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.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_aemet_unsupervised.py"
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.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_plot_aemet_unsupervised.py>`
        to download the full example code or to run this example in your browser via Binder

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_plot_aemet_unsupervised.py:


Meteorological data: data visualization, clustering, and functional PCA
=======================================================================

Shows the use of data visualization tools, clustering and functional
principal component analysis (FPCA).

.. GENERATED FROM PYTHON SOURCE LINES 8-33

.. code-block:: Python


    # License: MIT

    # sphinx_gallery_thumbnail_number = 4

    from __future__ import annotations

    from typing import Any, Mapping, Tuple

    import cartopy.crs as ccrs
    import matplotlib.pyplot as plt
    import numpy as np
    import sklearn.cluster
    from cartopy.io.img_tiles import GoogleTiles
    from matplotlib.axes import Axes
    from matplotlib.figure import Figure

    from skfda.datasets import fetch_aemet
    from skfda.exploratory.depth import ModifiedBandDepth
    from skfda.exploratory.visualization import Boxplot, MagnitudeShapePlot
    from skfda.exploratory.visualization.fpca import FPCAPlot
    from skfda.misc.metrics import l2_distance
    from skfda.ml.clustering import KMeans
    from skfda.preprocessing.dim_reduction import FPCA








.. GENERATED FROM PYTHON SOURCE LINES 34-52

In this example we explore the curves of daily temperatures at
different weather stations from Spain, included in the AEMET dataset\
:footcite:p:`meteorologicalstateagencyofspainaemet_2009_meteorological`.

We first show how the visualization tools of scikit-fda can be used to
detect and interpret magnitude and shape outliers.
We also explain how to employ a clustering method on these temperature
curves using scikit-fda.
Then, the location of each weather station is plotted into a map of Spain
with a different color according to its cluster.
This reveals a remarkable resemblance to a Spanish climate map.
A posterior analysis using functional principal component analysis (FPCA)
explains how the two first principal components are related with relevant
meteorological concepts, and can be used to reconstruct and interpret
the original clustering.

This is one of the examples presented in the ICTAI conference\
:footcite:p:`ramos-carreno++_2022_scikitfda`.

.. GENERATED FROM PYTHON SOURCE LINES 54-55

We first load the AEMET dataset and plot it.

.. GENERATED FROM PYTHON SOURCE LINES 55-61

.. code-block:: Python

    X, _ = fetch_aemet(return_X_y=True)
    X = X.coordinates[0]

    X.plot()
    plt.show()




.. image-sg:: /auto_examples/images/sphx_glr_plot_aemet_unsupervised_001.png
   :alt: AEMET
   :srcset: /auto_examples/images/sphx_glr_plot_aemet_unsupervised_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 62-65

A boxplot can show magnitude outliers, in this case Navacerrada.
Here the temperatures are lower than in the other curves, as this
weather station is at a high altitude, near a ski resort.

.. GENERATED FROM PYTHON SOURCE LINES 65-71

.. code-block:: Python

    Boxplot(
        X,
        depth_method=ModifiedBandDepth(),
    ).plot()
    plt.show()




.. image-sg:: /auto_examples/images/sphx_glr_plot_aemet_unsupervised_002.png
   :alt: AEMET
   :srcset: /auto_examples/images/sphx_glr_plot_aemet_unsupervised_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 72-77

A magnitude-shape plot can be used to detect shape outliers, such as the
Canary islands, with a less steeper temperature curve.
The Canary islands are at a lower latitude, closer to the equator.
Thus, they have a subtropical climate which presents less temperature
variation during the year.

.. GENERATED FROM PYTHON SOURCE LINES 77-82

.. code-block:: Python

    MagnitudeShapePlot(
        X,
    ).plot()
    plt.show()




.. image-sg:: /auto_examples/images/sphx_glr_plot_aemet_unsupervised_003.png
   :alt: AEMET
   :srcset: /auto_examples/images/sphx_glr_plot_aemet_unsupervised_003.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 83-84

We now attempt to cluster the curves using functional k-means.

.. GENERATED FROM PYTHON SOURCE LINES 84-95

.. code-block:: Python

    n_clusters = 5
    n_init = 10

    fda_kmeans = KMeans(
        n_clusters=n_clusters,
        n_init=n_init,
        metric=l2_distance,
        random_state=0,
    )
    fda_clusters = fda_kmeans.fit_predict(X)








.. GENERATED FROM PYTHON SOURCE LINES 96-98

We want to plot the cluster of each station in the map of Spain. We need to
define first auxiliary variables and functions for plotting.

