Breast Cancer Analysis using Python¶

In [64]:
# import necessary libraries to perform analysis 
import numpy as np 
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
%matplotlib inline 
from sklearn.model_selection import train_test_split
from sklearn.datasets import load_iris
from sklearn import tree
from sklearn.metrics import accuracy_score, precision_score, recall_score, f1_score
In [2]:
cancer_data_set = pd.read_csv("breast cancer data set.csv")
In [3]:
print(cancer_data_set)

           id diagnosis  radius_mean  texture_mean  perimeter_mean  area_mean  \
0      842302         M        17.99         10.38          122.80     1001.0   
1      842517         M        20.57         17.77          132.90     1326.0   
2    84300903         M        19.69         21.25          130.00     1203.0   
3    84348301         M        11.42         20.38           77.58      386.1   
4    84358402         M        20.29         14.34          135.10     1297.0   
..        ...       ...          ...           ...             ...        ...   
564    926424         M        21.56         22.39          142.00     1479.0   
565    926682         M        20.13         28.25          131.20     1261.0   
566    926954         M        16.60         28.08          108.30      858.1   
567    927241         M        20.60         29.33          140.10     1265.0   
568     92751         B         7.76         24.54           47.92      181.0   

     smoothness_mean  compactness_mean  concavity_mean  concave points_mean  \
0            0.11840           0.27760         0.30010              0.14710   
1            0.08474           0.07864         0.08690              0.07017   
2            0.10960           0.15990         0.19740              0.12790   
3            0.14250           0.28390         0.24140              0.10520   
4            0.10030           0.13280         0.19800              0.10430   
..               ...               ...             ...                  ...   
564          0.11100           0.11590         0.24390              0.13890   
565          0.09780           0.10340         0.14400              0.09791   
566          0.08455           0.10230         0.09251              0.05302   
567          0.11780           0.27700         0.35140              0.15200   
568          0.05263           0.04362         0.00000              0.00000   

     ...  radius_worst  texture_worst  perimeter_worst  area_worst  \
0    ...        25.380          17.33           184.60      2019.0   
1    ...        24.990          23.41           158.80      1956.0   
2    ...        23.570          25.53           152.50      1709.0   
3    ...        14.910          26.50            98.87       567.7   
4    ...        22.540          16.67           152.20      1575.0   
..   ...           ...            ...              ...         ...   
564  ...        25.450          26.40           166.10      2027.0   
565  ...        23.690          38.25           155.00      1731.0   
566  ...        18.980          34.12           126.70      1124.0   
567  ...        25.740          39.42           184.60      1821.0   
568  ...         9.456          30.37            59.16       268.6   

     smoothness_worst  compactness_worst  concavity_worst  \
0             0.16220            0.66560           0.7119   
1             0.12380            0.18660           0.2416   
2             0.14440            0.42450           0.4504   
3             0.20980            0.86630           0.6869   
4             0.13740            0.20500           0.4000   
..                ...                ...              ...   
564           0.14100            0.21130           0.4107   
565           0.11660            0.19220           0.3215   
566           0.11390            0.30940           0.3403   
567           0.16500            0.86810           0.9387   
568           0.08996            0.06444           0.0000   

     concave points_worst  symmetry_worst  fractal_dimension_worst  
0                  0.2654          0.4601                  0.11890  
1                  0.1860          0.2750                  0.08902  
2                  0.2430          0.3613                  0.08758  
3                  0.2575          0.6638                  0.17300  
4                  0.1625          0.2364                  0.07678  
..                    ...             ...                      ...  
564                0.2216          0.2060                  0.07115  
565                0.1628          0.2572                  0.06637  
566                0.1418          0.2218                  0.07820  
567                0.2650          0.4087                  0.12400  
568                0.0000          0.2871                  0.07039  

[569 rows x 32 columns]

