I am using iPython to do some coding. When I open the notebook and run some codes by doing SHIFT+ENTER it runs. But after one or two times, it stops giving any output. Why is that. I have to shutdown the notebook again open it and then it runs for few times and same problem again.
Here is the code I have used.
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Question 1: Rotational Invariance of PCA
I(1): Importing the data sets and plotting a scatter plot of the two.
In [1]:
# Channging the working directory
import os
os.getcwd()
path="/Users/file/"
os.chdir(path)
pwd=os.getcwd()
print(pwd)
# Importing the libraries
import pandas as pd
import numpy as np
import scipy as sp
# Mentioning the files to be imported
file=["2d-gaussian.csv","2d-gaussian-rotated.csv"]
# Importing the two csv files in pandas dataframes
XI=pd.read_csv(file[0],header=None)
XII=pd.read_csv(file[1],header=None)
#XI
XII
Out[5]:
0 1
0 1.372310 -2.111748
1 -0.397896 1.968246
2 0.336945 1.338646
3 1.983127 -2.462349
4 -0.846672 0.606716
5 0.582438 -0.645748
6 4.346416 -4.645564
7 0.830186 -0.599138
8 -2.460311 2.096945
9 -1.594642 2.828128
10 3.767641 -3.401645
11 0.455917 -0.224665
12 2.878315 -2.243932
13 -1.062223 0.142675
14 -0.698950 1.113589
15 -4.681619 4.289080
16 0.411498 -0.041293
17 0.276973 0.187699
18 1.500835 -0.284463
19 -0.387535 -0.265205
20 3.594708 -2.581400
21 2.263455 -2.660592
22 -1.686090 1.566998
23 1.381510 -0.944383
24 -0.085535 -1.697205
25 1.030609 -1.448967
26 3.647413 -3.322129
27 -3.474906 2.977695
28 -7.930797 8.506523
29 -0.931702 1.440784
... ... ...
70 4.433750 -2.515612
71 1.495646 -0.058674
72 -0.928938 0.605706
73 -0.890883 -0.005911
74 -2.245630 1.333171
75 -0.707405 0.121334
76 0.675536 -0.822801
77 1.975917 -1.757632
78 -1.239322 2.053495
79 -2.360047 1.842387
80 2.436710 -1.445505
81 0.348497 -0.635207
82 -1.423243 -0.017132
83 0.881054 -1.823523
84 0.052809 1.505141
85 -2.466735 2.406453
86 -0.499472 0.970673
87 4.489547 -4.443907
88 -2.000164 4.125330
89 1.833832 -1.611077
90 -0.944030 0.771001
91 -1.677884 1.920365
92 0.372318 -0.474329
93 -2.073669 2.020200
94 -0.131636 -0.844568
95 -1.011576 1.718216
96 -1.017175 -0.005438
97 5.677248 -4.572855
98 2.179323 -1.704361
99 1.029635 -0.420458
100 rows × 2 columns
The two raw csv files have been imported as data frames. Next we will concatenate both the dataframes into one dataframe to plot a combined scatter plot
In [6]:
# Joining two dataframes into one.
df_combined=pd.concat([XI,XII],axis=1,ignore_index=True)
df_combined
Out[6]:
0 1 2 3
0 2.463601 -0.522861 1.372310 -2.111748
1 -1.673115 1.110405 -0.397896 1.968246
2 -0.708310 1.184822 0.336945 1.338646
3 3.143426 -0.338861 1.983127 -2.462349
4 -1.027700 -0.169674 -0.846672 0.606716
5 0.868458 -0.044767 0.582438 -0.645748
6 6.358290 -0.211529 4.346416 -4.645564
7 1.010685 0.163375 0.830186 -0.599138
8 -3.222466 -0.256939 -2.460311 2.096945
9 -3.127371 0.872207 -1.594642 2.828128
10 5.069451 0.258798 3.767641 -3.401645
11 0.481244 0.163520 0.455917 -0.224665
12 3.621976 0.448577 2.878315 -2.243932
13 -0.851991 -0.650218 -1.062223 0.142675
14 -1.281659 0.293194 -0.698950 1.113589
15 -6.343242 -0.277567 -4.681619 4.289080
16 0.320172 0.261774 0.411498 -0.041293
17 0.063126 0.328573 0.276973 0.187699
18 1.262396 0.860105 1.500835 -0.284463
19 -0.086500 -0.461557 -0.387535 -0.265205
20 4.367168 0.716517 3.594708 -2.581400
21 3.481827 -0.280818 2.263455 -2.660592
22 -2.300280 -0.084211 -1.686090 1.566998
23 1.644655 0.309095 1.381510 -0.944383
24 1.139623 -1.260587 -0.085535 -1.697205
25 1.753325 -0.295824 1.030609 -1.448967
26 4.928210 0.230011 3.647413 -3.322129
27 -4.562678 -0.351581 -3.474906 2.977695
28 -11.622940 0.407100 -7.930797 8.506523
29 -1.677601 0.359976 -0.931702 1.440784
... ... ... ... ...
