In [204]:
import pandas as pd
import numpy as np
from io import StringIO
import numpy.linalg as la
import matplotlib.pyplot as plt
from matplotlib import cm as cm
import seaborn as sns
sns.set(font_scale=2)
plt.style.use('seaborn-whitegrid')
%matplotlib inline
In [205]:
params = ["radius", "texture", "perimeter", "area",
          "smoothness", "compactness", "concavity",
          "concave points", "symmetry", "fractal dimension"];
stats = ["(mean)", "(stderr)", "(worst)"]
labels = ["patient ID", "Malignant/Benign"]

for p in params:
    for s in stats:
        labels.append(p + " " + s)

tumor_data = pd.io.parsers.read_csv("breast-cancer-train.dat",header=None,names=labels)
In [206]:
new_data = pd.DataFrame(tumor_data[["Malignant/Benign", 'smoothness (mean)', 'radius (mean)']][272:278])


mean_smooth = new_data['smoothness (mean)'].mean()
mean_radius = new_data['radius (mean)'].mean()

print(mean_smooth,mean_radius)
new_data['smoothness (zero mean)'] = new_data['smoothness (mean)'] - new_data['smoothness (mean)'].mean()
new_data['radius (zero mean)'] = new_data['radius (mean)'] - new_data['radius (mean)'].mean()

new_data

3.555166666666667 15.241999999999999
Out[206]:
Malignant/Benign smoothness (mean) radius (mean) smoothness (zero mean) radius (zero mean)
272 M 8.867 21.750 5.311833 6.508
273 B 1.750 9.742 -1.805167 -5.500
274 M 2.765 17.930 -0.790167 2.688
275 B 4.021 11.890 0.465833 -3.352
276 B 1.565 11.330 -1.990167 -3.912
277 M 2.363 18.810 -1.192167 3.568
In [207]:
g1 = sns.lmplot('smoothness (mean)', 'radius (mean)', new_data,  hue="Malignant/Benign", scatter_kws={"s": 180}, fit_reg=False, size=8)
ax = g1.axes[0,0]
ax.axis('equal')

for i in range(272,278):
    x = new_data['smoothness (mean)'][i] + 0.1
    y = new_data['radius (mean)'][i] + 0.1
    ax.text(x,y,str(i),horizontalalignment='left',size='medium', color='black', weight='semibold', fontsize=16)
        
ax.scatter(mean_smooth,mean_radius,  s=180, c='r', marker=(5, 2))
Out[207]:
<matplotlib.collections.PathCollection at 0x1a2adbfe48>
In [203]:
g1 = sns.lmplot('smoothness (mean)', 'radius (mean)', new_data,  hue="Malignant/Benign", scatter_kws={"s": 180}, fit_reg=False, size=8)
ax = g1.axes[0,0]
plt.xlim(-2,24)
plt.ylim(-2,24)
for i in range(272,278):
    x = new_data['smoothness (mean)'][i] + 0.1
    y = new_data['radius (mean)'][i] + 0.1
    ax.text(x,y,str(i),horizontalalignment='left',size='medium', color='black', weight='semibold', fontsize=16)
        
ax.scatter(mean_smooth,mean_radius,  s=180, c='r', marker=(5, 2))
ax.axhline(y=0, color='k')
ax.axvline(x=0, color='k')
ax.axhline(y=mean_radius, color='m',linestyle='--')
ax.axvline(x=mean_smooth, color='m',linestyle='--')
Out[203]:
<matplotlib.lines.Line2D at 0x1a2aa16710>
In [189]:
g1 = sns.lmplot('smoothness (zero mean)', 'radius (zero mean)', new_data, hue="Malignant/Benign", scatter_kws={"s": 180}, fit_reg=False, size=8)
ax = g1.axes[0,0]
ax.axis('equal')

for i in range(272,278):
    x = new_data['smoothness (zero mean)'][i] + 0.1
    y = new_data['radius (zero mean)'][i] + 0.1
    ax.text(x,y,str(i),horizontalalignment='left',size='medium', color='black', weight='semibold', fontsize=16)

ax.scatter(0,0,  s=200, c='r', marker=(5, 2))

ax.axhline(y=0, color='k')
ax.axvline(x=0, color='k')
Out[189]:
<matplotlib.lines.Line2D at 0x1a26571dd8>