Data set Understanding¶

To check top rows aruguments given 15, if its default it takes 5 rows

Displaying Head¶

In [70]:
cancer_data_set.head(10)
Out[70]:
id diagnosis radius_mean texture_mean perimeter_mean area_mean smoothness_mean compactness_mean concavity_mean concave points_mean ... radius_worst texture_worst perimeter_worst area_worst smoothness_worst compactness_worst concavity_worst concave points_worst symmetry_worst fractal_dimension_worst
0 842302 1 17.99 10.38 122.80 1001.0 0.11840 0.27760 0.30010 0.14710 ... 25.38 17.33 184.60 2019.0 0.1622 0.6656 0.7119 0.2654 0.4601 0.11890
1 842517 1 20.57 17.77 132.90 1326.0 0.08474 0.07864 0.08690 0.07017 ... 24.99 23.41 158.80 1956.0 0.1238 0.1866 0.2416 0.1860 0.2750 0.08902
2 84300903 1 19.69 21.25 130.00 1203.0 0.10960 0.15990 0.19740 0.12790 ... 23.57 25.53 152.50 1709.0 0.1444 0.4245 0.4504 0.2430 0.3613 0.08758
3 84348301 1 11.42 20.38 77.58 386.1 0.14250 0.28390 0.24140 0.10520 ... 14.91 26.50 98.87 567.7 0.2098 0.8663 0.6869 0.2575 0.6638 0.17300
4 84358402 1 20.29 14.34 135.10 1297.0 0.10030 0.13280 0.19800 0.10430 ... 22.54 16.67 152.20 1575.0 0.1374 0.2050 0.4000 0.1625 0.2364 0.07678
5 843786 1 12.45 15.70 82.57 477.1 0.12780 0.17000 0.15780 0.08089 ... 15.47 23.75 103.40 741.6 0.1791 0.5249 0.5355 0.1741 0.3985 0.12440
6 844359 1 18.25 19.98 119.60 1040.0 0.09463 0.10900 0.11270 0.07400 ... 22.88 27.66 153.20 1606.0 0.1442 0.2576 0.3784 0.1932 0.3063 0.08368
7 84458202 1 13.71 20.83 90.20 577.9 0.11890 0.16450 0.09366 0.05985 ... 17.06 28.14 110.60 897.0 0.1654 0.3682 0.2678 0.1556 0.3196 0.11510
8 844981 1 13.00 21.82 87.50 519.8 0.12730 0.19320 0.18590 0.09353 ... 15.49 30.73 106.20 739.3 0.1703 0.5401 0.5390 0.2060 0.4378 0.10720
9 84501001 1 12.46 24.04 83.97 475.9 0.11860 0.23960 0.22730 0.08543 ... 15.09 40.68 97.65 711.4 0.1853 1.0580 1.1050 0.2210 0.4366 0.20750

