A Logistic Regression model using the Breast Cancer dataset

Arthur Danda introduces classification using the popular breast cancer dataset

Introduction to Logistic Regression

Used when we have to choose between 2 values, in this case choosing between malignant and benign. The regression produces an S shape graph assumptions of logistic regression:

There should not be any multi_collinearity in the model, which means the features must be independent of each other.
We must include meaningful variables in our model
We should choose a lage sample size for our logisitic regression

Solvers -> liblinear => is for multiclass classifiers

# import important modules
from sklearn.datasets import load_breast_cancer
import pandas as pd
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import roc_curve
import matplotlib.pyplot as plt

# Determines how many columns should be displayed on the output data
pd.options.display.max_columns = 30

Load the dataset, which comes with Scikit Learn and explore information about the data

# Loading the dataframe of breast cancer from sklearn.datasets
breast_cancer_dataset = load_breast_cancer()
breast_cancer = pd.DataFrame(breast_cancer_dataset.data, columns=breast_cancer_dataset.feature_names)
breast_cancer['result'] = breast_cancer_dataset['target']

# Give a detailed description of the dataset
print(breast_cancer_dataset.keys())
print(breast_cancer_dataset['DESCR'])

dict_keys(['data', 'target', 'frame', 'target_names', 'DESCR', 'feature_names', 'filename'])
.. _breast_cancer_dataset:

Breast cancer wisconsin (diagnostic) dataset
--------------------------------------------

**Data Set Characteristics:**

    :Number of Instances: 569

    :Number of Attributes: 30 numeric, predictive attributes and the class

    :Attribute Information:
        - radius (mean of distances from center to points on the perimeter)
        - texture (standard deviation of gray-scale values)
        - perimeter
        - area
        - smoothness (local variation in radius lengths)
        - compactness (perimeter^2 / area - 1.0)
        - concavity (severity of concave portions of the contour)
        - concave points (number of concave portions of the contour)
        - symmetry
        - fractal dimension ("coastline approximation" - 1)

        The mean, standard error, and "worst" or largest (mean of the three
        worst/largest values) of these features were computed for each image,
        resulting in 30 features.  For instance, field 0 is Mean Radius, field
        10 is Radius SE, field 20 is Worst Radius.

        - class:
                - WDBC-Malignant
                - WDBC-Benign

    :Summary Statistics:

    ===================================== ====== ======
                                           Min    Max
    ===================================== ====== ======
    radius (mean):                        6.981  28.11
    texture (mean):                       9.71   39.28
    perimeter (mean):                     43.79  188.5
    area (mean):                          143.5  2501.0
    smoothness (mean):                    0.053  0.163
    compactness (mean):                   0.019  0.345
    concavity (mean):                     0.0    0.427
    concave points (mean):                0.0    0.201
    symmetry (mean):                      0.106  0.304
    fractal dimension (mean):             0.05   0.097
    radius (standard error):              0.112  2.873
    texture (standard error):             0.36   4.885
    perimeter (standard error):           0.757  21.98
    area (standard error):                6.802  542.2
    smoothness (standard error):          0.002  0.031
    compactness (standard error):         0.002  0.135
    concavity (standard error):           0.0    0.396
    concave points (standard error):      0.0    0.053
    symmetry (standard error):            0.008  0.079
    fractal dimension (standard error):   0.001  0.03
    radius (worst):                       7.93   36.04
    texture (worst):                      12.02  49.54
    perimeter (worst):                    50.41  251.2
    area (worst):                         185.2  4254.0
    smoothness (worst):                   0.071  0.223
    compactness (worst):                  0.027  1.058
    concavity (worst):                    0.0    1.252
    concave points (worst):               0.0    0.291
    symmetry (worst):                     0.156  0.664
    fractal dimension (worst):            0.055  0.208
    ===================================== ====== ======

    :Missing Attribute Values: None

    :Class Distribution: 212 - Malignant, 357 - Benign

    :Creator:  Dr. William H. Wolberg, W. Nick Street, Olvi L. Mangasarian

    :Donor: Nick Street

    :Date: November, 1995

This is a copy of UCI ML Breast Cancer Wisconsin (Diagnostic) datasets.
https://goo.gl/U2Uwz2

Features are computed from a digitized image of a fine needle
aspirate (FNA) of a breast mass.  They describe
characteristics of the cell nuclei present in the image.

