我为项目实现的kmeans聚类算法有以下设置：
import numpy as np
import scipy
import sys
import random
import matplotlib.pyplot as plt
import operator
class KMeansClass:
#takes in an npArray like object
def __init__(self,dataset,k):
self.dataset=np.array(dataset)
#initialize mins to maximum possible value
self.min_x = sys.maxint
self.min_y = sys.maxint
#initialize maxs to minimum possible value
self.max_x = -(sys.maxint)-1
self.max_y = -(sys.maxint)-1
self.k = k
#a is the coefficient matrix that is continually updated as the centroids of the clusters change respectively.
# It is an mxk matrix where each row corresponds to a training_instance and each column corresponds to a centroid of a cluster
#Values are either 0 or 1. A value for a particular training_instance (data_point) is 1 only for that centroid to which the training_instance
# has the least distance else the value is 0.
self.a = np.zeros(shape=[self.dataset.shape[0],self.k])
self.distanceMatrix = np.empty(shape =[self.dataset.shape[0],self.k])
#initialize mu to zeros of the requisite shape array for now. Change this after implementing max and min methods.
self.mu = np.empty(shape=[k,2])
self.findMinMaxdataPoints()
self.initializeCentroids()
self.createDistanceMatrix()
self.scatterPlotOfInitializedPoints()
#pointa and pointb are npArray like vecors.
def euclideanDistance(self,pointa,pointb):
return np.sqrt(np.sum((pointa - pointb)**2))
""" Problem Initialization And Visualization Helper methods"""
##############################################################################
#@param: dataset : list of tuples [(x1,y1),(x2,y2),...(xm,ym)]
def findMinMaxdataPoints(self):
for item in self.dataset:
self.min_x = min(self.min_x,item[0])
self.min_y = min(self.min_y,item[1])
self.max_x = max(self.max_x,item[0])
self.max_y = max(self.max_y,item[1])
def initializeCentroids(self):
for i in range(self.k):
#each value of mu is a tuple with a random number between (min_x - max_x) and (min_y - max_y)
self.mu[i] = (random.randint(self.min_x,self.max_x),random.randint(self.min_y,self.max_y))
self.sortCentroids()
print self.mu
def sortCentroids(self):
#the following 3 lines of code are to ensure that the mu values are always sorted in ascending order first with respect to the
#x values and then with respect to the y values.
half_sorted = sorted(self.mu,key=operator.itemgetter(1)) #sort wrt y values
full_sorted = sorted(half_sorted,key=operator.itemgetter(0)) #sort the y-sorted array wrt x-values
self.mu = np.array(full_sorted)
def scatterPlotOfInitializedPoints(self):
plt.scatter([item[0] for item in self.dataset],[item[1] for item in self.dataset],color='b')
plt.scatter([item[0] for item in self.mu],[item[1] for item in self.mu],color='r')
plt.show()
###############################################################################
#minimizing euclidean distance is the same as minimizing the square of the euclidean distance.
def calcSquareEuclideanDistanceBetweenTwoPoints(point_a,point_b):
return np.sum((pointa-pointb)**2)
def createDistanceMatrix(self):
for i in range(self.dataset.shape[0]):
for j in range(self.k):
self.distanceMatrix[i,j] = calcSquareEuclideanDistanceBetweenTwoPoints(self.dataset[i],self.mu[j])
def createCoefficientMatrix(self):
for i in range(self.dataset.shape[0]):
self.a[i,self.distanceMatrix[i].argmin()] = 1
#update functions for CoefficientMatrix and Centroid values:
def updateCoefficientMatrix(self):
for i in range(self.dataset.shape[0]):
self.a[i,self.distanceMatrix[i].argmin()]= 1
def updateCentroids(self):
for j in range(self.k):
non_zero_indices = np.nonzero(self.a[:,j])
avg = 0
for i in range(len(non_zero_indices[0])):
avg+=self.a[non_zero_indices[0][i],j]
self.mu[j] = avg/len(non_zero_indices[0])
############################################################
def lossFunction(self):
loss=0;
for j in range(self.k):
#vectorized this implementation.
loss+=np.sum(np.dot(self.a[:,j],self.distanceMatrix[:,j]))
return loss
这里我的问题与lossFunction以及如何在scipy.optimize包中使用它有关。我想通过执行以下步骤迭代地最小化损失函数：
Repeat until convergence:
a> Optimize 'a' by keeping mu constant ( I have an
updateCoefficientMatrix method for updating 'a' matrix which is an
mXk matrix where we have m training instances and k clusters.)
b> Optimize 'mu' by keeping 'a' constant (I have an updateCentroids
method to do this. where mu is a mXk matrix wherein m is number of
training instances and k is the number of clusters and the number of
centroids)
但是我对使用scipy.optimize包非常陌生，所以我写信是要求如何调用scipy.optimize来实现我的优化目标？
基本上我有2个m x k矩阵，我希望通过优先保留另一个lossFunction() x m矩阵来最小化k常数并且在随后的步骤中优化第二矩阵，保持第一矩阵不变。这可以被认为是期望最大化问题的一个特例，但不幸的是我到目前为止还没有得到文档试图说的内容因此我认为我会求助于SO。
提前致谢！
这是课程作业的一部分，所以请不要发布代码！任何指导或解释都将受到高度赞赏。
答案 0 :(得分：0)
使用scipy.optimize.minimize两次使用不同的目标函数。
首先使用以a作为参数的目标函数运行优化，并返回目标值。
作为第二步，在以scipy.optimize.minimize为参数的第二个目标函数上第二次运行mu。
编写目标函数时，请记住Python具有嵌套函数，这样就不需要传递mu（在第一种情况下）或a（在第二种情况下）作为附加参数;虽然可以minimize(..., args=[mu])和minimize(..., args=[a])完成。
在for循环中重复两步过程，直到答案满足您的收敛条件。