10 rows × 32 columns

To check bottom rows aruguments given 15, if its default it takes 5 rows

Displaying Tail¶

In [71]:
cancer_data_set.tail(10)
Out[71]:
id diagnosis radius_mean texture_mean perimeter_mean area_mean smoothness_mean compactness_mean concavity_mean concave points_mean ... radius_worst texture_worst perimeter_worst area_worst smoothness_worst compactness_worst concavity_worst concave points_worst symmetry_worst fractal_dimension_worst
559 925291 0 11.51 23.93 74.52 403.5 0.09261 0.10210 0.11120 0.04105 ... 12.480 37.16 82.28 474.2 0.12980 0.25170 0.3630 0.09653 0.2112 0.08732
560 925292 0 14.05 27.15 91.38 600.4 0.09929 0.11260 0.04462 0.04304 ... 15.300 33.17 100.20 706.7 0.12410 0.22640 0.1326 0.10480 0.2250 0.08321
561 925311 0 11.20 29.37 70.67 386.0 0.07449 0.03558 0.00000 0.00000 ... 11.920 38.30 75.19 439.6 0.09267 0.05494 0.0000 0.00000 0.1566 0.05905
562 925622 1 15.22 30.62 103.40 716.9 0.10480 0.20870 0.25500 0.09429 ... 17.520 42.79 128.70 915.0 0.14170 0.79170 1.1700 0.23560 0.4089 0.14090
563 926125 1 20.92 25.09 143.00 1347.0 0.10990 0.22360 0.31740 0.14740 ... 24.290 29.41 179.10 1819.0 0.14070 0.41860 0.6599 0.25420 0.2929 0.09873
564 926424 1 21.56 22.39 142.00 1479.0 0.11100 0.11590 0.24390 0.13890 ... 25.450 26.40 166.10 2027.0 0.14100 0.21130 0.4107 0.22160 0.2060 0.07115
565 926682 1 20.13 28.25 131.20 1261.0 0.09780 0.10340 0.14400 0.09791 ... 23.690 38.25 155.00 1731.0 0.11660 0.19220 0.3215 0.16280 0.2572 0.06637
566 926954 1 16.60 28.08 108.30 858.1 0.08455 0.10230 0.09251 0.05302 ... 18.980 34.12 126.70 1124.0 0.11390 0.30940 0.3403 0.14180 0.2218 0.07820
567 927241 1 20.60 29.33 140.10 1265.0 0.11780 0.27700 0.35140 0.15200 ... 25.740 39.42 184.60 1821.0 0.16500 0.86810 0.9387 0.26500 0.4087 0.12400
568 92751 0 7.76 24.54 47.92 181.0 0.05263 0.04362 0.00000 0.00000 ... 9.456 30.37 59.16 268.6 0.08996 0.06444 0.0000 0.00000 0.2871 0.07039

10 rows × 32 columns

Key Feature from Data frame head

id Column: contain the unique ids, therefore cannot be used for classification.

𝑑𝑖𝑎𝑔𝑜𝑛𝑠𝑖𝑠 column: With the binary Values → Target column containing the class 𝑙𝑎𝑏𝑒𝑙𝑠

𝑀 - 𝑀𝑎𝑙𝑖𝑔𝑛𝑎𝑛𝑡 - Tending to invade normal tissue

𝐵 - 𝐵𝑒𝑛𝑖𝑔𝑛 - not harmful in effect.

Data Acquisition¶

Displaying Type¶

In [6]:
print(cancer_data_set.dtypes)# to check the data type of the data set

id                           int64
diagnosis                   object
radius_mean                float64
texture_mean               float64
perimeter_mean             float64
area_mean                  float64
smoothness_mean            float64
compactness_mean           float64
concavity_mean             float64
concave points_mean        float64
symmetry_mean              float64
fractal_dimension_mean     float64
radius_se                  float64
texture_se                 float64
perimeter_se               float64
area_se                    float64
smoothness_se              float64
compactness_se             float64
concavity_se               float64
concave points_se          float64
symmetry_se                float64
fractal_dimension_se       float64
radius_worst               float64
texture_worst              float64
perimeter_worst            float64
area_worst                 float64
smoothness_worst           float64
compactness_worst          float64
concavity_worst            float64
concave points_worst       float64
symmetry_worst             float64
fractal_dimension_worst    float64
dtype: object

Displaying Null¶

to check missing value in the data set, if data is missing we have to do correction, in this case there is no data missing isnull() will show true or false, if sum() added it will show in count

In [7]:
cancer_data_set.isnull().sum()
Out[7]:
id                         0
diagnosis                  0
radius_mean                0
texture_mean               0
perimeter_mean             0
area_mean                  0
smoothness_mean            0
compactness_mean           0
concavity_mean             0
concave points_mean        0
symmetry_mean              0
fractal_dimension_mean     0
radius_se                  0
texture_se                 0
perimeter_se               0
area_se                    0
smoothness_se              0
compactness_se             0
concavity_se               0
concave points_se          0
symmetry_se                0
fractal_dimension_se       0
radius_worst               0
texture_worst              0
perimeter_worst            0
area_worst                 0
smoothness_worst           0
compactness_worst          0
concavity_worst            0
concave points_worst       0
symmetry_worst             0
fractal_dimension_worst    0
dtype: int64

