA</span></code></a>(affinity, n_components, device, ...)</p></td>
<td><p>Kernel Principal Component Analysis module.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="gen_modules/torchdr.IncrementalPCA.html#torchdr.IncrementalPCA" title="torchdr.IncrementalPCA"><code class="xref py py-obj docutils literal notranslate"><span class="pre">IncrementalPCA</span></code></a>([n_components, copy, ...])</p></td>
<td><p>Incremental Principal Components Analysis (IPCA) leveraging PyTorch for GPU acceleration.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="neighbor-embedding">
<h3>Neighbor Embedding<a class="headerlink" href="#neighbor-embedding" title="Link to this heading">#</a></h3>
<p>TorchDR supports the following neighbor embedding methods.</p>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="gen_modules/torchdr.SNE.html#torchdr.SNE" title="torchdr.SNE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SNE</span></code></a>([perplexity, n_components, lr, ...])</p></td>
<td><p>Stochastic Neighbor Embedding (SNE) introduced in <span id="id2">[<a class="reference internal" href="torchdr.bibliography.html#id2" title="Geoffrey E Hinton and Sam Roweis. Stochastic neighbor embedding. Advances in neural information processing systems, 2002.">Hinton and Roweis, 2002</a>]</span>.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="gen_modules/torchdr.TSNE.html#torchdr.TSNE" title="torchdr.TSNE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">TSNE</span></code></a>([perplexity, n_components, lr, ...])</p></td>
<td><p>t-Stochastic Neighbor Embedding (t-SNE) introduced in <span id="id3">[<a class="reference internal" href="torchdr.bibliography.html#id3" title="Laurens Van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of machine learning research, 2008.">Van der Maaten and Hinton, 2008</a>]</span>.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="gen_modules/torchdr.TSNEkhorn.html#torchdr.TSNEkhorn" title="torchdr.TSNEkhorn"><code class="xref py py-obj docutils literal notranslate"><span class="pre">TSNEkhorn</span></code></a>([perplexity, n_components, lr, ...])</p></td>
<td><p>TSNEkhorn algorithm introduced in <span id="id4">[<a class="reference internal" href="torchdr.bibliography.html#id4" title="Hugues Van Assel, Titouan Vayer, Rémi Flamary, and Nicolas Courty. Snekhorn: dimension reduction with symmetric entropic affinities. Advances in Neural Information Processing Systems, 2024.">Van Assel <em>et al.</em>, 2024</a>]</span>.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="gen_modules/torchdr.InfoTSNE.html#torchdr.InfoTSNE" title="torchdr.InfoTSNE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">InfoTSNE</span></code></a>([perplexity, n_components, lr, ...])</p></td>
<td><p>InfoTSNE algorithm introduced in <span id="id5">[<a class="reference internal" href="torchdr.bibliography.html#id14" title="Sebastian Damrich, Jan Niklas Böhm, Fred A Hamprecht, and Dmitry Kobak. From $ t $-sne to umap with contrastive learning. arXiv preprint arXiv:2206.01816, 2022.">Damrich <em>et al.</em>, 2022</a>]</span>.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="gen_modules/torchdr.LargeVis.html#torchdr.LargeVis" title="torchdr.LargeVis"><code class="xref py py-obj docutils literal notranslate"><span class="pre">LargeVis</span></code></a>([perplexity, n_components, lr, ...])</p></td>
<td><p>LargeVis algorithm introduced in <span id="id6">[<a class="reference internal" href="torchdr.bibliography.html#id13" title="Jian Tang, Jingzhou Liu, Ming Zhang, and Qiaozhu Mei. Visualizing large-scale and high-dimensional data. In Proceedings of the 25th international conference on world wide web, 287–297. 2016.">Tang <em>et al.</em>, 2016</a>]</span>.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="gen_modules/torchdr.UMAP.html#torchdr.UMAP" title="torchdr.UMAP"><code class="xref py py-obj docutils literal notranslate"><span class="pre">UMAP</span></code></a>([n_neighbors, n_components, min_dist, ...])</p></td>
<td><p>UMAP introduced in <span id="id7">[<a class="reference internal" href="torchdr.bibliography.html#id9" title="Leland McInnes, John Healy, and James Melville. Umap: uniform manifold approximation and projection for dimension reduction. arXiv preprint arXiv:1802.03426, 2018.">McInnes <em>et al.</em>, 2018</a>]</span> and further studied in <span id="id8">[<a class="reference internal" href="torchdr.bibliography.html#id12" title="Sebastian Damrich and Fred A Hamprecht. On umap's true loss function. Advances in Neural Information Processing Systems, 34:5798–5809, 2021.">Damrich and Hamprecht, 2021</a>]</span>.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
</section>
<section id="advanced-dimensionality-reduction-with-torchdr">
