Hi,
I am learning unit4 of “machine learning for robotics”. In the example code of K-Means, I found some error. It is alright when only 2 cluster centroids are applied, but when I change self.K to higher digit, it goes wrong. The original code in course book is:
import warnings
warnings.filterwarnings('ignore')
import matplotlib.pyplot as plt
import numpy as np
import random
class Kmeans_dev:
"""
class definition
"""
def __init__(self,X,K):
"""
class constructor
"""
self.X = X
self.output = {}
self.centroids = np.array([]).reshape(self.X.shape[1],0)
self.K = K
self.m = self.X.shape[0]
def start_centroid_pos(self, X, K):
"""
Random initialization of K centroids.
"""
m,n = X.shape[0], X.shape[1]
centroids = np.zeros((K,n))
for i in range(K):
#for i in range(1,K+1,1):
centroids[i] = X[np.random.randint(0,m),:]
return centroids
def fit(self,n_iter):
"""
Method to train the data set (position of centroids()
"""
#randomly Initialize the centroids (callstart_centroid_pos() )
self.centroids=self.start_centroid_pos(self.X,self.K)
#compute Euclidian distances and assign clusters
for n in range(n_iter):
EuclidianDistance=np.array([]).reshape(self.m,0)
for k in range(self.K):
tempDist=np.sum((self.X-self.centroids[:,k])**2,axis=1)
EuclidianDistance=np.c_[EuclidianDistance,tempDist]
C=np.argmin(EuclidianDistance,axis=1)+1
#adjust the centroids
Y={}
for k in range(self.K):
Y[k+1]=np.array([]).reshape(2,0)
for i in range(self.m):
Y[C[i]]=np.c_[Y[C[i]],self.X[i]]
for k in range(self.K):
Y[k+1] = Y[k+1].T
for k in range(self.K):
self.centroids[:,k] = np.mean(Y[k+1],axis = 0)
self.output=Y
def predict(self):
"""
Return of data set adherence to certain cluster
"""
return self.output,self.centroids.T
# data set
X = np.array([[0.3,8.3 ], [3, 8], [2, 9],[0.3, 8.9],[1.7, 9.7 ],
[0.9, 10.5], [10.3, 2.1],[10, 2],[7, 7 ], [6.9, 6.5],
[6, 6],[1, 2], [1.5, 1.8], [5, 8 ], [8, 8], [1, 0.6],
[9,11],[12, 5], [4.5, 4.8], [4.5, 3 ], [2, 8], [9, 3], [9,7]])
"""
Run k-means algorithm on given data set. Printing the output (position of centrod) and adherence of point to
certain cluster
"""
K= 2 # number of cluster you would like to create
#creation of class object and training (fit)
kmeans=Kmeans_dev(X,K)
kmeans.fit(50)
color=['blue','green']
labels=['cluster1','cluster2']
fig, axs = plt.subplots(5,2, figsize=(14, 28), facecolor='w', edgecolor='k')
fig.subplots_adjust(hspace = .5, wspace=.001)
axs = axs.ravel()
#you print the test results iteration by iteration (in order to show how the centroids moves)
for i in range(10):
kmeans=Kmeans_dev(X,K)
kmeans.fit(1)
Output,Centroids=kmeans.predict()
for k in range(K):
axs[i].scatter(Output[k+1][:,0],Output[k+1][:,1],c=color[k],label=labels[k])
axs[i].scatter(Centroids[:,0],Centroids[:,1],s=300,c='red',label='Centroids', marker='*')
axs[i].set_title("Centroids movement. Iteration "+ str(1+i))
plt.show()
The errors take place:
1.
in def fit(self,n_iter):, the second for iteration,
for k in range(self.K):
tempDist=np.sum((self.X-self.centroids[:,k])**2,axis=1)
EuclidianDistance=np.c_[EuclidianDistance,tempDist]
it should be:
for k in range(self.K):
tempDist=np.sum((self.X-self.centroids[k,:])**2,axis=1)
EuclidianDistance=np.c_[EuclidianDistance,tempDist]
the index k is opposite.