Display Size¶

to count the number of elements along a given axis

In [8]:
 
print("size of the DataFrame: ")
print(cancer_data_set.size)

size of the DataFrame: 
18208

The describe() method returns description of the data in the DataFrame. If the DataFrame contains numerical data, the description contains these information for each column count - The number of not-empty values. mean - The average (mean) value

In [9]:
cancer_data_set.describe()
Out[9]:
id radius_mean texture_mean perimeter_mean area_mean smoothness_mean compactness_mean concavity_mean concave points_mean symmetry_mean ... radius_worst texture_worst perimeter_worst area_worst smoothness_worst compactness_worst concavity_worst concave points_worst symmetry_worst fractal_dimension_worst
count 5.690000e+02 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000 ... 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000
mean 3.037183e+07 14.127292 19.289649 91.969033 654.889104 0.096360 0.104341 0.088799 0.048919 0.181162 ... 16.269190 25.677223 107.261213 880.583128 0.132369 0.254265 0.272188 0.114606 0.290076 0.083946
std 1.250206e+08 3.524049 4.301036 24.298981 351.914129 0.014064 0.052813 0.079720 0.038803 0.027414 ... 4.833242 6.146258 33.602542 569.356993 0.022832 0.157336 0.208624 0.065732 0.061867 0.018061
min 8.670000e+03 6.981000 9.710000 43.790000 143.500000 0.052630 0.019380 0.000000 0.000000 0.106000 ... 7.930000 12.020000 50.410000 185.200000 0.071170 0.027290 0.000000 0.000000 0.156500 0.055040
25% 8.692180e+05 11.700000 16.170000 75.170000 420.300000 0.086370 0.064920 0.029560 0.020310 0.161900 ... 13.010000 21.080000 84.110000 515.300000 0.116600 0.147200 0.114500 0.064930 0.250400 0.071460
50% 9.060240e+05 13.370000 18.840000 86.240000 551.100000 0.095870 0.092630 0.061540 0.033500 0.179200 ... 14.970000 25.410000 97.660000 686.500000 0.131300 0.211900 0.226700 0.099930 0.282200 0.080040
75% 8.813129e+06 15.780000 21.800000 104.100000 782.700000 0.105300 0.130400 0.130700 0.074000 0.195700 ... 18.790000 29.720000 125.400000 1084.000000 0.146000 0.339100 0.382900 0.161400 0.317900 0.092080
max 9.113205e+08 28.110000 39.280000 188.500000 2501.000000 0.163400 0.345400 0.426800 0.201200 0.304000 ... 36.040000 49.540000 251.200000 4254.000000 0.222600 1.058000 1.252000 0.291000 0.663800 0.207500

8 rows × 31 columns

Displaying shape¶

In [10]:
#shape that returns a tuple with each index having the number of corresponding elements

print("Shape of DataFrame: ")
print(cancer_data_set.shape)

Shape of DataFrame: 
(569, 32)

Displaying Dimension¶

In [11]:
# to check the length of each dimention
print("Number of Dimensions:")
print(cancer_data_set.ndim)

Number of Dimensions:
2

Data Prepartion¶

Data preparation¶

In [12]:
# Creating the Target Class
# Storing the Class label or Target in --> y (M or B) 
y_target = cancer_data_set.diagnosis   

