Examples
========

Probabilistic FCM
-----------------

In the probabilistic algorithm, the total membership of every point must
equal unity - that is, membership is divided between each of the possible
cluster centers. Here, we produce a plot identifying the clusters in a
dataset. There is overlap between the clusters where ambiguity is detected.

Input
.....

.. code-block:: python
    :emphasize-lines: 6,8,9

    import numpy as np
    import matplotlib.pyplot as plt
    from skcmeans.algorithms import Probabilistic
    from sklearn.datasets import make_blobs
    plt.figure(figsize=(5, 5)).add_subplot(aspect='equal')
    n_clusters = 4
    data, labels = make_blobs(n_samples=300, centers=n_clusters, random_state=1)
    clusterer = Probabilistic(n_clusters=n_clusters, n_init=20)
    clusterer.fit(data)
    xx, yy = np.array(np.meshgrid(np.linspace(-10, 10, 1000), np.linspace(-10, 10, 1000)))
    z = np.rollaxis(clusterer.calculate_memberships(np.c_[xx.ravel(), yy.ravel()]).reshape(*xx.shape, -1), 2, 0)
    colors = 'rgbyco'
    for membership, color in zip(z, colors):
        plt.contour(xx, yy, membership, colors=color, alpha=0.5)
    plt.scatter(data[:, 0], data[:, 1], c='k')

Result
......

.. image:: _images/probabilistic.png
    :alt: Probabilistic fuzzy clustering result.



Changing the distance metric
----------------------------

Sometimes, it's useful to have a look at how different distance metrics
behave - for example, with higher-dimensional data, the cosine distance might
do better than the default Euclidean distance. It is possible to change the
distance measure of a clusterer instance on the fly, but it is probably
clearer to subclass the original algorithm:

Input
.....

.. code-block:: python
    :emphasize-lines: 5,6,10

    import numpy as np
    import matplotlib.pyplot as plt
    from skcmeans.algorithms import Probabilistic
    from sklearn.datasets import make_blobs
    class CosineProbabilistic(Probabilistic):
        metric = 'cityblock'
    plt.figure(figsize=(5, 5)).add_subplot(aspect='equal')
    n_clusters = 4
    data, labels = make_blobs(n_samples=300, centers=n_clusters, random_state=1)
    clusterer = CosineProbabilistic(n_clusters=n_clusters, n_init=20)
    clusterer.fit(data)
    xx, yy = np.array(np.meshgrid(np.linspace(-10, 10, 1000), np.linspace(-10, 10, 1000)))
    z = np.rollaxis(clusterer.calculate_memberships(np.c_[xx.ravel(), yy.ravel()]).reshape(*xx.shape, -1), 2, 0)
    colors = 'rgbyco'
    for membership, color in zip(z, colors):
        plt.contour(xx, yy, membership, colors=color, alpha=0.5)
    plt.scatter(data[:, 0], data[:, 1], c='k')

Result
......

.. image:: _images/metric.png
    :alt: Probabilistic fuzzy clustering with the cityblock distance metric.


Irregular Clusters
------------------

In real data science, the clusters are not usually nice circular (or
hyperspherical) shapes. One way of accounting for this is the
Gustafson-Kessel algorithm, which effectively adds a covariance matrix to
each cluster center, giving it ellipsoidal character, and an updated distance
calculation to go with it. This can be combined with either of the basic
algorithms.

Input
.....

.. code-block:: python
    :emphasize-lines: 5,6,12

    import numpy as np
    import matplotlib.pyplot as plt
    from skcmeans.algorithms import Probabilistic, GustafsonKesselMixin
    from sklearn.datasets import make_blobs
    class GKProbabilistic(Probabilistic, GustafsonKesselMixin):
        pass
    plt.figure(figsize=(5, 5)).add_subplot(aspect='equal')
    n_clusters = 4
    data, labels = make_blobs(n_samples=300, centers=n_clusters, random_state=1)
    transform = np.array([[1, 0.4], [1, 1]])
    data = np.dot(data, transform)
    clusterer = GKProbabilistic(n_clusters=n_clusters, n_init=20)
    clusterer.fit(data)
    xx, yy = np.array(np.meshgrid(np.linspace(-20, 10, 1000), np.linspace(-15, 10, 1000)))
    z = np.rollaxis(clusterer.calculate_memberships(np.c_[xx.ravel(), yy.ravel()]).reshape(*xx.shape, -1), 2, 0)
    colors = 'rgbyco'
    for membership, color in zip(z, colors):
        plt.contour(xx, yy, membership, colors=color, alpha=0.5)
    plt.scatter(data[:, 0], data[:, 1], c='k')


Result
......

.. image:: _images/gustafsonkessel.png
    :alt: Probabilistic fuzzy clustering with the Gustafson Kessel approach.