2.
the same function, in 6th for iteration:
for k in range(self.K):
self.centroids[k, :] = np.mean(Y[k+1], axis=0)
it is with the same index problem. It should be:
for k in range(self.K):
self.centroids[:, k] = np.mean(Y[k+1], axis=0)
in plot part, when we draw steriod mark on final centroids:
axs[i].scatter(Centroids[:,0],Centroids[:,1],s=300,c='red',label='Centroids', marker='*')
it should be:
axs[i].scatter(Centroids[0, :],Centroids[1, :],s=300,c='red',label='Centroids', marker='*')
the whole rectified code is:
import warnings
warnings.filterwarnings('ignore')
import matplotlib.pyplot as plt
import numpy as np
import random
class Kmeans_dev:
"""
class definition
"""
def __init__(self,X,K):
"""
class constructor
"""
self.X = X
self.output = {}
self.centroids = np.array([]).reshape(self.X.shape[1],0)
self.K = K
self.m = self.X.shape[0]
def start_centroid_pos(self, X, K):
"""
Random initialization of K centroids.
"""
m,n = X.shape[0], X.shape[1]
centroids = np.zeros((K,n))
for i in range(K):
#for i in range(1,K+1,1):
centroids[i] = X[np.random.randint(0,m),:]
return centroids
def fit(self,n_iter):
"""
Method to train the data set (position of centroids()
"""
#randomly Initialize the centroids (callstart_centroid_pos() )
self.centroids=self.start_centroid_pos(self.X,self.K)
#compute Euclidian distances and assign clusters
for n in range(n_iter):
EuclidianDistance=np.array([]).reshape(self.m,0)
for k in range(self.K):
tempDist=np.sum((self.X-self.centroids[k, :])**2,axis=1)
EuclidianDistance=np.c_[EuclidianDistance,tempDist]
C=np.argmin(EuclidianDistance,axis=1)+1
#adjust the centroids
Y={}
for k in range(self.K):
Y[k+1]=np.array([]).reshape(2,0)
for i in range(self.m):
Y[C[i]]=np.c_[Y[C[i]],self.X[i]]
for k in range(self.K):
Y[k+1] = Y[k+1].T
for k in range(self.K):
self.centroids[k, :] = np.mean(Y[k+1],axis = 0)
self.output=Y
def predict(self):
"""
Return of data set adherence to certain cluster
"""
return self.output,self.centroids.T
# data set
X = np.array([[0.3,8.3 ], [3, 8], [2, 9],[0.3, 8.9],[1.7, 9.7 ],
[0.9, 10.5], [10.3, 2.1],[10, 2],[7, 7 ], [6.9, 6.5],
[6, 6],[1, 2], [1.5, 1.8], [5, 8 ], [8, 8], [1, 0.6],
[9,11],[12, 5], [4.5, 4.8], [4.5, 3 ], [2, 8], [9, 3], [9,7]])
"""
Run k-means algorithm on given data set. Printing the output (position of centrod) and adherence of point to
certain cluster
"""
K= 2 # number of cluster you would like to create
#creation of class object and training (fit)
kmeans=Kmeans_dev(X,K)
kmeans.fit(50)
color=['blue','green']
labels=['cluster1','cluster2']
fig, axs = plt.subplots(5,2, figsize=(14, 28), facecolor='w', edgecolor='k')
fig.subplots_adjust(hspace = .5, wspace=.001)
axs = axs.ravel()
#you print the test results iteration by iteration (in order to show how the centroids moves)
for i in range(10):
kmeans=Kmeans_dev(X,K)
kmeans.fit(1)
Output,Centroids=kmeans.predict()
for k in range(K):
axs[i].scatter(Output[k+1][:,0],Output[k+1][:,1],c=color[k],label=labels[k])
axs[i].scatter(Centroids[0, :],Centroids[1, :],s=300,c='red',label='Centroids', marker='*')
axs[i].set_title("Centroids movement. Iteration "+ str(1+i))
plt.show()
change K from 2 to 3 or 4, the error will show up.