Get covariance matrix

In [156]:
A = new_data[['smoothness (zero mean)', 'radius (zero mean)']]
A.cov()
Out[156]:
smoothness (zero mean) radius (zero mean)
smoothness (zero mean) 7.539518 8.868854
radius (zero mean) 8.868854 23.819936
In [157]:
# Another way to get the covariance matrix
Xnp = np.array(X)
cov_matrix = (1/(len(X)-1))*Xnp.T@Xnp
print(cov_matrix)

[[  7.53951777   8.8688536 ]
 [  8.8688536   23.819936  ]]

Singular value decomposition

In [158]:
U, S, Vt = np.linalg.svd(X, full_matrices=False)

# variances = eig(covariance) = singular values squared
variances = S**2

print(variances)

print(S)

# principal directions
pc1_vec = Vt[0,:]
pc2_vec = Vt[1,:]

[ 138.58990634   18.20736249]
[ 11.77242143   4.26700861]

Diagonalization of covariance matrix

In [159]:
(Vt.T@np.diag(variances)@Vt)/(len(X)-1)
Out[159]:
array([[  7.53951777,   8.8688536 ],
       [  8.8688536 ,  23.819936  ]])
In [160]:
g1 = sns.lmplot('smoothness (zero mean)', 'radius (zero mean)', new_data, hue="Malignant/Benign", scatter_kws={"s": 180}, fit_reg=False, size=8)
ax = g1.axes[0,0]

for i in range(272,278):
    x = new_data['smoothness (zero mean)'][i] + 0.1
    y = new_data['radius (zero mean)'][i] + 0.1
    ax.text(x,y,str(i),horizontalalignment='left',size='medium', color='black', weight='semibold', fontsize=16)

ax.scatter(0,0,  s=200, c='r', marker=(5, 2))
ax.axis('equal')

ax.axhline(y=0, color='k')
ax.axvline(x=0, color='k')

scale = 7
ax.arrow(-scale*pc1_vec[0], -scale*pc1_vec[1], 2*scale*pc1_vec[0], 2*scale*pc1_vec[1], head_width=0.1, head_length=0.1, fc='r', ec='r', lw=5)
ax.arrow(-scale*pc2_vec[0], -scale*pc2_vec[1], 2*scale*pc2_vec[0], 2*scale*pc2_vec[1], head_width=0.1, head_length=0.1, fc='b', ec='b', lw=5)
Out[160]:
<matplotlib.patches.FancyArrow at 0x1a21514400>
In [161]:
tot = sum(variances)
var_exp = [(i / tot)*100 for i in variances]
cum_var_exp = np.cumsum(var_exp)

plt.bar(range(len(var_exp)),var_exp, align='center', label='individual explained variance')
plt.step(range(len(var_exp)), cum_var_exp, 'r', where='mid', label='cumulative explained variance')
plt.ylabel('Explained variance ratio')
plt.xlabel('Principal components')
plt.legend(bbox_to_anchor=(1.1, 1.05))

print()





































In [162]:



    


Xstar=X@Vt.T
new_data['pc1'] = Xstar[:,0]  
new_data['pc2'] = Xstar[:,1]  

















In [175]:



    


f1 = Vt[:,0]
f2 = Vt[:,1]

















In [184]:



    


g1 = sns.lmplot('pc1', 'pc2', new_data, hue="Malignant/Benign", fit_reg=False, size=8, scatter_kws={"s": 180})
ax = g1.axes[0,0]
ax.axhline(y=0, color='k')
ax.axvline(x=0, color='k')
ax.axis('equal')


for i in range(272,278):
    x = new_data['pc1'][i] + 0.1
    y = new_data['pc2'][i] + 0.1
    ax.text(x,y,str(i),horizontalalignment='left',size='medium', color='black', weight='semibold', fontsize=16)

    
scale = 7
ax.arrow(0,0, scale*f1[0], scale*f1[1], head_width=0.1, head_length=0.1, fc='m', ec='m', lw=3)
ax.text(scale*f1[0]+0.2, scale*f1[1], "smoothness (zero mean)", horizontalalignment='left',size='medium', color='black', weight='semibold', fontsize=16)
ax.arrow(0,0, scale*f2[0], scale*f2[1], head_width=0.1, head_length=0.1, fc='m', ec='m', lw=3)
ax.text(scale*f2[0]+0.2, scale*f2[1], "radius (zero mean)", horizontalalignment='left',size='medium', color='black', weight='semibold', fontsize=16)




















Out[184]:








Text(6.60834,-2.8166,'radius (zero mean)')