Kmeans算法（无监督学习、聚类算法）

算法思想

如果你想把多个样本自动学习后分成k类，就可以使用k-means算法。首先随机取里面的k个点作为初始中心点，每个点离哪个中心点距离最近就属于哪一个分类，然后再根据同一类的点求均值得出新的中心点。以上步骤不断迭代到中心点的位置不变或者次数达到某个阈值，算法停止。

代码

import numpy as np

#x是数据集，k是种类，maxIt最多循环次数
def kmeans(X, k, maxIt):

    numPoints, numDim = X.shape
    
    dataSet = np.zeros((numPoints, numDim + 1))
    dataSet[:, :-1] = X
    
    # Initialize centroids randomly
    #centroids = dataSet[np.random.randint(numPoints, size = k), :]#size是随机数的个数，
    centroids = dataSet[0:k, :]
    #print("dataset:"+str(dataSet))
    #print("centroids:"+str(centroids))
    #Randomly assign labels to initial centorid
    centroids[:, -1] = range(1, k +1)
    
    # Initialize book keeping vars.
    iterations = 0
    oldCentroids = None
    
    # Run the main k-means algorithm
    while not shouldStop(oldCentroids, centroids, iterations, maxIt):
        #print ("iteration: \n", iterations)
        #print ("dataSet: \n", dataSet)
        #print ("centroids: \n", centroids)
        # Save old centroids for convergence test. Book keeping.
        oldCentroids = np.copy(centroids)#复制一个数组
        iterations += 1
        
        # Assign labels to each datapoint based on centroids
        updateLabels(dataSet, centroids)#更新标签
        
        # Assign centroids based on datapoint labels
        centroids = getCentroids(dataSet, k)
        
    # 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):#是否停止
    if iterations > maxIt:
        return True
    return np.array_equal(oldCentroids, centroids)  
# Function: Get Labels
# -------------
# Update a label for each piece of data in the dataset. 
def updateLabels(dataSet, centroids):#更新标签
    # 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):#根据距离最近的那个中心点作为种类
    label = centroids[0, -1];
    minDist = np.linalg.norm(dataSetRow - centroids[0, :-1])
    for i in range(1 , centroids.shape[0]):
        dist = np.linalg.norm(dataSetRow - centroids[i, :-1])
        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):
        oneCluster = dataSet[dataSet[:, -1] == i, :-1]
        result[i - 1, :-1] = np.mean(oneCluster, axis = 0)#每一列求均值
        result[i - 1, -1] = i#上标签
    
    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))#合并成一个数组


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