Separating plane described above was obtained using
Multisurface Method-Tree (MSM-T) [K. P. Bennett, "Decision Tree
Construction Via Linear Programming." Proceedings of the 4th
Midwest Artificial Intelligence and Cognitive Science Society,
pp. 97-101, 1992], a classification method which uses linear
programming to construct a decision tree.  Relevant features
were selected using an exhaustive search in the space of 1-4
features and 1-3 separating planes.

The actual linear program used to obtain the separating plane
in the 3-dimensional space is that described in:
[K. P. Bennett and O. L. Mangasarian: "Robust Linear
Programming Discrimination of Two Linearly Inseparable Sets",
Optimization Methods and Software 1, 1992, 23-34].

This database is also available through the UW CS ftp server:

ftp ftp.cs.wisc.edu
cd math-prog/cpo-dataset/machine-learn/WDBC/

.. topic:: References

   - W.N. Street, W.H. Wolberg and O.L. Mangasarian. Nuclear feature extraction 
     for breast tumor diagnosis. IS&T/SPIE 1993 International Symposium on 
     Electronic Imaging: Science and Technology, volume 1905, pages 861-870,
     San Jose, CA, 1993.
   - O.L. Mangasarian, W.N. Street and W.H. Wolberg. Breast cancer diagnosis and 
     prognosis via linear programming. Operations Research, 43(4), pages 570-577, 
     July-August 1995.
   - W.H. Wolberg, W.N. Street, and O.L. Mangasarian. Machine learning techniques
     to diagnose breast cancer from fine-needle aspirates. Cancer Letters 77 (1994) 
     163-171.

In order to know what the target set represents, output is -> [‘malignant’ ‘benign’] showing that a 0=>malignant and 1=>benign


print(breast_cancer_dataset['target_names'])

['malignant' 'benign']

Exploration of features..

breast_cancer.describe()

	mean radius	mean texture	mean perimeter	mean area	mean smoothness	mean compactness	mean concavity	mean concave points	mean symmetry	mean fractal dimension	radius error	texture error	perimeter error	area error	smoothness error	...	concavity error	concave points error	symmetry error	fractal dimension error	worst radius	worst texture	worst perimeter	worst area	worst smoothness	worst compactness	worst concavity	worst concave points	worst symmetry	worst fractal dimension	result
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	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	0.405172	1.216853	2.866059	40.337079	0.007041	...	0.031894	0.011796	0.020542	0.003795	16.269190	25.677223	107.261213	880.583128	0.132369	0.254265	0.272188	0.114606	0.290076	0.083946	0.627417
std	3.524049	4.301036	24.298981	351.914129	0.014064	0.052813	0.079720	0.038803	0.027414	0.007060	0.277313	0.551648	2.021855	45.491006	0.003003	...	0.030186	0.006170	0.008266	0.002646	4.833242	6.146258	33.602542	569.356993	0.022832	0.157336	0.208624	0.065732	0.061867	0.018061	0.483918
min	6.981000	9.710000	43.790000	143.500000	0.052630	0.019380	0.000000	0.000000	0.106000	0.049960	0.111500	0.360200	0.757000	6.802000	0.001713	...	0.000000	0.000000	0.007882	0.000895	7.930000	12.020000	50.410000	185.200000	0.071170	0.027290	0.000000	0.000000	0.156500	0.055040	0.000000
25%	11.700000	16.170000	75.170000	420.300000	0.086370	0.064920	0.029560	0.020310	0.161900	0.057700	0.232400	0.833900	1.606000	17.850000	0.005169	...	0.015090	0.007638	0.015160	0.002248	13.010000	21.080000	84.110000	515.300000	0.116600	0.147200	0.114500	0.064930	0.250400	0.071460	0.000000
50%	13.370000	18.840000	86.240000	551.100000	0.095870	0.092630	0.061540	0.033500	0.179200	0.061540	0.324200	1.108000	2.287000	24.530000	0.006380	...	0.025890	0.010930	0.018730	0.003187	14.970000	25.410000	97.660000	686.500000	0.131300	0.211900	0.226700	0.099930	0.282200	0.080040	1.000000
75%	15.780000	21.800000	104.100000	782.700000	0.105300	0.130400	0.130700	0.074000	0.195700	0.066120	0.478900	1.474000	3.357000	45.190000	0.008146	...	0.042050	0.014710	0.023480	0.004558	18.790000	29.720000	125.400000	1084.000000	0.146000	0.339100	0.382900	0.161400	0.317900	0.092080	1.000000
max	28.110000	39.280000	188.500000	2501.000000	0.163400	0.345400	0.426800	0.201200	0.304000	0.097440	2.873000	4.885000	21.980000	542.200000	0.031130	...	0.396000	0.052790	0.078950	0.029840	36.040000	49.540000	251.200000	4254.000000	0.222600	1.058000	1.252000	0.291000	0.663800	0.207500	1.000000

