Predicting Breast Cancer Diagnosis: A Machine Learning Example Using Logistic Regression

Data set:

It is one of the challenges posed by Kaggle in the UCI Machine Learning repository

It is a dataset of breast cancer patients with malignant and benign tumors.

Logistic regression is used to predict whether a given patient will have a malignant or benign tumor based on the attributes in a given data set.

code:loading libraries

# performing linear algebra
import numpy as np 
  
# data processing
import pandas as pd
  
# visualisation
import matplotlib.pyplot as plt

Code: Load the dataset

data = pd.read_csv( "..\\breast-cancer-wisconsin-data\\data.csv" )
  
print (data.head)

Output:

Code: Load the dataset

data.info()

Output:

RangeIndex: 569 entries, 0 to 568
Data columns (total 33 columns):
id                         569 non-null int64
diagnosis                  569 non-null object
radius_mean                569 non-null float64
texture_mean               569 non-null float64
perimeter_mean             569 non-null float64
area_mean                  569 non-null float64
smoothness_mean            569 non-null float64
compactness_mean           569 non-null float64
concavity_mean             569 non-null float64
concave points_mean        569 non-null float64
symmetry_mean              569 non-null float64
fractal_dimension_mean     569 non-null float64
radius_se                  569 non-null float64
texture_se                 569 non-null float64
perimeter_se               569 non-null float64
area_se                    569 non-null float64
smoothness_se              569 non-null float64
compactness_se             569 non-null float64
concavity_se               569 non-null float64
concave points_se          569 non-null float64
symmetry_se                569 non-null float64
fractal_dimension_se       569 non-null float64
radius_worst               569 non-null float64
texture_worst              569 non-null float64
perimeter_worst            569 non-null float64
area_worst                 569 non-null float64
smoothness_worst           569 non-null float64
compactness_worst          569 non-null float64
concavity_worst            569 non-null float64
concave points_worst       569 non-null float64
symmetry_worst             569 non-null float64
fractal_dimension_worst    569 non-null float64
Unnamed: 32                0 non-null float64
dtypes: float64(31), int64(1), object(1)
memory usage: 146.8+ KB

Code: We removed the “id” and “Unnamed:32” columns because they have no role in the prediction

data.drop([ 'Unnamed: 32' , 'id' ], axis = 1 )
data.diagnosis = [ 1 if each = = "M" else 0 for each in data.diagnosis]

Code: Input and output data

y = data.diagnosis.values
x_data = data.drop([ 'diagnosis' ], axis = 1 )

code:normalizing

x = (x_data - np. min (x_data)) /(np. max (x_data) - np. min (x_data)).values

Code: Split data for training and testing.

from sklearn.model_selection import train_test_split
x_train, x_test, y_train, y_test = train_test_split(
     x, y, test_size = 0.15 , random_state = 42 )
  
x_train = x_train.T
x_test = x_test.T
y_train = y_train.T
y_test = y_test.T
  
print ( "x train: " , x_train.shape)
print ( "x test: " , x_test.shape)
print ( "y train: " , y_train.shape)
print ( "y test: " , y_test.shape)

Code: Weight and bias

def initialize_weights_and_bias(dimension):
     w = np.full((dimension, 1 ), 0.01 )
     b = 0.0
     return w, b

Code: Sigmoid function – calculates z-value.

# z = np.dot(w.T, x_train)+b
def sigmoid(z):
     y_head = 1 /( 1 + np.exp( - z))
     return y_head

Code: Propagating from front to back

def forward_backward_propagation(w, b, x_train, y_train):
     z = np.dot(w.T, x_train) + b
     y_head = sigmoid(z)
     loss = - y_train * np.log(y_head) - ( 1 - y_train) * np.log( 1 - y_head)
     # x_train.shape[1]  is for scaling
     cost = (np. sum (loss)) /x_train.shape[ 1 ]      
  