.. GENERATED FROM PYTHON SOURCE LINES 98-165

.. code-block:: Python

    coords_spain = (-10, 5, 34.98, 44.8)
    coords_canary = (-18.5, -13, 27.5, 29.5)

    # It is easier to obtain the longitudes and latitudes from the data in
    # a Pandas dataframe.
    aemet, _ = fetch_aemet(return_X_y=True, as_frame=True)

    station_longitudes = aemet.loc[:, "longitude"].values
    station_latitudes = aemet.loc[:, "latitude"].values


    def create_map(
        coords: Tuple[float, float, float, float],
        figsize: Tuple[float, float],
    ) -> Figure:
        """Create a map for a region of the world."""
        tiler = GoogleTiles(style="satellite")
        mercator = tiler.crs

        fig = plt.figure(figsize=figsize)
        ax = fig.add_axes([0, 0, 1, 1], projection=mercator)
        ax.set_extent(coords, crs=ccrs.PlateCarree())

        ax.add_image(tiler, 8)
        ax.set_adjustable('datalim')

        return fig


    def plot_cluster_points(
        longitudes: np.typing.NDArray[np.floating[Any]],
        latitudes: np.typing.NDArray[np.floating[Any]],
        clusters: np.typing.NDArray[np.integer[Any]],
        color_map: Mapping[int, str],
        ax: Axes,
    ) -> None:
        """Plot the stations in a map with their cluster color."""
        for cluster in range(n_clusters):
            selection = (clusters == cluster)
            ax.scatter(
                longitudes[selection],
                latitudes[selection],
                s=64,
                color=color_map[cluster],
                edgecolors='white',
                transform=ccrs.Geodetic(),
            )


    # Colors for each cluster
    fda_color_map = {
        0: "purple",
        1: "yellow",
        2: "green",
        3: "red",
        4: "orange",
    }

    # Names of each climate (for this particular seed)
    climate_names = {
        0: "Cold/mountain",
        1: "Mediterranean",
        2: "Atlantic",
        3: "Subtropical",
        4: "Continental",
    }








.. GENERATED FROM PYTHON SOURCE LINES 166-188

We now plot the obtained clustering in the maps.

It is possible to notice that each cluster seems to roughly correspond with
a particular climate:

- Red points, only present in the Canary islands, correspond to a subtropical
  climate.
- Yellow points, in the Mediterranean coast, correspond to a Mediterranean
  climate.
- Green points, in the Atlantic coast of mainland Spain, correspond to an
  Atlantic or oceanic climate.
- Orange points, in the center of mainland Spain, correspond to a continental
  climate.
- Finally the purple points are located at the coldest regions of Spain, such
  as in high mountain ranges.
  Thus, it can be associated with a cold or mountain climate.

Notice that a couple of points in the Canary islands are not red.
The purple one is easy to explain, as it is in mount Teide, the highest
mountain of Spain.
The yellow one is in the airport of Los Rodeos, which has its own
microclimate\ :footcite:p:`romeo+marzoljaen_2014_analisis`.

.. GENERATED FROM PYTHON SOURCE LINES 188-210

.. code-block:: Python


    # Mainland
    fig_spain = create_map(coords_spain, figsize=(8, 6))
    plot_cluster_points(
        longitudes=station_longitudes,
        latitudes=station_latitudes,
        clusters=fda_clusters,
        color_map=fda_color_map,
        ax=fig_spain.axes[0],
    )

    # Canary Islands
    fig_canary = create_map(coords_canary, figsize=(8, 3))
    plot_cluster_points(
        longitudes=station_longitudes,
        latitudes=station_latitudes,
        clusters=fda_clusters,
        color_map=fda_color_map,
        ax=fig_canary.axes[0],
    )
    plt.show()




.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /auto_examples/images/sphx_glr_plot_aemet_unsupervised_004.png
         :alt: plot aemet unsupervised
         :srcset: /auto_examples/images/sphx_glr_plot_aemet_unsupervised_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/images/sphx_glr_plot_aemet_unsupervised_005.png
         :alt: plot aemet unsupervised
         :srcset: /auto_examples/images/sphx_glr_plot_aemet_unsupervised_005.png
         :class: sphx-glr-multi-img





.. GENERATED FROM PYTHON SOURCE LINES 211-213

We now can compute the first two principal components for interpretability,
and project the data over these directions.

