8.2聚类（clustering）:K-means 算法应用

K-means算法实现代码：（接上一节的小例子，如图）

CODE:

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", str(iterations))
        print ("dataSet: \n", str(dataSet))
        print ("centroids: \n", str(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:", str(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)

RESULT:

iteration: 
 0
dataSet: 
 [[1. 1. 1.]
 [2. 1. 2.]
 [4. 3. 0.]
 [5. 4. 0.]]
centroids: 
 [[1. 1. 1.]
 [2. 1. 2.]]
minDist: 0.0
minDist: 0.0
minDist: 2.8284271247461903
minDist: 4.242640687119285
iteration: 
 1
dataSet: 
 [[1. 1. 1.]
 [2. 1. 2.]
 [4. 3. 2.]
 [5. 4. 2.]]
centroids: 
 [[1.         1.         1.        ]
 [3.66666667 2.66666667 2.        ]]
minDist: 0.0
minDist: 1.0
minDist: 0.4714045207910319
minDist: 1.885618083164127
iteration: 
 2
dataSet: 
 [[1. 1. 1.]
 [2. 1. 1.]
 [4. 3. 2.]
 [5. 4. 2.]]
centroids: 
 [[1.5 1.  1. ]
 [4.5 3.5 2. ]]
minDist: 0.5
minDist: 0.5
minDist: 0.7071067811865476
minDist: 0.7071067811865476
final result:
[[1. 1. 1.]
 [2. 1. 1.]
 [4. 3. 2.]
 [5. 4. 2.]]