<h2>Advanced Dimensionality Reduction with TorchDR<a class="headerlink" href="#advanced-dimensionality-reduction-with-torchdr" title="Link to this heading">#</a></h2>
<p>TorchDR provides a set of generic classes that can be used to implement new
dimensionality reduction methods. These classes provide a modular and extensible framework that allows you to focus on the core components of your method.</p>
<section id="base-classes">
<h3>Base Classes<a class="headerlink" href="#base-classes" title="Link to this heading">#</a></h3>
<p>The <a class="reference internal" href="stubs/torchdr.DRModule.html#torchdr.DRModule" title="torchdr.DRModule"><code class="xref py py-class docutils literal notranslate"><span class="pre">torchdr.DRModule</span></code></a> class is the base class for a dimensionality
reduction estimator. It is the base class for all the DR classes in TorchDR.</p>
<p><a class="reference internal" href="stubs/torchdr.AffinityMatcher.html#torchdr.AffinityMatcher" title="torchdr.AffinityMatcher"><code class="xref py py-class docutils literal notranslate"><span class="pre">torchdr.AffinityMatcher</span></code></a> is the base class for all the DR methods that
use gradient-based optimization to minimize a loss function constructed from
two affinities in input and embedding spaces.</p>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="stubs/torchdr.DRModule.html#torchdr.DRModule" title="torchdr.DRModule"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DRModule</span></code></a>([n_components, device, backend, ...])</p></td>
<td><p>Base class for DR methods.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="stubs/torchdr.AffinityMatcher.html#torchdr.AffinityMatcher" title="torchdr.AffinityMatcher"><code class="xref py py-obj docutils literal notranslate"><span class="pre">AffinityMatcher</span></code></a>(affinity_in, affinity_out[, ...])</p></td>
<td><p>Perform dimensionality reduction by matching two affinity matrices.</p></td>
</tr>
</tbody>
</table>
</div>
<section id="base-neighbor-embedding-modules">
<h4>Base Neighbor Embedding Modules<a class="headerlink" href="#base-neighbor-embedding-modules" title="Link to this heading">#</a></h4>
<p>Neighbor embedding base modules inherit from the <a class="reference internal" href="stubs/torchdr.AffinityMatcher.html#torchdr.AffinityMatcher" title="torchdr.AffinityMatcher"><code class="xref py py-class docutils literal notranslate"><span class="pre">torchdr.AffinityMatcher</span></code></a>
class and implement specific strategies that are common to all neighbor embedding
methods such as early exaggeration.</p>
<p>In particular, <a class="reference internal" href="gen_modules/torchdr.SparseNeighborEmbedding.html#torchdr.SparseNeighborEmbedding" title="torchdr.SparseNeighborEmbedding"><code class="xref py py-class docutils literal notranslate"><span class="pre">torchdr.SparseNeighborEmbedding</span></code></a> relies on the sparsity of the
input affinity to compute the attractive term in linear time. <a class="reference internal" href="gen_modules/torchdr.SampledNeighborEmbedding.html#torchdr.SampledNeighborEmbedding" title="torchdr.SampledNeighborEmbedding"><code class="xref py py-class docutils literal notranslate"><span class="pre">torchdr.SampledNeighborEmbedding</span></code></a> inherits from this class and adds the possibility to
approximate the repulsive term of the loss via negative samples.</p>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="gen_modules/torchdr.NeighborEmbedding.html#torchdr.NeighborEmbedding" title="torchdr.NeighborEmbedding"><code class="xref py py-obj docutils literal notranslate"><span class="pre">NeighborEmbedding</span></code></a>(affinity_in, affinity_out)</p></td>
<td><p>Solves the neighbor embedding problem.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="gen_modules/torchdr.SparseNeighborEmbedding.html#torchdr.SparseNeighborEmbedding" title="torchdr.SparseNeighborEmbedding"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SparseNeighborEmbedding</span></code></a>(affinity_in, ...[, ...])</p></td>
<td><p>Solves the neighbor embedding problem with a sparse input affinity matrix.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="gen_modules/torchdr.SampledNeighborEmbedding.html#torchdr.SampledNeighborEmbedding" title="torchdr.SampledNeighborEmbedding"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SampledNeighborEmbedding</span></code></a>(affinity_in, ...[, ...])</p></td>
<td><p>Solves the neighbor embedding problem with both sparsity and sampling.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
</section>
<section id="affinity-classes">
<h3>Affinity Classes<a class="headerlink" href="#affinity-classes" title="Link to this heading">#</a></h3>
<p>The following classes are used to compute the affinities between the data points.