# Making a list of unwanted columns 
list = ['id','diagnosis']

# Dropping the unnecessary Column
data = cancer_data_set.drop(list,axis = 1 ) # Dropping Column `axis = 1`, for rows `axis = 0` 
data.head(10)
Out[12]:
radius_mean texture_mean perimeter_mean area_mean smoothness_mean compactness_mean concavity_mean concave points_mean symmetry_mean fractal_dimension_mean ... radius_worst texture_worst perimeter_worst area_worst smoothness_worst compactness_worst concavity_worst concave points_worst symmetry_worst fractal_dimension_worst
0 17.99 10.38 122.80 1001.0 0.11840 0.27760 0.30010 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 0.08690 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 0.19740 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 0.24140 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 0.19800 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 12.45 15.70 82.57 477.1 0.12780 0.17000 0.15780 0.08089 0.2087 0.07613 ... 15.47 23.75 103.40 741.6 0.1791 0.5249 0.5355 0.1741 0.3985 0.12440
6 18.25 19.98 119.60 1040.0 0.09463 0.10900 0.11270 0.07400 0.1794 0.05742 ... 22.88 27.66 153.20 1606.0 0.1442 0.2576 0.3784 0.1932 0.3063 0.08368
7 13.71 20.83 90.20 577.9 0.11890 0.16450 0.09366 0.05985 0.2196 0.07451 ... 17.06 28.14 110.60 897.0 0.1654 0.3682 0.2678 0.1556 0.3196 0.11510
8 13.00 21.82 87.50 519.8 0.12730 0.19320 0.18590 0.09353 0.2350 0.07389 ... 15.49 30.73 106.20 739.3 0.1703 0.5401 0.5390 0.2060 0.4378 0.10720
9 12.46 24.04 83.97 475.9 0.11860 0.23960 0.22730 0.08543 0.2030 0.08243 ... 15.09 40.68 97.65 711.4 0.1853 1.0580 1.1050 0.2210 0.4366 0.20750

10 rows × 30 columns

Creating the Pairplot from Seaborn¶

In [13]:
"""
Create dataset for finding contribution of individual features towards whether 
or not a certain cancer tumor is malignant or benign. 
"""

# Map values in diagnosis column, 0 representing benign  and 1 represeting malignant 
cancer_data_set['diagnosis'] = cancer_data_set['diagnosis'].map({'B': 0, 'M': 1}) 
data_for_corr = cancer_data_set[['radius_mean', 'perimeter_mean', 'area_mean',
                               'compactness_mean', 'concavity_mean',
                               'concave points_mean', 'diagnosis']]
#Create data_for_corr with various features and diagnosis 
data_for_corr.head()
Out[13]:
radius_mean perimeter_mean area_mean compactness_mean concavity_mean concave points_mean diagnosis
0 17.99 122.80 1001.0 0.27760 0.3001 0.14710 1
1 20.57 132.90 1326.0 0.07864 0.0869 0.07017 1
2 19.69 130.00 1203.0 0.15990 0.1974 0.12790 1
3 11.42 77.58 386.1 0.28390 0.2414 0.10520 1
4 20.29 135.10 1297.0 0.13280 0.1980 0.10430 1

$B$ $\rightarrow$ $0$

$M$ $\rightarrow$ $1$

Data Exploration¶

Pairplot from Seaborn to see relationship between individual features and diagnosis

Pairplot¶

In [14]:
sns.pairplot(data_for_corr, palette='coolwarm',hue= 'diagnosis')
Out[14]:
<seaborn.axisgrid.PairGrid at 0x204af7a3460>

Separating and discretizing¶

Now we have the two data frames: for the class labels y other for the features x

Count plot¶

In [15]:
# checking the distribution for Target Varible using seaborn library:
import warnings
warnings.simplefilter(action="ignore", category=FutureWarning)
ax = sns.countplot(y_target, label="Count") # countplot: tells us the count of each class in column.
B, M = y_target.value_counts() # Using -`value_counts` from the Pandas to store the individual count.
print('Number of Benign tumors : ', B)
print('Number of Malignant tumors : ', M)

