:orphan:

Examples
========

Examples of several functionalities of the package.



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Representation
--------------

Examples that illustrate the available objects in scikit-fda used to represent functional data inside the computer.



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    <div class="sphx-glr-thumbcontainer" tooltip="Shows how to make a discretized representation of a function.">

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  .. image:: /auto_examples/representation/images/thumb/sphx_glr_plot_discrete_representation_thumb.png
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  :ref:`sphx_glr_auto_examples_representation_plot_discrete_representation.py`

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      <div class="sphx-glr-thumbnail-title">Discretized function representation</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Shows the usage of the different types of extrapolation.">

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  .. image:: /auto_examples/representation/images/thumb/sphx_glr_plot_extrapolation_thumb.png
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  :ref:`sphx_glr_auto_examples_representation_plot_extrapolation.py`

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      <div class="sphx-glr-thumbnail-title">Extrapolation</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example shows the composition of multidimensional FDataGrids.">

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  .. image:: /auto_examples/representation/images/thumb/sphx_glr_plot_composition_thumb.png
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  :ref:`sphx_glr_auto_examples_representation_plot_composition.py`

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      <div class="sphx-glr-thumbnail-title">Function composition</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example shows the types of interpolation used in the evaluation of FDataGrids.">

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  .. image:: /auto_examples/representation/images/thumb/sphx_glr_plot_interpolation_thumb.png
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  :ref:`sphx_glr_auto_examples_representation_plot_interpolation.py`

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      <div class="sphx-glr-thumbnail-title">Interpolation</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates how to build and visualize mixed datasets containing both scalar and functional elements using the Canadian weather dataset. In particular, we show how to include both a function and its derivative, either jointly in a vector-valued functional object, or separately as independent entries. We also explore how to structure and visualize this data using pandas and scikit-fda&#x27;s visualization tools.">

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  .. image:: /auto_examples/representation/images/thumb/sphx_glr_plot_mixed_data_thumb.png
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  :ref:`sphx_glr_auto_examples_representation_plot_mixed_data.py`

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      <div class="sphx-glr-thumbnail-title">Mixed data structure and visualization.</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example converts irregular data to a basis representation using a mixed effects model.">

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  .. image:: /auto_examples/representation/images/thumb/sphx_glr_plot_irregular_to_basis_mixed_effects_thumb.png
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  :ref:`sphx_glr_auto_examples_representation_plot_irregular_to_basis_mixed_effects.py`

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      <div class="sphx-glr-thumbnail-title">Mixed effects model for irregular data</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example converts irregular data to a basis representation using a mixed effects model and checks the robustness of the method by fitting the model with decreasing number of measurement points per curve.">

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  .. image:: /auto_examples/representation/images/thumb/sphx_glr_plot_irregular_mixed_effects_robustness_thumb.png
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  :ref:`sphx_glr_auto_examples_representation_plot_irregular_mixed_effects_robustness.py`

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      <div class="sphx-glr-thumbnail-title">Mixed effects model for irregular data: robustness of the conversion</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Explores the different representations of functional data.">

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  .. image:: /auto_examples/representation/images/thumb/sphx_glr_plot_representation_thumb.png
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  :ref:`sphx_glr_auto_examples_representation_plot_representation.py`

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      <div class="sphx-glr-thumbnail-title">Representation of functional data</div>
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Datasets
--------

Examples illustrating a particular dataset or data generation technique.



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    <div class="sphx-glr-thumbcontainer" tooltip="Shows the use of data visualization tools, clustering and functional principal component analysis (FPCA).">

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  .. image:: /auto_examples/datasets/images/thumb/sphx_glr_plot_aemet_unsupervised_thumb.png
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  :ref:`sphx_glr_auto_examples_datasets_plot_aemet_unsupervised.py`

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      <div class="sphx-glr-thumbnail-title">Meteorological data: data visualization, clustering, and functional PCA</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example shows how to use numeric SDE solvers to simulate solutions of Stochastic Differential Equations (SDEs).">

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  .. image:: /auto_examples/datasets/images/thumb/sphx_glr_plot_langevin_dynamics_thumb.png
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  :ref:`sphx_glr_auto_examples_datasets_plot_langevin_dynamics.py`

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      <div class="sphx-glr-thumbnail-title">SDE simulation: Langevin dynamics</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example shows how to use numeric SDE solvers to simulate solutions of Stochastic Differential Equations (SDEs).">

