Python代码实现K-Means算法
"""
K-Means算法的实现。
"""
import math
import csv
import random
class Sample(object):
"""样本，或者分类的中心点。
假如一个二维平面的点，(1, 2)，那么 Sample([1, 2]) 可以用来代表这个点。
"""
def __init__(self, data = [], label = ''):
"""初始化，参数data是每一个维度的数据组成的列表。"""
self._data = data
self._label = label
def getData(self):
"""以列表的形式获取样本的坐标。"""
return self._data
def getLabel(self):
"""返回标签。"""
return self._label
def lengthWith(self, anotherSample):
"""返回当前样本与指定的样本的距离。"""
anotherData = anotherSample.getData()
total = len(anotherData)
sumValue = 0
for i in range(total):
sumValue = sumValue + pow(self._data[i] - anotherData[i], 2)
return math.sqrt(sumValue)
def copyMyself(self):
"""复制并返回新的Sample实例。这个实例和当前实例的坐标是一样的。"""
return Sample(self._data, self._label)
def gauss(self, sigma = 1.0):
"""使用正态分布方法对当前实例的坐标进行随机地移动。可以用sigma控制移动的随机程度，sigma越大移动距离越大。"""
total = len(self._data)
for i in range(total):
self._data[i] = random.gauss(self._data[i], sigma)
class Category(object):
"""代表样本所属的分类。
必须指定分类的中心点，比如二维平面，分类的中心点是坐标(2, 2)，那么实例化分类需要这样做：Category(Sample([2, 2]))。
注意传给分类的Sample实例不可以再用于样本的表示。
"""
def __init__(self, center):
"""实例化分类类，center指定分类的中心位置。在K-Means算法初始化的时候，可以指定一个随机的中心。"""
self._center = center
self._samples = []
def getCenter(self):
"""返回当前分类的中心。返回的是一个Sample实例，它的坐标是分类的中心。"""
return self._center
def addSample(self, sample):
"""往分类实例中添加样本，用意是这些样本属于这个分类。"""
self._samples.append(sample)
def cleanSample(self):
"""清空通过addSample添加的样本。"""
self._samples = []
def updateCenter(self):
"""通过addSample添加样本之后，此方法将通过样本计算和更新当前分类的中心。"""
if len(self._samples) == 0:
return
dataLength = len(self._samples[0].getData())
sumDist = [0 for i in range(dataLength)]
for s in self._samples:
data = s.getData()
for i in range(dataLength):
sumDist[i] = sumDist[i] + data[i]
sampleTotal = len(self._samples)
for i in range(dataLength):
sumDist[i] = sumDist[i] / sampleTotal
self._center = Sample(sumDist)
def createData(csvFileName, dataTotal = 10, centersPositions = None):
"""随机地创建样本，创建的样本将写入文件csvFileName。
参数和参数的含义：
csvFileName CSV文件名，会创建并向这个文件写数据。
dataTotal 随机生成多少个样本。
centersPositions 可选，你可以用这个参数指定样本的分类中心。
返回值：
无。
"""
if centersPositions is None:
centers = [{'x': 5, 'y': 5}, {'x': -5, 'y': -5}]
else:
centers = centersPositions
sigma = 1.0
with open(csvFileName, 'w', newline='') as fp:
write = csv.writer(fp)
write.writerow(['ID', 'x', 'y'])
for i in range(dataTotal):
center = random.choices(centers)[0]
x = random.gauss(center['x'], sigma)
y = random.gauss(center['y'], sigma)
write.writerow([i + 1, x, y])
def readData(csvFileName):
"""从文件中读取数据，迭代并返回列表。
参数和参数的含义：
csvFileName CSV文件名
返回值：
通过生成器返回列表。
"""
lineNo = 0
with open(csvFileName, 'r') as fp:
reader = csv.reader(fp)
for row in reader:
lineNo = lineNo + 1
if 1 == lineNo:
continue
yield [float(row[1]), float(row[2])]
class AlgorithmLogic(object):
"""K-Means算法主体逻辑。
你需要先创建此类的实例，然后用addSampleData添加多个样本，再用run来执行这个算法。
"""
def __init__(self):
"""不用传什么参数，这个初始化方法只是设置几个私有的成员。"""
self._samples = []
self._categorys = []
self._centerMoves = []
self._centerMoveLength = []
def addSampleData(self, data, label = ''):
"""添加样本点。data参数是列表，代表样本的坐标。label是字符串，一个区分数据用的标签，相当于备注。你需要保证这些样本的维数是一样的。"""
self._samples.append(Sample(data, label))
def getCategorys(self):
"""返回所有的分类对象。"""
return self._categorys
def getCenterMoveSteps(self):
"""返回所有的分类的中心在每一次迭代后移动的距离总和的变化情况。返回值是一个列表。"""
return self._centerMoveLength
def getCenterMoveDetails(self):
"""返回迭代时分类中心的变化情况。返回值是二维的列表，列表的每一个元素是所有的分类中心曾经的位置。"""
return self._centerMoves
def run(self, categoryTotal = 2, loopTotal = 50, minLength = 1E-3):
"""运行算法。categoryTotal指定分类数量，loopTotal是最大迭代次数，minLength意味着分类中心移动量总和小于这个数字的时候停止迭代。"""
self._categorys = []
for c in random.choices(self._samples, k = categoryTotal):
centerPoint = c.copyMyself()
centerPoint.gauss()
self._categorys.append(Category(centerPoint))
move = []
for c in self._categorys:
move.append(c.getCenter().getData())
self._centerMoves.append(move)
