聚類K-Means和大數據集的Mini Batch K-Means算法

import numpy as np

from sklearn.datasets import make_blobs
from sklearn.cluster import KMeans
from sklearn.metrics import pairwise_distances
import matplotlib.pyplot as plt
import matplotlib as mpl
from cycler import cycler

from .tools import discrete_scatter
from .plot_2d_separator import plot_2d_classification
from .plot_helpers import cm3


def plot_kmeans_algorithm():

    X, y = make_blobs(random_state=1)
    # we don't want cyan in there
    with mpl.rc_context(rc={'axes.prop_cycle': cycler('color', ['#0000aa',
                                                                '#ff2020',
                                                                '#50ff50'])}):
        fig, axes = plt.subplots(3, 3, figsize=(10, 8), subplot_kw={'xticks': (), 'yticks': ()})
        axes = axes.ravel()
        axes[0].set_title("Input data")
        discrete_scatter(X[:, 0], X[:, 1], ax=axes[0], markers=['o'], c='w')

        axes[1].set_title("Initialization")
        init = X[:3, :]
        discrete_scatter(X[:, 0], X[:, 1], ax=axes[1], markers=['o'], c='w')
        discrete_scatter(init[:, 0], init[:, 1], [0, 1, 2], ax=axes[1],
                         markers=['^'], markeredgewidth=2)

        axes[2].set_title("Assign Points (1)")
        km = KMeans(n_clusters=3, init=init, max_iter=1, n_init=1).fit(X)
        centers = km.cluster_centers_
        # need to compute labels by hand. scikit-learn does two e-steps for max_iter=1
        # (and it's totally my fault)
        labels = np.argmin(pairwise_distances(init, X), axis=0)
        discrete_scatter(X[:, 0], X[:, 1], labels, markers=['o'],
                         ax=axes[2])
        discrete_scatter(init[:, 0], init[:, 1], [0, 1, 2],
                         ax=axes[2], markers=['^'], markeredgewidth=2)

        axes[3].set_title("Recompute Centers (1)")
        discrete_scatter(X[:, 0], X[:, 1], labels, markers=['o'],
                         ax=axes[3])
        discrete_scatter(centers[:, 0], centers[:, 1], [0, 1, 2],
                         ax=axes[3], markers=['^'], markeredgewidth=2)

        axes[4].set_title("Reassign Points (2)")
        km = KMeans(n_clusters=3, init=init, max_iter=1, n_init=1).fit(X)
        labels = km.labels_
        discrete_scatter(X[:, 0], X[:, 1], labels, markers=['o'],
                         ax=axes[4])
        discrete_scatter(centers[:, 0], centers[:, 1], [0, 1, 2],
                         ax=axes[4], markers=['^'], markeredgewidth=2)

        km = KMeans(n_clusters=3, init=init, max_iter=2, n_init=1).fit(X)
        axes[5].set_title("Recompute Centers (2)")
        centers = km.cluster_centers_
        discrete_scatter(X[:, 0], X[:, 1], labels, markers=['o'],
                         ax=axes[5])
        discrete_scatter(centers[:, 0], centers[:, 1], [0, 1, 2],
                         ax=axes[5], markers=['^'], markeredgewidth=2)

        axes[6].set_title("Reassign Points (3)")
        labels = km.labels_
        discrete_scatter(X[:, 0], X[:, 1], labels, markers=['o'],
                         ax=axes[6])
        markers = discrete_scatter(centers[:, 0], centers[:, 1], [0, 1, 2],
                                   ax=axes[6], markers=['^'],
                                   markeredgewidth=2)

        axes[7].set_title("Recompute Centers (3)")
        km = KMeans(n_clusters=3, init=init, max_iter=3, n_init=1).fit(X)
        centers = km.cluster_centers_
        discrete_scatter(X[:, 0], X[:, 1], labels, markers=['o'],
                         ax=axes[7])
        discrete_scatter(centers[:, 0], centers[:, 1], [0, 1, 2],
                         ax=axes[7], markers=['^'], markeredgewidth=2)
        axes[8].set_axis_off()
        axes[8].legend(markers, ["Cluster 0", "Cluster 1", "Cluster 2"], loc='best')


def plot_kmeans_boundaries():
    X, y = make_blobs(random_state=1)
    init = X[:3, :]
    km = KMeans(n_clusters=3, init=init, max_iter=2, n_init=1).fit(X)
    discrete_scatter(X[:, 0], X[:, 1], km.labels_, markers=['o'])
    discrete_scatter(km.cluster_centers_[:, 0], km.cluster_centers_[:, 1],
                     [0, 1, 2], markers=['^'], markeredgewidth=2)
    plot_2d_classification(km, X, cm=cm3, alpha=.4)


def plot_kmeans_faces(km, pca, X_pca, X_people, y_people, target_names):
    n_clusters = 10
    image_shape = (87, 65)
    fig, axes = plt.subplots(n_clusters, 11, subplot_kw={'xticks': (), 'yticks': ()},
                             figsize=(10, 15), gridspec_kw={"hspace": .3})

    for cluster in range(n_clusters):
        center = km.cluster_centers_[cluster]
        mask = km.labels_ == cluster
        dists = np.sum((X_pca - center) ** 2, axis=1)
        dists[~mask] = np.inf
        inds = np.argsort(dists)[:5]
        dists[~mask] = -np.inf
        inds = np.r_[inds, np.argsort(dists)[-5:]]
        axes[cluster, 0].imshow(pca.inverse_transform(center).reshape(image_shape), vmin=0, vmax=1)
        for image, label, asdf, ax in zip(X_people[inds], y_people[inds],
                                          km.labels_[inds], axes[cluster, 1:]):
            ax.imshow(image.reshape(image_shape), vmin=0, vmax=1)
            ax.set_title("%s" % (target_names[label].split()[-1]), fontdict={'fontsize': 9})

    # add some boxes to illustrate which are similar and which dissimilar
    rec = plt.Rectangle([-5, -30], 73, 1295, fill=False, lw=2)
    rec = axes[0, 0].add_patch(rec)
    rec.set_clip_on(False)
    axes[0, 0].text(0, -40, "Center")

    rec = plt.Rectangle([-5, -30], 385, 1295, fill=False, lw=2)
    rec = axes[0, 1].add_patch(rec)
    rec.set_clip_on(False)
    axes[0, 1].text(0, -40, "Close to center")

    rec = plt.Rectangle([-5, -30], 385, 1295, fill=False, lw=2)
    rec = axes[0, 6].add_patch(rec)
    rec.set_clip_on(False)
    axes[0, 6].text(0, -40, "Far from center")

過程解析：

在大數據集的情況下還可以使用scikit-learn 提供了MiniBatchKMeans算法，大致思想就是對數據進行抽樣，每次不使用所有的數據來計算，這就會導致准確率的損失。

MiniBatchKmeans 繼承自Kmeans 因為MiniBathcKmeans 本質上還利用了Kmeans 的思想.從構造方法和文檔大致能看到這些參數的含義，了解了這些參數會對使用的時候有很大的幫助。batch_size 是每次選取的用於計算的數據的樣本量，默認為100.Mini Batch K-Means算法是K-Means算法的變種，采用小批量的數據子集減小計算時間，同時仍試圖優化目標函數，這里所謂的小批量是指每次訓練算法時所隨機抽取的數據子集，采用這些隨機產生的子集進行訓練算法，大大減小了計算時間，與其他算法相比，減少了k-均值的收斂時間，小批量k-均值產生的結果，一般只略差於標准算法。

代碼只需要修改一行：

clf = MiniBatchKMeans(n_clusters = 3)