70 4.913941 1.356329 4.433750 -2.515612
71 1.099070 1.016093 1.495646 -0.058674
72 -1.085156 -0.228560 -0.928938 0.605706
73 -0.625769 -0.634129 -0.890883 -0.005911
74 -2.530594 -0.645206 -2.245630 1.333171
75 -0.586007 -0.414415 -0.707405 0.121334
76 1.059484 -0.104132 0.675536 -0.822801
77 2.640018 0.154351 1.975917 -1.757632
78 -2.328373 0.575707 -1.239322 2.053495
79 -2.971570 -0.366041 -2.360047 1.842387
80 2.745141 0.700888 2.436710 -1.445505
81 0.695584 -0.202735 0.348497 -0.635207
82 -0.994271 -1.018499 -1.423243 -0.017132
83 1.912425 -0.666426 0.881054 -1.823523
84 -1.026954 1.101637 0.052809 1.505141
85 -3.445865 -0.042626 -2.466735 2.406453
86 -1.039549 0.333189 -0.499472 0.970673
87 6.316906 0.032272 4.489547 -4.443907
88 -4.331379 1.502719 -2.000164 4.125330
89 2.435918 0.157511 1.833832 -1.611077
90 -1.212710 -0.122350 -0.944030 0.771001
91 -2.544347 0.171460 -1.677884 1.920365
92 0.598670 -0.072133 0.372318 -0.474329
93 -2.894802 -0.037809 -2.073669 2.020200
94 0.504119 -0.690281 -0.131636 -0.844568
95 -1.930254 0.499670 -1.011576 1.718216
96 -0.715406 -0.723096 -1.017175 -0.005438
97 7.247917 0.780923 5.677248 -4.572855
98 2.746180 0.335849 2.179323 -1.704361
99 1.025371 0.430754 1.029635 -0.420458
100 rows × 4 columns
Plotting two separate scatter plot of all the four columns onto one scatter diagram
In [ ]:
import matplotlib.pyplot as plt
# Fucntion for scatter plot
def scatter_plot():
# plots scatter for first two columns(Unrotated Gaussian data)
plt.scatter(df_combined.ix[:,0], df_combined.ix[:,1],color='red',marker='+')
# plots scatter for Rotated Gaussian data
plt.scatter(df_combined.ix[:,2], df_combined.ix[:,3] ,color='green', marker='x')
legend = plt.legend(loc='upper right')
# set ranges of x and y axes
plt.xlim([-12,12])
plt.ylim([-12,12])
plt.show()
# Function call
scatter_plot()
In [ ]:
def plot_me1():
# create figure and axes
fig = plt.figure()
# split the page into a 1x1 array of subplots and put me in the first one (111)
# (as a matter of fact, the only one)
ax = fig.add_subplot(111)
# plots scatter for x, y1
ax.scatter(df_combined.ix[:,0], df_combined.ix[:,1], color='red', marker='+', s=100)
# plots scatter for x, y2
ax.scatter(df_combined.ix[:,2], df_combined.ix[:,3], color='green', marker='x', s=100)
plt.xlim([-12,12])
plt.ylim([-12,12])
plt.show()
plot_me1()
In [ ]: