.. _kmeansl1rst:

===================
KMeans with norm L1
===================


.. only:: html

    **Links:** :download:`notebook <kmeans_l1.ipynb>`, :downloadlink:`html <kmeans_l12html.html>`, :download:`PDF <kmeans_l1.pdf>`, :download:`python <kmeans_l1.py>`, :downloadlink:`slides <kmeans_l1.slides.html>`, :githublink:`GitHub|_doc/notebooks/sklearn/kmeans_l1.ipynb|*`


This demonstrates how results change when using norm L1 for a k-means
algorithm.

.. code:: ipython3

    from jyquickhelper import add_notebook_menu
    add_notebook_menu()






.. contents::
    :local:





.. code:: ipython3

    %matplotlib inline

.. code:: ipython3

    import matplotlib.pyplot as plt

Simple datasets
---------------

.. code:: ipython3

    import numpy
    import numpy.random as rnd
    N = 1000
    X = numpy.zeros((N * 2, 2), dtype=numpy.float64)
    X[:N] = rnd.rand(N, 2)
    X[N:] = rnd.rand(N, 2)
    #X[N:, 0] += 0.75
    X[N:, 1] += 1
    X[:N//10, 0] -= 2
    X.shape




.. parsed-literal::
    (2000, 2)



.. code:: ipython3

    fig, ax = plt.subplots(1, 1)
    ax.plot(X[:, 0], X[:, 1], '.')
    ax.set_title("Two squares");



.. image:: kmeans_l1_6_0.png


Classic KMeans
--------------

It uses euclidean distance.

.. code:: ipython3

    from sklearn.cluster import KMeans
    km = KMeans(2)
    km.fit(X)




.. parsed-literal::
    KMeans(n_clusters=2)



.. code:: ipython3

    km.cluster_centers_




.. parsed-literal::
    array([[0.27360385, 0.50114694],
           [0.49920054, 1.50108811]])



.. code:: ipython3

    def plot_clusters(km_, X, ax):
        lab = km_.predict(X)
        for i in range(km_.cluster_centers_.shape[0]):
            sub = X[lab == i]
            ax.plot(sub[:, 0], sub[:, 1], '.', label='c=%d' % i)
        C = km_.cluster_centers_
        ax.plot(C[:, 0], C[:, 1], 'o', ms=15, label="centers")
        ax.legend()
    
    fig, ax = plt.subplots(1, 1)
    plot_clusters(km, X, ax)
    ax.set_title("L2 KMeans");



.. image:: kmeans_l1_10_0.png


KMeans with L1 norm
-------------------

.. code:: ipython3

    from mlinsights.mlmodel import KMeansL1L2
    kml1 = KMeansL1L2(2, norm='L1')
    kml1.fit(X)




.. parsed-literal::
    KMeansL1L2(n_clusters=2, norm='l1')



.. code:: ipython3

    kml1.cluster_centers_




.. parsed-literal::
    array([[0.5812874 , 1.49145705],
           [0.33319472, 0.4959633 ]])



.. code:: ipython3

    fig, ax = plt.subplots(1, 1)
    plot_clusters(kml1, X, ax)
    ax.set_title("L1 KMeans");



.. image:: kmeans_l1_14_0.png


When clusters are completely different
--------------------------------------

.. code:: ipython3

    N = 1000
    X = numpy.zeros((N * 2, 2), dtype=numpy.float64)
    X[:N] = rnd.rand(N, 2)
    X[N:] = rnd.rand(N, 2)
    #X[N:, 0] += 0.75
    X[N:, 1] += 1
    X[:N//10, 0] -= 4
    X.shape




.. parsed-literal::
    (2000, 2)



.. code:: ipython3

    km = KMeans(2)
    km.fit(X)




.. parsed-literal::
    KMeans(n_clusters=2)



.. code:: ipython3

    kml1 = KMeansL1L2(2, norm='L1')
    kml1.fit(X)




.. parsed-literal::
    KMeansL1L2(n_clusters=2, norm='l1')



.. code:: ipython3

    fig, ax = plt.subplots(1, 2, figsize=(10, 4))
    plot_clusters(km, X, ax[0])
    plot_clusters(kml1, X, ax[1])
    ax[0].set_title("L2 KMeans")
    ax[1].set_title("L1 KMeans");



.. image:: kmeans_l1_19_0.png