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  .. image:: /auto_examples/datasets/images/thumb/sphx_glr_plot_sde_simulation_thumb.png
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  :ref:`sphx_glr_auto_examples_datasets_plot_sde_simulation.py`

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      <div class="sphx-glr-thumbnail-title">SDE simulation: creating synthetic datasets using SDEs</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Shows the use of derivatives, functional regression and variable selection for functional data.">

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  .. image:: /auto_examples/datasets/images/thumb/sphx_glr_plot_tecator_regression_thumb.png
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  :ref:`sphx_glr_auto_examples_datasets_plot_tecator_regression.py`

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      <div class="sphx-glr-thumbnail-title">Spectrometric data: derivatives, regression, and variable selection</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Shows the use of functional preprocessing tools such as smoothing and registration, and functional classification methods.">

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  .. image:: /auto_examples/datasets/images/thumb/sphx_glr_plot_phonemes_classification_thumb.png
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  :ref:`sphx_glr_auto_examples_datasets_plot_phonemes_classification.py`

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      <div class="sphx-glr-thumbnail-title">Voice signals: smoothing, registration, and classification</div>
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Preprocessing
-------------

Examples of preprocessing techniques available in scikit-fda.



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    <div class="sphx-glr-thumbcontainer" tooltip="Shows the usage of the elastic registration to perform a groupwise alignment.">

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  .. image:: /auto_examples/preprocessing/images/thumb/sphx_glr_plot_elastic_registration_thumb.png
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  :ref:`sphx_glr_auto_examples_preprocessing_plot_elastic_registration.py`

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      <div class="sphx-glr-thumbnail-title">Elastic registration</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Functional Diffusion Maps">

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  .. image:: /auto_examples/preprocessing/images/thumb/sphx_glr_plot_fdm_thumb.png
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  :ref:`sphx_glr_auto_examples_preprocessing_plot_fdm.py`

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      <div class="sphx-glr-thumbnail-title">Functional Diffusion Maps</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Explores the two possible ways to do functional principal component analysis.">

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  .. image:: /auto_examples/preprocessing/images/thumb/sphx_glr_plot_fpca_thumb.png
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  :ref:`sphx_glr_auto_examples_preprocessing_plot_fpca.py`

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      <div class="sphx-glr-thumbnail-title">Functional Principal Component Analysis</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example uses different kernel smoothing methods over the phoneme data set (phoneme) and shows how cross validations scores vary over a range of different parameters used in the smoothing methods. It also shows examples of undersmoothing and oversmoothing.">

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  .. image:: /auto_examples/preprocessing/images/thumb/sphx_glr_plot_kernel_smoothing_thumb.png
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  :ref:`sphx_glr_auto_examples_preprocessing_plot_kernel_smoothing.py`

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      <div class="sphx-glr-thumbnail-title">Kernel Smoothing</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example shows the basic usage of the landmark registration.">

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  .. image:: /auto_examples/preprocessing/images/thumb/sphx_glr_plot_landmark_registration_thumb.png
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  :ref:`sphx_glr_auto_examples_preprocessing_plot_landmark_registration.py`

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      <div class="sphx-glr-thumbnail-title">Landmark registration</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example shows how to shift functional data objects to align its samples with a particular reference point.">

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  .. image:: /auto_examples/preprocessing/images/thumb/sphx_glr_plot_landmark_shift_thumb.png
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  :ref:`sphx_glr_auto_examples_preprocessing_plot_landmark_shift.py`

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      <div class="sphx-glr-thumbnail-title">Landmark shift</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Example of using the inverse_transform method in the FPCA class to detect outlier(s) from the reconstruction (truncation) error.">

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  .. image:: /auto_examples/preprocessing/images/thumb/sphx_glr_plot_fpca_inverse_transform_outl_detection_thumb.png
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  :ref:`sphx_glr_auto_examples_preprocessing_plot_fpca_inverse_transform_outl_detection.py`

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      <div class="sphx-glr-thumbnail-title">Outlier detection with FPCA</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Shows the usage of the elastic registration to perform a pairwise alignment.">

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  .. image:: /auto_examples/preprocessing/images/thumb/sphx_glr_plot_pairwise_alignment_thumb.png
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  :ref:`sphx_glr_auto_examples_preprocessing_plot_pairwise_alignment.py`

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      <div class="sphx-glr-thumbnail-title">Pairwise alignment</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Shows the use of shift registration applied to a sinusoidal process represented in a Fourier basis.">

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  .. image:: /auto_examples/preprocessing/images/thumb/sphx_glr_plot_shift_registration_thumb.png
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  :ref:`sphx_glr_auto_examples_preprocessing_plot_shift_registration.py`

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      <div class="sphx-glr-thumbnail-title">Shift Registration</div>
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Exploratory analysis
--------------------

Examples of exploratory analysis functionalities available in scikit-fda.



