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聚类(Clustering) K-means算法

聚类(Clustering) K-means算法

作者: foochane | 来源:发表于2018-01-19 16:05 被阅读15次

    1. 归类:

    • 聚类(clustering) 属于非监督学习(unsupervised learning)

    • 无类别标记(class label)

    2. 举例:

    3. K-means 算法:

    3.1 Clustering 中的经典算法,数据挖掘十大经典算法之一

    3.2 算法接受参数 k ;然后将事先输入的n个数据对象划分为 k个聚类以便使得所获得的聚类满足:同一聚类中的对象相似度较高;而不同聚类中的对象相似度较小。

    3.3 算法思想:
    以空间中k个点为中心进行聚类,对最靠近他们的对象归类。通过迭代的方法,逐次更新各聚类中心 的值,直至得到最好的聚类结果

    3.4 算法描述:

    (1)适当选择c个类的初始中心;
    (2)在第k次迭代中,对任意一个样本,求其到c各中心的距离,将该样本归到距离最短的中心所在的类;
    (3)利用均值等方法更新该类的中心值;
    (4)对于所有的c个聚类中心,如果利用(2)(3)的迭代法更新后,值保持不变,则迭代结束, 否则继续迭代。

    3.5 算法流程:

    输入:k, data[n];
    (1) 选择k个初始中心点,例如c[0]=data[0],…c[k-1]=data[k-1];
    (2) 对于data[0]….data[n], 分别与c[0]…c[k-1]比较,假定与c[i]差值最少,就标记为i;
    (3) 对于所有标记为i点,重新计算c[i]={ 所有标记为i的data[j]之和}/标记为i的个数;
    (4) 重复(2)(3),直到所有c[i]值的变化小于给定阈值。

    4. 举例

    优点:速度快,简单

    缺点:最终结果跟初始点选择相关,容易陷入局部最优,需直到k值

    Reference:http://croce.ggf.br/dados/K%20mean%20Clustering1.pdf

    5.代码

     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
    
        dataSet = np.zeros((numPoints, numDim + 1))
    
        dataSet[:, :-1] = X
    
        # Initialize centroids randomly
    
        centroids = dataSet[np.random.randint(numPoints, size = k), :]
    
        centroids = dataSet[0:2, :]
    
        #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)
    
            iterations += 1
    
            # Assign labels to each datapoint based on centroids
    
            updateLabels(dataSet, centroids)
    
            # 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):
    
        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):
    
        # 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])
    
        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)
    
            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
    
    





                【注】:本文为麦子学院机器学习课程的学习笔记

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