     # backward propagation
     derivative_weight = (np.dot(x_train, (
         (y_head - y_train).T))) /x_train.shape[ 1 ] 
     derivative_bias = np. sum (
         y_head - y_train) /x_train.shape[ 1 ]                 
     gradients = { "derivative_weight" : derivative_weight, "derivative_bias" : derivative_bias}
     return cost, gradients

code: Update parameters

def update(w, b, x_train, y_train, learning_rate, number_of_iterarion):
     cost_list = []
     cost_list2 = []
     index = []
  
     # updating(learning) parameters is number_of_iterarion times
     for i in range (number_of_iterarion):
         # make forward and backward propagation and find cost and gradients
         cost, gradients = forward_backward_propagation(w, b, x_train, y_train)
         cost_list.append(cost)
  
         # lets update
         w = w - learning_rate * gradients[ "derivative_weight" ]
         b = b - learning_rate * gradients[ "derivative_bias" ]
         if i % 10 = = 0 :
             cost_list2.append(cost)
             index.append(i)
             print ( "Cost after iteration % i: % f" % (i, cost))
  
     # update(learn) parameters weights and bias
     parameters = { "weight" : w, "bias" : b}
     plt.plot(index, cost_list2)
     plt.xticks(index, rotation = 'vertical' )
     plt.xlabel( "Number of Iterarion" )
     plt.ylabel( "Cost" )
     plt.show()
     return parameters, gradients, cost_list

Code: Prediction

def predict(w, b, x_test):
     # x_test is a input for forward propagation
     z = sigmoid(np.dot(w.T, x_test) + b)
     Y_prediction = np.zeros(( 1 , x_test.shape[ 1 ]))
  
     # if z is bigger than 0.5, our prediction is sign one (y_head = 1), # if z is smaller than 0.5, our prediction is sign zero (y_head = 0), for i in range (z.shape[ 1 ]):
         if z[ 0 , i]<= 0.5 :
             Y_prediction[ 0 , i] = 0
         else :
             Y_prediction[ 0 , i] = 1
  
     return Y_prediction

Code: Logistic Regression

def logistic_regression(x_train, y_train, x_test, y_test, learning_rate, num_iterations):
  
     dimension = x_train.shape[ 0 ]
     w, b = initialize_weights_and_bias(dimension)
      
     parameters, gradients, cost_list = update(
         w, b, x_train, y_train, learning_rate, num_iterations)
      
     y_prediction_test = predict(
         parameters[ "weight" ], parameters[ "bias" ], x_test)
     y_prediction_train = predict(
         arameters[ "weight" ], parameters[ "bias" ], x_train)
  
     # train /test Errors
     print ( "train accuracy: {} %" . format (
         100 - np.mean(np. abs (y_prediction_train - y_train)) * 100 ))
     print ( "test accuracy: {} %" . format (
         100 - np.mean(np. abs (y_prediction_test - y_test)) * 100 ))
      
logistic_regression(x_train, y_train, x_test, y_test, learning_rate = 1 , num_iterations = 100 )

Output:

Cost after iteration 0: 0.692836
Cost after iteration 10: 0.498576
Cost after iteration 20: 0.404996
Cost after iteration 30: 0.350059
Cost after iteration 40: 0.313747
Cost after iteration 50: 0.287767
Cost after iteration 60: 0.268114
Cost after iteration 70: 0.252627
Cost after iteration 80: 0.240036
Cost after iteration 90: 0.229543
Cost after iteration 100: 0.220624
Cost after iteration 110: 0.212920
Cost after iteration 120: 0.206175
Cost after iteration 130: 0.200201
Cost after iteration 140: 0.194860

Output:

train accuracy: 95.23809523809524 %
test accuracy: 94.18604651162791 %

code:using linear_model. LogisticRegression test results

from sklearn import linear_model
logreg = linear_model.LogisticRegression(random_state = 42 , max_iter = 150 )
print ( "test accuracy: {} " . format (
     logreg.fit(x_train.T, y_train.T).score(x_test.T, y_test.T)))
print ( "train accuracy: {} " . format (
     logreg.fit(x_train.T, y_train.T).score(x_train.T, y_train.T)))

Output:

test accuracy: 0.9651162790697675 
train accuracy: 0.9668737060041408

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