Broadly speaking, they define a notion of similarity between samples.</p>
<section id="simple-affinities">
<h4>Simple Affinities<a class="headerlink" href="#simple-affinities" title="Link to this heading">#</a></h4>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="gen_modules/torchdr.GaussianAffinity.html#torchdr.GaussianAffinity" title="torchdr.GaussianAffinity"><code class="xref py py-obj docutils literal notranslate"><span class="pre">GaussianAffinity</span></code></a>([sigma, metric, zero_diag, ...])</p></td>
<td><p>Compute the Gaussian affinity matrix.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="gen_modules/torchdr.StudentAffinity.html#torchdr.StudentAffinity" title="torchdr.StudentAffinity"><code class="xref py py-obj docutils literal notranslate"><span class="pre">StudentAffinity</span></code></a>([degrees_of_freedom, ...])</p></td>
<td><p>Compute the Student affinity matrix based on the Student-t distribution.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="gen_modules/torchdr.ScalarProductAffinity.html#torchdr.ScalarProductAffinity" title="torchdr.ScalarProductAffinity"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ScalarProductAffinity</span></code></a>([device, backend, verbose])</p></td>
<td><p>Compute the scalar product affinity matrix.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="gen_modules/torchdr.NormalizedGaussianAffinity.html#torchdr.NormalizedGaussianAffinity" title="torchdr.NormalizedGaussianAffinity"><code class="xref py py-obj docutils literal notranslate"><span class="pre">NormalizedGaussianAffinity</span></code></a>([sigma, metric, ...])</p></td>
<td><p>Compute the Gaussian affinity matrix which can be normalized along a dimension.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="gen_modules/torchdr.NormalizedStudentAffinity.html#torchdr.NormalizedStudentAffinity" title="torchdr.NormalizedStudentAffinity"><code class="xref py py-obj docutils literal notranslate"><span class="pre">NormalizedStudentAffinity</span></code></a>([...])</p></td>
<td><p>Compute the Student affinity matrix which can be normalized along a dimension.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="affinities-normalized-by-knn-distances">
<h4>Affinities Normalized by kNN Distances<a class="headerlink" href="#affinities-normalized-by-knn-distances" title="Link to this heading">#</a></h4>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="gen_modules/torchdr.SelfTuningAffinity.html#torchdr.SelfTuningAffinity" title="torchdr.SelfTuningAffinity"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SelfTuningAffinity</span></code></a>([K, normalization_dim, ...])</p></td>
<td><p>Self-tuning affinity introduced in <span id="id9">[<a class="reference internal" href="torchdr.bibliography.html#id19" title="Lihi Zelnik-Manor and Pietro Perona. Self-tuning spectral clustering. Advances in neural information processing systems, 2004.">Zelnik-Manor and Perona, 2004</a>]</span>.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="gen_modules/torchdr.MAGICAffinity.html#torchdr.MAGICAffinity" title="torchdr.MAGICAffinity"><code class="xref py py-obj docutils literal notranslate"><span class="pre">MAGICAffinity</span></code></a>([K, metric, zero_diag, ...])</p></td>
<td><p>Compute the MAGIC affinity introduced in <span id="id10">[<a class="reference internal" href="torchdr.bibliography.html#id20" title="David Van Dijk, Roshan Sharma, Juozas Nainys, Kristina Yim, Pooja Kathail, Ambrose J Carr, Cassandra Burdziak, Kevin R Moon, Christine L Chaffer, Diwakar Pattabiraman, and others. Recovering gene interactions from single-cell data using data diffusion. Cell, 174(3):716–729, 2018.">Van Dijk <em>et al.</em>, 2018</a>]</span>.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="entropic-affinities">
<h4>Entropic Affinities<a class="headerlink" href="#entropic-affinities" title="Link to this heading">#</a></h4>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="gen_modules/torchdr.SinkhornAffinity.html#torchdr.SinkhornAffinity" title="torchdr.SinkhornAffinity"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SinkhornAffinity</span></code></a>([eps, tol, max_iter, ...])</p></td>
<td><p>Compute the symmetric doubly stochastic affinity matrix.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="gen_modules/torchdr.EntropicAffinity.html#torchdr.EntropicAffinity" title="torchdr.EntropicAffinity"><code class="xref py py-obj docutils literal notranslate"><span class="pre">EntropicAffinity</span></code></a>([perplexity, tol, ...])</p></td>
<td><p>Solve the directed entropic affinity problem introduced in <span id="id11">[<a class="reference internal" href="torchdr.bibliography.html#id2" title="Geoffrey E Hinton and Sam Roweis. Stochastic neighbor embedding. Advances in neural information processing systems, 2002.">Hinton and Roweis, 2002</a>]</span>.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="gen_modules/torchdr.SymmetricEntropicAffinity.html#torchdr.SymmetricEntropicAffinity" title="torchdr.SymmetricEntropicAffinity"><code class="xref py py-obj docutils literal notranslate"><span class="pre">SymmetricEntropicAffinity</span></code></a>([perplexity, lr, ...])</p></td>