for i in range(loopTotal):
for s in self._samples:
minCate = None
minCateLength = None
for c in self._categorys:
l1 = s.lengthWith(c.getCenter())
if minCateLength is None or l1 < minCateLength:
minCate = c
minCateLength = l1
minCate.addSample(s)
for c in self._categorys:
c.updateCenter()
c.cleanSample()
lastMove = self._centerMoves[-1]
move = []
for c in self._categorys:
move.append(c.getCenter().getData())
self._centerMoves.append(move)
moveLength = 0
dataLength = len(move[0])
for k in range(categoryTotal):
value = 0
for e in range(dataLength):
value = value + pow(lastMove[k][e] - move[k][e], 2)
moveLength = moveLength + math.sqrt(value)
self._centerMoveLength.append(moveLength)
if moveLength < minLength:
break
def getSilhouetteCoefficient(self):
"""返回轮廓系数"""
categorys = []
categorysNum = [0 for i in range(len(self._categorys))]
lengthMatrix = [[0 for j in range(len(self._samples))] for i in range(len(self._samples))]
for i in range(len(self._samples)):
for j in range(len(self._samples)):
if i == j:
lengthMatrix[i][j] = 0.0
else:
if j > i:
lengthMatrix[i][j] = self._samples[i].lengthWith(self._samples[j])
else:
lengthMatrix[i][j] = lengthMatrix[j][i]
for s in self._samples:
minCategoryKey = None
minLength = None
for i in range(len(self._categorys)):
l = s.lengthWith(self._categorys[i].getCenter())
if minCategoryKey is None or l < minLength:
minCategoryKey = i
minLength = l
categorys.append(minCategoryKey)
categorysNum[minCategoryKey] = categorysNum[minCategoryKey] + 1
# 每个样本与所有和自己同类的其它样本的距离的平均值。
a = [0.0 for i in range(len(self._samples))]
# 每个样本与非自己的分类的所有样本的平均值最小值。
b = [[None for j in range(len(self._categorys))] for i in range(len(self._samples))]
# 轮廓系数
s = []
for i in range(len(self._samples)):
for j in range(len(self._samples)):
if i == j:
continue
if categorys[i] == categorys[j]:
a[i] = a[i] + lengthMatrix[i][j]
else:
if b[i][categorys[j]] is None:
b[i][categorys[j]] = 0.0
b[i][categorys[j]] = b[i][categorys[j]] + lengthMatrix[i][j]
a[i] = a[i] / categorysNum[categorys[i]]
item = []
for k in range(len(self._categorys)):
if b[i][k] is not None:
item.append(b[i][k] / categorysNum[k])
b[i] = min(item)
s.append((b[i] - a[i]) / max(a[i], b[i]))
sSum = 0.0
for i in s:
sSum = sSum + i
return sSum / len(s)
def getSampleCategory(self):
"""返回样本的分类"""
categorys = []
for s in self._samples:
minCategoryKey = None
minLength = None
for i in range(len(self._categorys)):
l = s.lengthWith(self._categorys[i].getCenter())
if minCategoryKey is None or l < minLength:
minCategoryKey = i
minLength = l
categorys.append(minCategoryKey)
return categorys
if __name__ == '__main__':
"""算是示例代码，演示如何使用文件提供的算法类。"""
fileName = 'km_test_data.csv'
createData(fileName, 100)
logic = AlgorithmLogic()
for data in readData(fileName):
logic.addSampleData(data)
logic.run()
print('Central location:')
for c in logic.getCategorys():
print(c.getCenter().getData())
print('Silhouette Coefficient: ' + str(logic.getSilhouetteCoefficient()))
print('Detailed path movement information:')
with open('km_test_move.csv', 'w', newline = '') as fp:
write = csv.writer(fp)
loc = logic.getCenterMoveDetails()
headers = []
for k in loc[0]:
headers = headers + ['x', 'y']
write.writerow(headers)
for m in loc:
print(m)
rows = []
for c in m:
rows = rows + c
write.writerow(rows)
print('The sum of the center moving distances:')
print(logic.getCenterMoveSteps())
使用方法如下，直接执行这个文件即可。
$ python km.py
Central location:
[-4.784267537802826, -4.9919970949000065]
[5.022562088185882, 5.126544857297353]
Silhouette Coefficient: 0.878699362556456
Detailed path movement information:
[[-4.419180737327517, -7.552966064179474], [8.229303256255214, 5.521797853248163]]
[[-4.784267537802826, -4.9919970949000065], [5.022562088185882, 5.126544857297353]]
[[-4.784267537802826, -4.9919970949000065], [5.022562088185882, 5.126544857297353]]
The sum of the center moving distances:
[5.817869294545022, 0.0]