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    <div class="sphx-glr-thumbcontainer" tooltip="Shows the use of the functional Boxplot applied to the Canadian Weather dataset.">

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  .. image:: /auto_examples/exploratory/images/thumb/sphx_glr_plot_boxplot_thumb.png
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  :ref:`sphx_glr_auto_examples_exploratory_plot_boxplot.py`

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      <div class="sphx-glr-thumbnail-title">Boxplot</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Explores the Tecator data set by plotting the functional data and calculating means and derivatives.">

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  .. image:: /auto_examples/exploratory/images/thumb/sphx_glr_plot_explore_thumb.png
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  :ref:`sphx_glr_auto_examples_exploratory_plot_explore.py`

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      <div class="sphx-glr-thumbnail-title">Exploring data</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Shows the use of the MS-Plot applied to the Canadian Weather dataset.">

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  .. image:: /auto_examples/exploratory/images/thumb/sphx_glr_plot_magnitude_shape_thumb.png
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  :ref:`sphx_glr_auto_examples_exploratory_plot_magnitude_shape.py`

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      <div class="sphx-glr-thumbnail-title">Magnitude-Shape Plot</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Shows the use of the MS-Plot applied to a synthetic dataset.">

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  .. image:: /auto_examples/exploratory/images/thumb/sphx_glr_plot_magnitude_shape_synthetic_thumb.png
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  :ref:`sphx_glr_auto_examples_exploratory_plot_magnitude_shape_synthetic.py`

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      <div class="sphx-glr-thumbnail-title">Magnitude-Shape Plot synthetic example</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Shows the use of the surface boxplot, which is a generalization of the functional boxplot for FDataGrid whose domain dimension is 2.">

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  .. image:: /auto_examples/exploratory/images/thumb/sphx_glr_plot_surface_boxplot_thumb.png
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  :ref:`sphx_glr_auto_examples_exploratory_plot_surface_boxplot.py`

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      <div class="sphx-glr-thumbnail-title">Surface Boxplot</div>
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Statistical inference
---------------------

Examples of statistical inference functionalities in scikit-fda.



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    <div class="sphx-glr-thumbcontainer" tooltip="This example shows how to perform a functional one-way ANOVA test using a real dataset.">

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  .. image:: /auto_examples/inference/images/thumb/sphx_glr_plot_oneway_thumb.png
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  :ref:`sphx_glr_auto_examples_inference_plot_oneway.py`

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      <div class="sphx-glr-thumbnail-title">One-way functional ANOVA with real data</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example shows how to perform a functional one-way ANOVA test with synthetic data.">

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  .. image:: /auto_examples/inference/images/thumb/sphx_glr_plot_oneway_synthetic_thumb.png
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  :ref:`sphx_glr_auto_examples_inference_plot_oneway_synthetic.py`

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      <div class="sphx-glr-thumbnail-title">One-way functional ANOVA with synthetic data</div>
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Machine learning
----------------

Examples the machine learning methods (clustering, classification and regression) for functional data that can be used in scikit-fda.



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    <div class="sphx-glr-thumbcontainer" tooltip="It shows a comparison between the accuracies of different classification methods. There has been selected one method of each kind present in the library. In particular, there is one based on depths, Maximum Depth Classifier, another one based on centroids, Nearest Centroid Classifier, another one based on the K-Nearest Neighbors, K-Nearest Neighbors Classifier, and finally, one based on the quadratic discriminant analysis, Parameterized Functional QDA.">

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  .. image:: /auto_examples/ml/images/thumb/sphx_glr_plot_classification_methods_thumb.png
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  :ref:`sphx_glr_auto_examples_ml_plot_classification_methods.py`

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      <div class="sphx-glr-thumbnail-title">Classification methods</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, the use of the clustering plot methods is shown applied to the Canadian Weather dataset. K-Means and Fuzzy K-Means algorithms are employed to calculate the results plotted.">

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  .. image:: /auto_examples/ml/images/thumb/sphx_glr_plot_clustering_thumb.png
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  :ref:`sphx_glr_auto_examples_ml_plot_clustering.py`

