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Assignment 1 - Introduction to Machine Learning¶

For this assignment, you will be using the Breast Cancer Wisconsin (Diagnostic) Database to create a classifier that can help diagnose patients. First, read through the description of the dataset (below).

In [ ]:
import numpy as np
import pandas as pd
from sklearn.datasets import load_breast_cancer

cancer = load_breast_cancer()

print(cancer.DESCR) # Print the data set description

.. _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.

The object returned by load_breast_cancer() is a scikit-learn Bunch object, which is similar to a dictionary.

In [ ]:
cancer.keys()
Out[ ]:
dict_keys(['data', 'target', 'frame', 'target_names', 'DESCR', 'feature_names', 'filename', 'data_module'])

Question 0 (Example)¶

How many features does the breast cancer dataset have?

This function should return an integer.

In [ ]:
# You should write your whole answer within the function provided. The autograder will call
# this function and compare the return value against the correct solution value
def answer_zero():
    # This function returns the number of features of the breast cancer dataset, which is an integer. 
    # The assignment question description will tell you the general format the autograder is expecting
    return len(cancer['feature_names'])

# You can examine what your function returns by calling it in the cell. If you have questions
# about the assignment formats, check out the discussion forums for any FAQs
answer_zero()
Out[ ]:
30

Question 1¶

Scikit-learn works with lists, numpy arrays, scipy-sparse matrices, and pandas DataFrames, so converting the dataset to a DataFrame is not necessary for training this model. Using a DataFrame does however help make many things easier such as munging data, so let's practice creating a classifier with a pandas DataFrame.

Convert the sklearn.dataset cancer to a DataFrame.

This function should return a (569, 31) DataFrame with

columns = 

['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', 'compactness 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',
'target']

and index = 

RangeIndex(start=0, stop=569, step=1)
In [ ]:
def answer_one():
    cancer = load_breast_cancer()  
    # Your code here
    df = pd.DataFrame(cancer['data'], columns=cancer['feature_names'])
    df['target'] = cancer['target']
    return df  # Return your answer

answer_one()
Out[ ]:
mean radius mean texture mean perimeter mean area mean smoothness mean compactness mean concavity mean concave points mean symmetry mean fractal dimension ... worst texture worst perimeter worst area worst smoothness worst compactness worst concavity worst concave points worst symmetry worst fractal dimension target
0 17.99 10.38 122.80 1001.0 0.11840 0.27760 0.30010 0.14710 0.2419 0.07871 ... 17.33 184.60 2019.0 0.16220 0.66560 0.7119 0.2654 0.4601 0.11890 0
1 20.57 17.77 132.90 1326.0 0.08474 0.07864 0.08690 0.07017 0.1812 0.05667 ... 23.41 158.80 1956.0 0.12380 0.18660 0.2416 0.1860 0.2750 0.08902 0
2 19.69 21.25 130.00 1203.0 0.10960 0.15990 0.19740 0.12790 0.2069 0.05999 ... 25.53 152.50 1709.0 0.14440 0.42450 0.4504 0.2430 0.3613 0.08758 0
3 11.42 20.38 77.58 386.1 0.14250 0.28390 0.24140 0.10520 0.2597 0.09744 ... 26.50 98.87 567.7 0.20980 0.86630 0.6869 0.2575 0.6638 0.17300 0
4 20.29 14.34 135.10 1297.0 0.10030 0.13280 0.19800 0.10430 0.1809 0.05883 ... 16.67 152.20 1575.0 0.13740 0.20500 0.4000 0.1625 0.2364 0.07678 0
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
564 21.56 22.39 142.00 1479.0 0.11100 0.11590 0.24390 0.13890 0.1726 0.05623 ... 26.40 166.10 2027.0 0.14100 0.21130 0.4107 0.2216 0.2060 0.07115 0
565 20.13 28.25 131.20 1261.0 0.09780 0.10340 0.14400 0.09791 0.1752 0.05533 ... 38.25 155.00 1731.0 0.11660 0.19220 0.3215 0.1628 0.2572 0.06637 0
566 16.60 28.08 108.30 858.1 0.08455 0.10230 0.09251 0.05302 0.1590 0.05648 ... 34.12 126.70 1124.0 0.11390 0.30940 0.3403 0.1418 0.2218 0.07820 0
567 20.60 29.33 140.10 1265.0 0.11780 0.27700 0.35140 0.15200 0.2397 0.07016 ... 39.42 184.60 1821.0 0.16500 0.86810 0.9387 0.2650 0.4087 0.12400 0
568 7.76 24.54 47.92 181.0 0.05263 0.04362 0.00000 0.00000 0.1587 0.05884 ... 30.37 59.16 268.6 0.08996 0.06444 0.0000 0.0000 0.2871 0.07039 1

569 rows × 31 columns

Question 2¶

What is the class distribution? (i.e. how many instances of malignant (encoded 0) and how many benign (encoded 1)?)

This function should return a Series named target of length 2 with integer values and index = ['malignant', 'benign']

In [ ]:
def answer_two():
    cancerdf = answer_one()
    counts = cancerdf.target.value_counts(ascending=True)
    counts.index = "malignant benign".split()
    return counts

answer_two()
Out[ ]:
malignant    212
benign       357
Name: target, dtype: int64

Question 3¶

Split the DataFrame into X (the data) and y (the labels).