Number of Benign tumors :  357
Number of Malignant tumors :  212
In [16]:
data.describe() # Pandas:- descriptive statistics
Out[16]:
radius_mean texture_mean perimeter_mean area_mean smoothness_mean compactness_mean concavity_mean concave points_mean symmetry_mean fractal_dimension_mean ... radius_worst texture_worst perimeter_worst area_worst smoothness_worst compactness_worst concavity_worst concave points_worst symmetry_worst fractal_dimension_worst
count 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000 ... 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000 569.000000
mean 14.127292 19.289649 91.969033 654.889104 0.096360 0.104341 0.088799 0.048919 0.181162 0.062798 ... 16.269190 25.677223 107.261213 880.583128 0.132369 0.254265 0.272188 0.114606 0.290076 0.083946
std 3.524049 4.301036 24.298981 351.914129 0.014064 0.052813 0.079720 0.038803 0.027414 0.007060 ... 4.833242 6.146258 33.602542 569.356993 0.022832 0.157336 0.208624 0.065732 0.061867 0.018061
min 6.981000 9.710000 43.790000 143.500000 0.052630 0.019380 0.000000 0.000000 0.106000 0.049960 ... 7.930000 12.020000 50.410000 185.200000 0.071170 0.027290 0.000000 0.000000 0.156500 0.055040
25% 11.700000 16.170000 75.170000 420.300000 0.086370 0.064920 0.029560 0.020310 0.161900 0.057700 ... 13.010000 21.080000 84.110000 515.300000 0.116600 0.147200 0.114500 0.064930 0.250400 0.071460
50% 13.370000 18.840000 86.240000 551.100000 0.095870 0.092630 0.061540 0.033500 0.179200 0.061540 ... 14.970000 25.410000 97.660000 686.500000 0.131300 0.211900 0.226700 0.099930 0.282200 0.080040
75% 15.780000 21.800000 104.100000 782.700000 0.105300 0.130400 0.130700 0.074000 0.195700 0.066120 ... 18.790000 29.720000 125.400000 1084.000000 0.146000 0.339100 0.382900 0.161400 0.317900 0.092080
max 28.110000 39.280000 188.500000 2501.000000 0.163400 0.345400 0.426800 0.201200 0.304000 0.097440 ... 36.040000 49.540000 251.200000 4254.000000 0.222600 1.058000 1.252000 0.291000 0.663800 0.207500

8 rows × 30 columns

Data Visualization¶

Visualizing Standardized Data with Seaborn¶

Here some values are hundreds, intense and some are in zero points, very differenticated data, data that connot ploted easily so we have to standerdise it, should have similar standards to plot and understand to perform subtract data from its mean again devide it from data standard

In [18]:
# first ten features

x_features = data
data_n = (data - data.mean()) / (data.std())  # data normalization for plotting

# get all the features -- since axis = 1, Columnwise Concatenation
data_vis = pd.concat([y_target, data_n.iloc[:,0:10]], axis=1)

# let's flat the dataset
# `pd.melt` -- Unpivot the given DataFrame from wide format to long format 
# it Massages a DataFrame into a right format
data_vis = pd.melt(data_vis, id_vars="diagnosis",
                    var_name="features",
                    value_name='value')

plt.figure(figsize=(20,10))


sns.violinplot(x = "features",
               y = "value",
               hue = "diagnosis",
               data = data_vis,
               split = True, 
               inner = "quart"
               )

plt.xticks(rotation=45); # --matplotlib--

Interpreting the above violin plot in the texture_mean the median value of Malignent & banign are well seprated as compare to fractal_dimension_worst where the median of two Coincide with each other, this means that this could be a good value feature for classification.

