.. _sphx_glr_auto_examples_distance_metrics:

Distance Metrics and Representations
------------------------------------

Examples demonstrating non-Euclidean metrics, sparse matrices, precomputed graphs, text sequences, time series, and mixed tabular data.


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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates how CLARANS efficiently clusters high-dimensional sparse data stored as SciPy CSR/CSC sparse matrices.">

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  .. image:: /auto_examples/distance_metrics/images/thumb/sphx_glr_plot_sparse_input_thumb.png
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  :doc:`/auto_examples/distance_metrics/plot_sparse_input`

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      <div class="sphx-glr-thumbnail-title">Clustering Sparse CSR Matrices with CLARANS</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates how to use CLARANS and FastCLARANS with precomputed pairwise distance matrices (`metric=&#x27;precomputed&#x27;`), enabling clustering on graph, geodesic, or custom non-Euclidean distance data.">

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  .. image:: /auto_examples/distance_metrics/images/thumb/sphx_glr_plot_precomputed_distances_thumb.png
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  :doc:`/auto_examples/distance_metrics/plot_precomputed_distances`

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      <div class="sphx-glr-thumbnail-title">Clustering with Precomputed Distance Matrices</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates how different distance metrics and their hyperparameters via metric_params (Euclidean, Manhattan, Minkowski with p=3, and Mahalanobis with covariance inverse V^{-1}) affect cluster partition boundaries and medoid placements in CLARANS.">

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  .. image:: /auto_examples/distance_metrics/images/thumb/sphx_glr_plot_metrics_demo_thumb.png
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  :doc:`/auto_examples/distance_metrics/plot_metrics_demo`

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      <div class="sphx-glr-thumbnail-title">Distance Metrics and Metric Parameters in CLARANS Clustering</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example clusters graph nodes with FastCLARANS using shortest-path distances.">

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  .. image:: /auto_examples/distance_metrics/images/thumb/sphx_glr_plot_graph_clustering_thumb.png
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  :doc:`/auto_examples/distance_metrics/plot_graph_clustering`

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      <div class="sphx-glr-thumbnail-title">Graph Clustering with Precomputed Shortest-Path Distances</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates how CLARANS and FastCLARANS natively accept any user-defined distance function (``metric=callable``). We apply a custom Haversine distance function to cluster geographic coordinates (latitude and longitude) on the Earth&#x27;s spherical surface.">

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  .. image:: /auto_examples/distance_metrics/images/thumb/sphx_glr_plot_custom_callable_metric_thumb.png
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  :doc:`/auto_examples/distance_metrics/plot_custom_callable_metric`

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      <div class="sphx-glr-thumbnail-title">Custom Callable Distance Metric: Geospatial Haversine Clustering</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates how CLARANS and FastCLARANS cluster directed networks and asymmetric dissimilarity matrices (where D_{ij} \neq D_{ji}).">

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  .. image:: /auto_examples/distance_metrics/images/thumb/sphx_glr_plot_asymmetric_distances_thumb.png
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  :doc:`/auto_examples/distance_metrics/plot_asymmetric_distances`

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      <div class="sphx-glr-thumbnail-title">Clustering on Asymmetric Precomputed Distance Matrices (D != D^T)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates how CLARANS and FastCLARANS cluster feature matrices containing missing values (NaN) using metric=&#x27;nan_euclidean&#x27;.">

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  .. image:: /auto_examples/distance_metrics/images/thumb/sphx_glr_plot_nan_data_clustering_thumb.png
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  :doc:`/auto_examples/distance_metrics/plot_nan_data_clustering`

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      <div class="sphx-glr-thumbnail-title">Clustering Incomplete Data with Missing Values (NaN)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates how CLARANS and FastCLARANS cluster non-vector objects (such as text strings, search queries, DNA/amino-acid motifs) where traditional centroid-based algorithms like K-Means fail.">

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  .. image:: /auto_examples/distance_metrics/images/thumb/sphx_glr_plot_string_clustering_thumb.png
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  :doc:`/auto_examples/distance_metrics/plot_string_clustering`

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      <div class="sphx-glr-thumbnail-title">Clustering Non-Vector Data: Text Sequences with Edit Distance</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example shows how FastCLARANS clusters time series using Dynamic Time Warping (DTW) as a precomputed distance matrix.">

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  .. image:: /auto_examples/distance_metrics/images/thumb/sphx_glr_plot_time_series_dtw_thumb.png
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  :doc:`/auto_examples/distance_metrics/plot_time_series_dtw`

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      <div class="sphx-glr-thumbnail-title">Clustering Time Series with Dynamic Time Warping (DTW)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example shows how FastCLARANS clusters mixed-type tabular data combining continuous, binary, and categorical attributes using Gower&#x27;s dissimilarity.">

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  :doc:`/auto_examples/distance_metrics/plot_mixed_data_gower`

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      <div class="sphx-glr-thumbnail-title">Clustering Mixed-Type Tabular Data with Gower's Dissimilarity</div>
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.. toctree::
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   /auto_examples/distance_metrics/plot_sparse_input
   /auto_examples/distance_metrics/plot_precomputed_distances
   /auto_examples/distance_metrics/plot_metrics_demo
   /auto_examples/distance_metrics/plot_graph_clustering
   /auto_examples/distance_metrics/plot_custom_callable_metric
   /auto_examples/distance_metrics/plot_asymmetric_distances
   /auto_examples/distance_metrics/plot_nan_data_clustering
   /auto_examples/distance_metrics/plot_string_clustering
   /auto_examples/distance_metrics/plot_time_series_dtw
   /auto_examples/distance_metrics/plot_mixed_data_gower