In [1]:
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 [2]:
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)

features = tumor_data[labels[2:]]

features.head()
Out[2]:
radius (mean) radius (stderr) radius (worst) texture (mean) texture (stderr) texture (worst) perimeter (mean) perimeter (stderr) perimeter (worst) area (mean) ... concavity (worst) concave points (mean) concave points (stderr) concave points (worst) symmetry (mean) symmetry (stderr) symmetry (worst) fractal dimension (mean) fractal dimension (stderr) fractal dimension (worst)
0 17.99 10.38 122.80 1001.0 0.11840 0.27760 0.3001 0.14710 0.2419 0.07871 ... 25.38 17.33 184.60 2019.0 0.1622 0.6656 0.7119 0.2654 0.4601 0.11890
1 20.57 17.77 132.90 1326.0 0.08474 0.07864 0.0869 0.07017 0.1812 0.05667 ... 24.99 23.41 158.80 1956.0 0.1238 0.1866 0.2416 0.1860 0.2750 0.08902
2 19.69 21.25 130.00 1203.0 0.10960 0.15990 0.1974 0.12790 0.2069 0.05999 ... 23.57 25.53 152.50 1709.0 0.1444 0.4245 0.4504 0.2430 0.3613 0.08758
3 11.42 20.38 77.58 386.1 0.14250 0.28390 0.2414 0.10520 0.2597 0.09744 ... 14.91 26.50 98.87 567.7 0.2098 0.8663 0.6869 0.2575 0.6638 0.17300
4 20.29 14.34 135.10 1297.0 0.10030 0.13280 0.1980 0.10430 0.1809 0.05883 ... 22.54 16.67 152.20 1575.0 0.1374 0.2050 0.4000 0.1625 0.2364 0.07678

5 rows × 30 columns

In [3]:
mean_label = [labels[1]] + labels[2::3] 
print(mean_label)

['Malignant/Benign', 'radius (mean)', 'texture (mean)', 'perimeter (mean)', 'area (mean)', 'smoothness (mean)', 'compactness (mean)', 'concavity (mean)', 'concave points (mean)', 'symmetry (mean)', 'fractal dimension (mean)']
In [4]:
sns.pairplot(tumor_data[mean_label], hue="Malignant/Benign", plot_kws = {'alpha': 0.6, 's': 80, 'edgecolor': 'k'})
Out[4]:
<seaborn.axisgrid.PairGrid at 0x10dd45ba8>
In [5]:
corr_matrix = features.corr()
# plot correlation matrix
fig = plt.figure()
ax1 = fig.add_subplot(111)
cax = ax1.imshow(corr_matrix, cmap=cm.get_cmap('jet'))
plt.title('Tumor features correlation matrix')
plt.grid('off')
ax1.set_xticks(np.arange(features.shape[1]))
ax1.set_yticks(np.arange(features.shape[1]))
ax1.set_xticklabels(labels[2:],fontsize=10,rotation=90)
ax1.set_yticklabels(labels[2:],fontsize=10)
fig.colorbar(cax)
Out[5]:
<matplotlib.colorbar.Colorbar at 0x1a1fcebf98>
In [6]:
fig = plt.figure(figsize = (14,8))
ax1 = fig.add_subplot(111)
cax = ax1.imshow(tumor_data[mean_label[1:]].corr(), cmap=cm.get_cmap('jet'))
plt.title('Tumor features correlation matrix')
plt.grid('off')
ax1.set_xticks(np.arange(len(mean_label[1:])))
ax1.set_yticks(np.arange(len(mean_label[1:])))
ax1.set_xticklabels(mean_label[1:],fontsize=16,rotation=90)
ax1.set_yticklabels(mean_label[1:],fontsize=16)
fig.colorbar(cax)
Out[6]:
<matplotlib.colorbar.Colorbar at 0x1a1fe65470>
In [7]:
X = (features - features.mean())/features.std()

U, S, Vt = np.linalg.svd(X, full_matrices=False)

variances = S**2

V = Vt.T
In [8]:
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))
Out[8]:
<matplotlib.legend.Legend at 0x1a1febca58>
In [9]:
cum_var_exp
Out[9]:
array([  43.39946344,   62.59238425,   73.40687734,   79.43377319,
         84.38534142,   88.44267647,   90.70202752,   92.40314689,
         93.81109327,   95.00733279,   96.09327633,   96.94979856,
         97.76955554,   98.28341965,   98.62610703,   98.9147503 ,
         99.12033911,   99.31807613,   99.46078286,   99.57431509,
         99.67744567,   99.76450833,   99.83132474,   99.89027957,
         99.93992972,   99.96606966,   99.99033414,   99.99631036,
         99.99951529,  100.        ])
In [10]:
k = 6
Xstar=X@V[:,:k]
tumor_pca_data = tumor_data[labels[:2]].copy()
pca_labels = []
for i in range(k):
    lab = 'p'+str(i)
    pca_labels += [lab]
    tumor_pca_data[lab] = Xstar[:,i]
In [11]:
sns.stripplot(x="p0",y="Malignant/Benign", data=tumor_pca_data, jitter=0.05, linewidth=1)
Out[11]:
<matplotlib.axes._subplots.AxesSubplot at 0x1a1fd0a780>
In [12]:
def plot_arrow(vector,scale,text_label,text_posx,text_posy):
    plt.arrow(0, 0, scale*vector[0], scale*vector[1], head_width=0.1, head_length=0.1, fc='r', ec='r', lw=5)
    plt.text(scale*vector[0]*text_posx, scale*vector[1]*text_posy, text_label , color='black', ha='center', va='center', fontsize=18)
In [13]:
g1 = sns.lmplot('p0', 'p1', tumor_pca_data, hue='Malignant/Benign', fit_reg=False, size=8, scatter_kws={'alpha':0.7,'s':60})

ax = g1.axes[0,0]
ax.axhline(y=0, color='k')
ax.axvline(x=0, color='k')
Out[13]:
<matplotlib.lines.Line2D at 0x1a213744e0>
In [14]:
labelset = ['Malignant/Benign','p0', 'p1','p2','p3']
sns.pairplot(tumor_pca_data[labelset],hue='Malignant/Benign', plot_kws = {'alpha': 0.6, 's': 80, 'edgecolor': 'k'})
Out[14]:
<seaborn.axisgrid.PairGrid at 0x1a202e37f0>
In [15]:
plt.subplots(figsize = (14,8))
plt.bar(labels[2:],V[:,0])
plt.xticks(rotation=90)
plt.title('influence of original features in p0')
Out[15]:
Text(0.5,1,'influence of original features in p0')