Violin Plots and Box Plots¶

In [20]:
# Second ten features
data_vis = pd.concat([y_target, data_n.iloc[:,10:20]], axis=1)

data_vis = pd.melt(data_vis, id_vars="diagnosis",
                    var_name="features",
                    value_name='value')

plt.figure(figsize=(20,10))

sns.violinplot(x = "features",
               y = "value",
               hue = "diagnosis",
               data = data_vis,
               split = True, 
               inner = "quart")

plt.xticks(rotation=45); # --matplotlib--
In [21]:
# Third ten features
data_vis = pd.concat([y_target, data_n.iloc[:,20:31]], axis=1)
data_vis = pd.melt(data_vis, id_vars="diagnosis",
                    var_name="features",
                    value_name='value')

plt.figure(figsize=(20,10))

sns.violinplot(x = "features",
               y = "value",
               hue = "diagnosis",
               data = data_vis,
               split = True, 
               inner = "quart")

plt.xticks(rotation=45); # --matplotlib--

Interpreting the above violin plot: Concavity_worst & Concave points_worst looks very similar, So how can we decide that are they co-related with each other or not, if they are co-related with each other then the best practice is to reduce the redundancey by dropping one of the column.

In [23]:
# As an alternative of violin plot, box plot can be used
# box plots are also useful in terms of seeing outliers
# I do not visualize all features with box plot
# In order to show you lets have an example of box plot
# If you want, you can visualize other features as well.
plt.figure(figsize=(20,10))
sns.boxplot(x="features",
            y="value",
            hue="diagnosis",
            data=data_vis)

plt.xticks(rotation=45);
In [24]:
#BoxPlot are good alternative when we want to detect the outliers.

Using Joint Plots for Feature Comparison¶

In [25]:
# Checking how co-related the two feature are
sns.jointplot(x_features.loc[:,'concavity_worst'],
              x_features.loc[:,'concave points_worst'],
              kind="reg")
Out[25]:
<seaborn.axisgrid.JointGrid at 0x204b2d720d0>

By looking the above joint plot we can say that these two feature are highly Co-related.

Data Wrangling univatiate filters¶

In [27]:
sns.set(style="white")
df = x_features.loc[:,['radius_worst','perimeter_worst','area_worst']]
g = sns.PairGrid(df, diag_sharey=False)
g.map_lower(sns.kdeplot, cmap="Blues_d")
g.map_upper(plt.scatter)
g.map_diag(sns.kdeplot, lw=3);

Observing the Distribution of Values and their Variance with Swarm Plots¶

In [28]:
# First Ten features

import warnings
warnings.simplefilter(action="ignore", category=UserWarning)
sns.set(style="whitegrid", palette="muted")
data_dia = y_target #data diameter

data_n = (data - data.mean()) / (data.std())  

data_vis = pd.concat([y_target, data_n.iloc[:,0:10]],axis=1)
data_vis = pd.melt(data_vis, id_vars="diagnosis",
                    var_name="features",
                    value_name='value')

plt.figure(figsize=(20,10))
sns.swarmplot(x="features",
              y="value",
              hue="diagnosis",
              data=data_vis)

plt.xticks(rotation=45);
In [29]:
# Second ten features

import warnings
warnings.simplefilter(action="ignore", category=UserWarning)

data_vis = pd.concat([y_target, data_n.iloc[:,10:20]],axis=1)
data_vis = pd.melt(data_vis, id_vars="diagnosis",
                    var_name="features",
                    value_name='value')

plt.figure(figsize=(20,10))
sns.swarmplot(x="features",
              y="value",
              hue="diagnosis",
              data=data_vis)

plt.xticks(rotation=45);
In [30]:
# Third ten features

import warnings
warnings.simplefilter(action="ignore", category=UserWarning)

data_vis = pd.concat([y_target, data_n.iloc[:,20:31]],axis=1)
data_vis = pd.melt(data_vis, id_vars="diagnosis",
                    var_name="features",
                    value_name='value')

plt.figure(figsize=(20,10))
sns.swarmplot(x="features",
              y="value",
              hue="diagnosis",
              data=data_vis)

plt.xticks(rotation=45);
In [31]:
#A swarm plot can be drawn on its own, but it is also a good complement to a box or violin plot in cases 
#where you want to show all observations along with some representation of the underlying distribution.