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      <div class="sphx-glr-thumbnail-title">Clustering</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example shows the use of the depth based classification methods applied to the Berkeley Growth Study data. An attempt to show the differences and similarities between MaximumDepthClassifier, DDClassifier, and DDGClassifier is made.">

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  .. image:: /auto_examples/ml/images/thumb/sphx_glr_plot_depth_classification_thumb.png
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  :ref:`sphx_glr_auto_examples_ml_plot_depth_classification.py`

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      <div class="sphx-glr-thumbnail-title">Depth based classification</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="This example explores the use of the linear regression with multivariate (scalar) covariates and functional response.">

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  .. image:: /auto_examples/ml/images/thumb/sphx_glr_plot_functional_regression_thumb.png
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  :ref:`sphx_glr_auto_examples_ml_plot_functional_regression.py`

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      <div class="sphx-glr-thumbnail-title">Functional Linear Regression with multivariate covariates.</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example explores the use of the functional principal component analysis (FPCA) in regression problems.">

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  .. image:: /auto_examples/ml/images/thumb/sphx_glr_plot_fpca_regression_thumb.png
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  :ref:`sphx_glr_auto_examples_ml_plot_fpca_regression.py`

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      <div class="sphx-glr-thumbnail-title">Functional Principal Component Analysis Regression.</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Shows the usage of the k-nearest neighbors classifier.">

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  .. image:: /auto_examples/ml/images/thumb/sphx_glr_plot_k_neighbors_classification_thumb.png
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  :ref:`sphx_glr_auto_examples_ml_plot_k_neighbors_classification.py`

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      <div class="sphx-glr-thumbnail-title">K-nearest neighbors classification</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="In this example we will see and compare the performance of different kernel regression methods.">

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  .. image:: /auto_examples/ml/images/thumb/sphx_glr_plot_kernel_regression_thumb.png
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  :ref:`sphx_glr_auto_examples_ml_plot_kernel_regression.py`

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      <div class="sphx-glr-thumbnail-title">Kernel Regression</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Shows the usage of the nearest neighbors regressor with functional response.">

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  .. image:: /auto_examples/ml/images/thumb/sphx_glr_plot_neighbors_functional_regression_thumb.png
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  :ref:`sphx_glr_auto_examples_ml_plot_neighbors_functional_regression.py`

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      <div class="sphx-glr-thumbnail-title">Neighbors Functional Regression</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Shows the usage of the nearest neighbors regressor with scalar response.">

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  .. image:: /auto_examples/ml/images/thumb/sphx_glr_plot_neighbors_scalar_regression_thumb.png
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  :ref:`sphx_glr_auto_examples_ml_plot_neighbors_scalar_regression.py`

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      <div class="sphx-glr-thumbnail-title">Neighbors Scalar Regression</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Shows the usage of the radius nearest neighbors classifier.">

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  .. image:: /auto_examples/ml/images/thumb/sphx_glr_plot_radius_neighbors_classification_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_ml_plot_radius_neighbors_classification.py`

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      <div class="sphx-glr-thumbnail-title">Radius neighbors classification</div>
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Expand scikit-fda
-----------------

Examples of how to expand the functionality of scikit-fda with custom behaviors.



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    <div class="sphx-glr-thumbcontainer" tooltip="Shows how to add new bases for FDataBasis by creating subclasses.">

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  .. image:: /auto_examples/expand_skfda/images/thumb/sphx_glr_plot_basis_subclass_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_expand_skfda_plot_basis_subclass.py`

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      <div class="sphx-glr-thumbnail-title">Creating a new basis</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Shows how to add new interpolation and extrapolation strategies.">

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  .. image:: /auto_examples/expand_skfda/images/thumb/sphx_glr_plot_new_evaluator_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_expand_skfda_plot_new_evaluator.py`

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      <div class="sphx-glr-thumbnail-title">Creating a new interpolation or extrapolation strategy</div>
    </div>


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.. toctree::
   :hidden:
   :includehidden:


   /auto_examples/representation/index.rst
   /auto_examples/datasets/index.rst
   /auto_examples/preprocessing/index.rst
   /auto_examples/exploratory/index.rst
   /auto_examples/inference/index.rst
   /auto_examples/ml/index.rst
   /auto_examples/expand_skfda/index.rst


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      :download:`Download all examples in Jupyter notebooks: auto_examples_jupyter.zip </auto_examples/auto_examples_jupyter.zip>`


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