聚类（K-Means）

import numpy as np


# Function: K Means
# -------------
# K-Means is an algorithm that takes in a dataset and a constant
# k and returns k centroids (which define clusters of data in the
# dataset which are similar to one another).
def kmeans(X, k, maxIt):
    numPoints, numDim = X.shape #多少数据，多少特征

    dataSet = np.zeros((numPoints, numDim + 1))#加一列
    dataSet[:, :-1] = X#赋值（所有行，除去最后一列）

    # Initialize centroids randomly
    #新的中心点
    centroids = dataSet[np.random.randint(numPoints, size=k), :]#随机选择K行 要所有列 作为中心点
    centroids = dataSet[0:2, :]
    # Randomly assign labels to initial centorid
    centroids[:, -1] = range(1, k + 1)#为选好的K个中心点(最后一列)赋值12345...K

    # Initialize book keeping vars.
    iterations = 0
    oldCentroids = None#旧的中心点

    # Run the main k-means algorithm
    while not shouldStop(oldCentroids, centroids, iterations, maxIt):
        print "iteration: 
", iterations
        print "dataSet: 
", dataSet
        print "centroids: 
", centroids
        # Save old centroids for convergence test. Book keeping.
        oldCentroids = np.copy(centroids)
        iterations += 1

        # Assign labels to each datapoint based on centroids
        updateLabels(dataSet, centroids)#计算数据集中每一个点的属于哪个中心点

        # Assign centroids based on datapoint labels
        centroids = getCentroids(dataSet, k)#计算新的中心点

    # We can get the labels too by calling getLabels(dataSet, centroids)
    return dataSet


# Function: Should Stop
# -------------
# Returns True or False if k-means is done. K-means terminates either
# because it has run a maximum number of iterations OR the centroids
# stop changing.
def shouldStop(oldCentroids, centroids, iterations, maxIt):
    if iterations > maxIt:
        return True
    return np.array_equal(oldCentroids, centroids)#判断值是否相等


# Function: Get Labels
# -------------
# Update a label for each piece of data in the dataset.
def updateLabels(dataSet, centroids):
    # For each element in the dataset, chose the closest centroid.
    # Make that centroid the element's label.
    numPoints, numDim = dataSet.shape
    for i in range(0, numPoints):
        dataSet[i, -1] = getLabelFromClosestCentroid(dataSet[i, :-1], centroids)


def getLabelFromClosestCentroid(dataSetRow, centroids):
    label = centroids[0, -1];
    minDist = np.linalg.norm(dataSetRow - centroids[0, :-1])#算两点距离的函数
    for i in range(1, centroids.shape[0]):
        dist = np.linalg.norm(dataSetRow - centroids[i, :-1])#每一行数据到中心点的距离  ：-1 不算最后一列 最后一列是中心编号1234-K
        if dist < minDist:
            minDist = dist
            label = centroids[i, -1]
    print "minDist:", minDist
    return label


# Function: Get Centroids
# -------------
# Returns k random centroids, each of dimension n.
def getCentroids(dataSet, k):
    # Each centroid is the geometric mean of the points that
    # have that centroid's label. Important: If a centroid is empty (no points have
    # that centroid's label) you should randomly re-initialize it.
    result = np.zeros((k, dataSet.shape[1]))
    for i in range(1, k + 1):#所有归于一类的点求均值
        oneCluster = dataSet[dataSet[:, -1] == i, :-1]#所有数据集中归为一类的点除去最后一列
        result[i - 1, :-1] = np.mean(oneCluster, axis=0)#axis=0对所有行的列求均值得到新的中心点
        result[i - 1, -1] = i

    return result


x1 = np.array([1, 1])
x2 = np.array([2, 1])
x3 = np.array([4, 3])
x4 = np.array([5, 4])
testX = np.vstack((x1, x2, x3, x4))

result = kmeans(testX, 2, 10)
print "final result:"
print result