.. GENERATED FROM PYTHON SOURCE LINES 213-222

.. code-block:: Python

    fpca = FPCA(n_components=2)
    fpca.fit(X)

    # The sign of the components is arbitrary, but this way it is easier to
    # understand.
    fpca.components_ *= -1

    X_red = fpca.transform(X)








.. GENERATED FROM PYTHON SOURCE LINES 223-233

We now plot the first two principal components as perturbations over the
mean.

The ``factor`` parameters is a number that multiplies each component in
order to make their effect more noticeable.

It is possible to observe that the first component measures a global
increase/decrease in temperature.
The second component instead has the effect of increasing/decreasing
the variability of the temperatures during the year.

.. GENERATED FROM PYTHON SOURCE LINES 233-242

.. code-block:: Python

    fig = plt.figure(figsize=(8, 4))
    FPCAPlot(
        fpca.mean_,
        fpca.components_,
        factor=50,
        fig=fig,
    ).plot()
    plt.show()




.. image-sg:: /auto_examples/images/sphx_glr_plot_aemet_unsupervised_006.png
   :alt: AEMET, Principal component 1, Principal component 2
   :srcset: /auto_examples/images/sphx_glr_plot_aemet_unsupervised_006.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 243-251

We also plot the projections over the first two principal components,
keeping the cluster colors.
Here we can easily observe the corresponding characteristics of each
climate in terms of global temperature and annual variability.
The two outliers of the Mediterranean climate correspond to the
aforementioned airport of Los Rodeos, and to Tarifa, which is
located at the strait of Gibraltar and thus receives also the cold
waters of the Atlantic, explaining its lower annual variability.

.. GENERATED FROM PYTHON SOURCE LINES 251-266

.. code-block:: Python

    fig, ax = plt.subplots(1, 1)
    for cluster in range(n_clusters):
        selection = fda_clusters == cluster
        ax.scatter(
            X_red[selection, 0],
            X_red[selection, 1],
            color=fda_color_map[cluster],
            label=climate_names[cluster],
        )

    ax.set_xlabel('First principal component')
    ax.set_ylabel('Second principal component')
    ax.legend()
    plt.show()




.. image-sg:: /auto_examples/images/sphx_glr_plot_aemet_unsupervised_007.png
   :alt: plot aemet unsupervised
   :srcset: /auto_examples/images/sphx_glr_plot_aemet_unsupervised_007.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 267-268

We now attempt a multivariate clustering using only these projections.

.. GENERATED FROM PYTHON SOURCE LINES 268-275

.. code-block:: Python

    mv_kmeans = sklearn.cluster.KMeans(
        n_clusters=n_clusters,
        n_init=n_init,
        random_state=0,
    )
    mv_clusters = mv_kmeans.fit_predict(X_red)








.. GENERATED FROM PYTHON SOURCE LINES 276-281

We now plot the multivariate clustering in the maps. We define a different
color map to match cluster colors with the previously obtained ones.
As you can see, the clustering using only the two first principal components
matches almost perfectly with the original one, that used the complete
temperature curves.

.. GENERATED FROM PYTHON SOURCE LINES 281-311

.. code-block:: Python


    mv_color_map = {
        0: "yellow",
        1: "orange",
        2: "red",
        3: "purple",
        4: "green",
    }

    # Mainland
    fig_spain = create_map(coords_spain, figsize=(8, 6))
    plot_cluster_points(
        longitudes=station_longitudes,
        latitudes=station_latitudes,
        clusters=mv_clusters,
        color_map=mv_color_map,
        ax=fig_spain.axes[0],
    )

    # Canary Islands
    fig_canary = create_map(coords_canary, figsize=(8, 3))
    plot_cluster_points(
        longitudes=station_longitudes,
        latitudes=station_latitudes,
        clusters=mv_clusters,
        color_map=mv_color_map,
        ax=fig_canary.axes[0],
    )
    plt.show()




.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /auto_examples/images/sphx_glr_plot_aemet_unsupervised_008.png
         :alt: plot aemet unsupervised
         :srcset: /auto_examples/images/sphx_glr_plot_aemet_unsupervised_008.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/images/sphx_glr_plot_aemet_unsupervised_009.png
         :alt: plot aemet unsupervised
         :srcset: /auto_examples/images/sphx_glr_plot_aemet_unsupervised_009.png
         :class: sphx-glr-multi-img





.. GENERATED FROM PYTHON SOURCE LINES 312-316

References
----------

.. footbibliography::


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 5.764 seconds)


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