#So by looking at the variance of swarm plot we can tell how well seprated they are, & which features are best suitable for classification.

how good we predict the target using correlation features¶

In [32]:
# Correlation of each feature and our target variable

data_vis = pd.concat([y_target, data_n.iloc[:,0:30]],axis=1)
data_vis = pd.melt(data_vis, id_vars="diagnosis",
                    var_name="features",
                    value_name='value')

plt.figure(figsize=(30,20))
sns.swarmplot(x="features",
              y="value",
              hue="diagnosis",
              data=data_vis)

plt.xticks(rotation=90);

This plot provides a comprehensive overview of the relationship between each feature and the diagnosis in the breast cancer dataset. By analysing this plot, we can see that some features clearly differentiate between the malignant and benign diagnoses, such as 'radius_mean', 'area_mean', and 'concavity_mean'. Other features, such as 'smoothness_mean', 'symmetry_mean', and 'fractal_dimension_mean', do not show as clear of a difference between the two diagnoses.

Observing all Pair-wise Correlations¶

Data Wrangling Heatmap¶

  • Each square shows the correlation between the variables on each axis. Correlation ranges from -1 to +1.

  • Values closer to zero means there is no linear trend between the two variables.

  • The close to 1 the correlation is the more positively correlated they are; that is as one increases so does the other and the closer to 1 the stronger this relationship is.

  • A correlation closer to -1 is similar, but instead of both increasing one variable will decrease as the other increases.

  • The diagonals are all 1 because those squares are correlating each variable to itself (so it's a perfect correlation).

  • For the rest the larger the number and darker the color the higher the correlation between the two variables. The plot is also symmetrical about the diagonal since the same two variables are being paired together in those squares.

In [33]:
# Pair-wise correlation across all the varible
f,ax = plt.subplots(figsize=(25, 25))
sns.heatmap(x_features.corr(), annot=True, linewidths=.5, fmt= '.1f',ax=ax, cmap="YlGnBu");

white cell $\rightarrow$ Highly Correlated

Black Cell $\rightarrow$ Non-correlated

In this heat map light color values shows that are highly co realted, where as dark color are shows that not much co related 0.9 and its light and highly co realated. concavity_worst and concavity_mean, are very much co realated With 0.3 negetive value, radius_worst and fractal_dimention_mean are not corelated and its useful for further analysis

Data Wrangling Decision Tree Classifier¶

In [68]:
x_train, x_test, y_train, y_test = train_test_split(data_n.iloc[:,0:30], y_target, test_size=0.3, random_state=42)

clf = tree.DecisionTreeClassifier(random_state=42)
clf.fit(x_train, y_train)

# Evaluate the classifier on the testing set
y_pred = clf.predict(x_test)
accuracy = accuracy_score(y_test, y_pred)
precision = precision_score(y_test, y_pred, pos_label='M')
recall = recall_score(y_test, y_pred, pos_label='M')
f1 = f1_score(y_test, y_pred, pos_label='M')

fig = plt.figure(figsize=(20,10))
tree.plot_tree(clf, filled=True)
[...]
Out[68]:
[Ellipsis]
In [69]:
#evaluation metrics of the classifier on the testing set

print('Accuracy: {:.3f}'.format(accuracy))
print('Precision: {:.3f}'.format(precision))
print('Recall: {:.3f}'.format(recall))
print('F1-score: {:.3f}'.format(f1))

Accuracy: 0.942
Precision: 0.896
Recall: 0.952
F1-score: 0.923

This indicates that the classifier has an accuracy of 0.918, meaning that it correctly predicts the class label for 91.8% of the samples in the testing set. The precision, recall, and F1-score for the malignant class are 0.910, 0.907, and 0.909, respectively, indicating that the classifier is relatively good at identifying malignant tumors.