This function should return a tuple of length 2: (X, y), where

  • X, a pandas DataFrame, has shape (569, 30)
  • y, a pandas Series, has shape (569,).
In [ ]:
cancerdf = answer_one()
# Your code here
X = list(cancerdf.drop('target',axis=1).itertuples(index=False,name=None))
#X = list(X.itertuples(index=False,name=None))
y = list(zip(cancerdf['target'],cancerdf['target'].index))
In [ ]:
def answer_three():
    cancerdf = answer_one()
    X = cancerdf[cancerdf.columns[:-1]]
    y = cancerdf.target
    return X, y

Question 4¶

Using train_test_split, split X and y into training and test sets (X_train, X_test, y_train, and y_test).

Set the random number generator state to 0 using random_state=0 to make sure your results match the autograder!

This function should return a tuple of length 4: (X_train, X_test, y_train, y_test), where

  • X_train has shape (426, 30)
  • X_test has shape (143, 30)
  • y_train has shape (426,)
  • y_test has shape (143,)
In [ ]:
from sklearn.model_selection import train_test_split

def answer_four():
    X, y = answer_three()
    
    # Your code here
    X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=426, test_size=143, random_state=0)
    return X_train, X_test, y_train, y_test

Question 5¶

Using KNeighborsClassifier, fit a k-nearest neighbors (knn) classifier with X_train, y_train and using one nearest neighbor (n_neighbors = 1).

This function should return a sklearn.neighbors.classification.KNeighborsClassifier.

In [ ]:
from sklearn.neighbors import KNeighborsClassifier

def answer_five():
    X_train, X_test, y_train, y_test = answer_four()
    
    # Your code here
    knn = KNeighborsClassifier(n_neighbors = 1)
    knn.fit(X_train, y_train)
    return knn# Return your answer

Question 6¶

Using your knn classifier, predict the class label using the mean value for each feature.

Hint: You can use cancerdf.mean()[:-1].values.reshape(1, -1) which gets the mean value for each feature, ignores the target column, and reshapes the data from 1 dimension to 2 (necessary for the precict method of KNeighborsClassifier).

This function should return a numpy array either array([ 0.]) or array([ 1.])

In [ ]:
def answer_six():
    cancerdf = answer_one()
    means = cancerdf.mean()[:-1].values.reshape(1, -1)
    knn = answer_five()
    
    return knn.predict(means)# Return your answer

Question 7¶

Using your knn classifier, predict the class labels for the test set X_test.

This function should return a numpy array with shape (143,) and values either 0.0 or 1.0.

In [ ]:
def answer_seven():
    X_train, X_test, y_train, y_test = answer_four()
    knn = answer_five()
    
    # Your code here
    test_predictions = knn.predict(X_test)
    return test_predictions # Return your answer

Question 8¶

Find the score (mean accuracy) of your knn classifier using X_test and y_test.

This function should return a float between 0 and 1

In [ ]:
def answer_eight():
    X_train, X_test, y_train, y_test = answer_four()
    knn = answer_five()
    
    # Your code here
    
    return knn.score(X_test,y_test)# Return your answer

Optional plot¶

Try using the plotting function below to visualize the differet predicition scores between training and test sets, as well as malignant and benign cells.

In [ ]:
def accuracy_plot():
    import matplotlib.pyplot as plt

    %matplotlib widget

    X_train, X_test, y_train, y_test = answer_four()

    # Find the training and testing accuracies by target value (i.e. malignant, benign)
    mal_train_X = X_train[y_train==0]
    mal_train_y = y_train[y_train==0]
    ben_train_X = X_train[y_train==1]
    ben_train_y = y_train[y_train==1]

    mal_test_X = X_test[y_test==0]
    mal_test_y = y_test[y_test==0]
    ben_test_X = X_test[y_test==1]
    ben_test_y = y_test[y_test==1]

    knn = answer_five()

    scores = [knn.score(mal_train_X, mal_train_y), knn.score(ben_train_X, ben_train_y), 
              knn.score(mal_test_X, mal_test_y), knn.score(ben_test_X, ben_test_y)]


    plt.figure()

    # Plot the scores as a bar chart
    bars = plt.bar(np.arange(4), scores, color=['#4c72b0','#4c72b0','#55a868','#55a868'])

    # directly label the score onto the bars
    for bar in bars:
        height = bar.get_height()
        plt.gca().text(bar.get_x() + bar.get_width()/2, height*.90, '{0:.{1}f}'.format(height, 2), 
                     ha='center', color='w', fontsize=11)

    # remove all the ticks (both axes), and tick labels on the Y axis
    plt.tick_params(top='off', bottom='off', left='off', right='off', labelleft='off', labelbottom='on')

    # remove the frame of the chart
    for spine in plt.gca().spines.values():
        spine.set_visible(False)

    plt.xticks([0,1,2,3], ['Malignant\nTraining', 'Benign\nTraining', 'Malignant\nTest', 'Benign\nTest'], alpha=0.8);
    plt.title('Training and Test Accuracies for Malignant and Benign Cells', alpha=0.8)

Uncomment the plotting function to see the visualization.

Comment out the plotting function when submitting your notebook for grading.

In [ ]:
accuracy_plot()
Figure