<td><p>Compute the symmetric entropic affinity (SEA) introduced in <span id="id12">[<a class="reference internal" href="torchdr.bibliography.html#id4" title="Hugues Van Assel, Titouan Vayer, Rémi Flamary, and Nicolas Courty. Snekhorn: dimension reduction with symmetric entropic affinities. Advances in Neural Information Processing Systems, 2024.">Van Assel <em>et al.</em>, 2024</a>]</span>.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="quadratic-affinities">
<h4>Quadratic Affinities<a class="headerlink" href="#quadratic-affinities" title="Link to this heading">#</a></h4>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="gen_modules/torchdr.DoublyStochasticQuadraticAffinity.html#torchdr.DoublyStochasticQuadraticAffinity" title="torchdr.DoublyStochasticQuadraticAffinity"><code class="xref py py-obj docutils literal notranslate"><span class="pre">DoublyStochasticQuadraticAffinity</span></code></a>([eps, ...])</p></td>
<td><p>Compute the symmetric doubly stochastic affinity.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="umap-affinities">
<h4>UMAP Affinities<a class="headerlink" href="#umap-affinities" title="Link to this heading">#</a></h4>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="gen_modules/torchdr.UMAPAffinityIn.html#torchdr.UMAPAffinityIn" title="torchdr.UMAPAffinityIn"><code class="xref py py-obj docutils literal notranslate"><span class="pre">UMAPAffinityIn</span></code></a>([n_neighbors, tol, max_iter, ...])</p></td>
<td><p>Compute the input affinity used in UMAP <span id="id13">[<a class="reference internal" href="torchdr.bibliography.html#id9" title="Leland McInnes, John Healy, and James Melville. Umap: uniform manifold approximation and projection for dimension reduction. arXiv preprint arXiv:1802.03426, 2018.">McInnes <em>et al.</em>, 2018</a>]</span>.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="gen_modules/torchdr.UMAPAffinityOut.html#torchdr.UMAPAffinityOut" title="torchdr.UMAPAffinityOut"><code class="xref py py-obj docutils literal notranslate"><span class="pre">UMAPAffinityOut</span></code></a>([min_dist, spread, a, b, ...])</p></td>
<td><p>Compute the affinity used in embedding space in UMAP <span id="id14">[<a class="reference internal" href="torchdr.bibliography.html#id9" title="Leland McInnes, John Healy, and James Melville. Umap: uniform manifold approximation and projection for dimension reduction. arXiv preprint arXiv:1802.03426, 2018.">McInnes <em>et al.</em>, 2018</a>]</span>.</p></td>
</tr>
</tbody>
</table>
</div>
</section>
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<section id="scores">
<h3>Scores<a class="headerlink" href="#scores" title="Link to this heading">#</a></h3>
<p>The following classes are used to evaluate the embeddings.</p>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="gen_modules/torchdr.silhouette_score.html#torchdr.silhouette_score" title="torchdr.silhouette_score"><code class="xref py py-obj docutils literal notranslate"><span class="pre">silhouette_score</span></code></a>(X, labels[, weights, ...])</p></td>
<td><p>Compute the Silhouette score as the mean of silhouette coefficients.</p></td>
</tr>
</tbody>
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</section>
<section id="utils">
<h3>Utils<a class="headerlink" href="#utils" title="Link to this heading">#</a></h3>
<p>The following classes are used to perform various operations such as computing
the pairwise distances between the data points as well as solving root search problems.</p>
<div class="pst-scrollable-table-container"><table class="autosummary longtable table autosummary">
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="gen_modules/torchdr.pairwise_distances.html#torchdr.pairwise_distances" title="torchdr.pairwise_distances"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pairwise_distances</span></code></a>(X[, Y, metric, backend, ...])</p></td>
<td><p>Compute pairwise distances matrix between points in two datasets.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="gen_modules/torchdr.binary_search.html#torchdr.binary_search" title="torchdr.binary_search"><code class="xref py py-obj docutils literal notranslate"><span class="pre">binary_search</span></code></a>(f, n[, begin, end, max_iter, ...])</p></td>
<td><p>Implement the binary search root finding method.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="gen_modules/torchdr.false_position.html#torchdr.false_position" title="torchdr.false_position"><code class="xref py py-obj docutils literal notranslate"><span class="pre">false_position</span></code></a>(f, n[, begin, end, max_iter, ...])</p></td>
<td><p>Implement the false position root finding method.</p></td>
</tr>
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