8 rows × 31 columns

breast_cancer.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 569 entries, 0 to 568
Data columns (total 31 columns):
 #   Column                   Non-Null Count  Dtype  
---  ------                   --------------  -----  
 0   mean radius              569 non-null    float64
 1   mean texture             569 non-null    float64
 2   mean perimeter           569 non-null    float64
 3   mean area                569 non-null    float64
 4   mean smoothness          569 non-null    float64
 5   mean compactness         569 non-null    float64
 6   mean concavity           569 non-null    float64
 7   mean concave points      569 non-null    float64
 8   mean symmetry            569 non-null    float64
 9   mean fractal dimension   569 non-null    float64
 10  radius error             569 non-null    float64
 11  texture error            569 non-null    float64
 12  perimeter error          569 non-null    float64
 13  area error               569 non-null    float64
 14  smoothness error         569 non-null    float64
 15  compactness error        569 non-null    float64
 16  concavity error          569 non-null    float64
 17  concave points error     569 non-null    float64
 18  symmetry error           569 non-null    float64
 19  fractal dimension error  569 non-null    float64
 20  worst radius             569 non-null    float64
 21  worst texture            569 non-null    float64
 22  worst perimeter          569 non-null    float64
 23  worst area               569 non-null    float64
 24  worst smoothness         569 non-null    float64
 25  worst compactness        569 non-null    float64
 26  worst concavity          569 non-null    float64
 27  worst concave points     569 non-null    float64
 28  worst symmetry           569 non-null    float64
 29  worst fractal dimension  569 non-null    float64
 30  result                   569 non-null    int32  
dtypes: float64(30), int32(1)
memory usage: 135.7 KB

The dataset does not include any null or missing values so there won’t be any need for data wrangling (dealing with missing values).

X = breast_cancer.values
y = breast_cancer['result'].values

It is also possible to instantiate X and y without .values (.values changes the Dataframe to a numpy array)

For good training and testing the dataset, we should split our data. We are going to split our data into 70% training size and 30% test size. It’s more convenient to test our dataset with the small portion of the dataset, but it shouldn’t be too small.

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.7, random_state=1)

model = LogisticRegression(solver='liblinear')
model.fit(X_train, y_train)

LogisticRegression(solver='liblinear')

If we try to fit using the default solver, we get a convergence warning meaning the model needs more time to find the optimal solution, This can be solved by using a different solver. In this instance we shall use the ‘liblinear’ solver.

y_pred = model.predict(X_test)

from sklearn.metrics import accuracy_score, precision_score, recall_score, f1_score

# each function takes two 1-dimensional numpy arrays: the true values and the predicted values of the target
print("accuracy: ", accuracy_score(y_test, y_pred))
print("precision: ", precision_score(y_test, y_pred))
print("recall: ", recall_score(y_test, y_pred))
print("f1_score: ", f1_score(y_test, y_pred))

# using scikit-learn we are able to get the four values in the confusion matrix
from sklearn.metrics import confusion_matrix
print(confusion_matrix(y_test, y_pred))

accuracy:  0.9624060150375939
precision:  0.95703125
recall:  0.9839357429718876
f1_score:  0.9702970297029703
[[139  11]
 [  4 245]]

All of the metric calculations show good scores which means that our Logistic Regression model is good

        # USING ROC CURVE #

An ROC curve (receiver operating characteristic curve) is a graph showing the performance of a classification model at all classification thresholds. The ROC curve is a graph of the specificity vs sensitivity i.e specificity is the % actual negatives correctly predicted and sensitivity being the % actual positives correctly predicted.

y_pred_proba = model.predict_proba(X_test)
fpr, tpr, thresholds = roc_curve(y_test, y_pred_proba[:, 1])

plt.plot(fpr, tpr)
plt.plot([0, 1], [0, 1], linestyle='--')
# plt.xlim(0.0, 1.0)
# plt.ylim(0.0, 1.0)
plt.xlabel('1 - specificity')
plt.ylabel('sensitivity')

plt.show()