Basic Steps to k-NN Classification

18 Jan 2020

Import libraries
Load the dataset(s)
Split into data ( $X$ ) and labels ( $y$ )
Split into training ( $X_{t r a i n}$ , $y_{t r a i n}$ ) and test ( $X_{t e s t}$ , $y_{t e s t}$ ) data
Fit the classifier
Calculate the accuracy of the classifier using $y_{t e s t}$
Use the fitted classifier for prediction

Optionally, visualize the accuracy of the classifier on the various types of data:

Positive training
Negative training
Positive testing
Negative testing

1. Import libraries

import numpy as np
import pandas as pd
import matplotlib as mpl
import sklearn

import matplotlib.pyplot as plt

from sklearn.datasets import load_breast_cancer
from sklearn.model_selection import train_test_split
from sklearn.neighbors import KNeighborsClassifier
from sklearn.metrics import accuracy_score

print('     Numpy version ' + str(np.__version__))
print('    Pandas version ' + str(pd.__version__))
print('Matplotlib version ' + str(mpl.__version__))
print('   Sklearn version ' + str(sklearn.__version__))

%matplotlib notebook

     Numpy version 1.17.4
    Pandas version 0.25.3
Matplotlib version 3.1.1
   Sklearn version 0.22.1

2. Load the Dataset

First, load the dataset from scikit-learn. It is a scikit-learn “Bunch” object, which is similar to a dictionary.

Information about the dataset included at the bottom of this notebook.

cancer = load_breast_cancer()
print(type(cancer))
print(cancer.keys())

<class 'sklearn.utils.Bunch'>
dict_keys(['data', 'target', 'target_names', 'DESCR', 'feature_names', 'filename'])

Convert the Bunch object to a Pandas DataFrame.

d = pd.DataFrame(cancer['data'],
                 columns = cancer['feature_names'])
d['target'] = cancer['target']

target_mapping = {
    0 : 'malignant',
    1 : 'benign'
}
(d['target']
 .replace(target_mapping)
 .value_counts())

benign       357
malignant    212
Name: target, dtype: int64

3. Split into the data, $X$ , and labels, $y$

X = d[d.columns[:-1]].copy()
y = d['target'].copy()
print(X.shape, y.shape)

(569, 30) (569,)

4. Split into Training and Testing datasets

X_train, X_test, y_train, y_test = train_test_split(X, y,
                                                    random_state=0)
print(X_train.shape, X_test.shape, y_train.shape, y_test.shape)

(426, 30) (143, 30) (426,) (143,)

5. Fit a K-Nearest Neighbors (KNN) Classifier

knn = KNeighborsClassifier(n_neighbors = 1)
knn.fit(X_train, y_train);
print(knn)

KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',
                     metric_params=None, n_jobs=None, n_neighbors=1, p=2,
                     weights='uniform')

6. Calculate the accuracy of the classifier using $y_{t e s t}$

The knn can also predict across the entire $X_{t e s t}$ set. $y_{p r e d}$ will contain the predicted output of the classifier when run on the test set. accuracy_score compares the prediction against the correct classification and returns a percent accuracy.

y_pred = knn.predict(X_test)
accuracy = accuracy_score(y_test, y_pred)
print("{:2.1f}%"
      .format(accuracy*100.)
     )

91.6%

7. Use the fitted classifier for prediction

As a test, predict the class label using the mean value for each value in the dataset.

The values attribute of a Pandas Series is the raw values it contains in a 1D numpy array.
The numpy reshape method converts the 1D array into a an array containing the 1D array (an array of 1D arrays). The -1 parameter means infer the length from the length of the array.
The classifier returns a 1x1 array that is accessible using the usual Python list accessor.

First, predict using the mean values across all fields in the dataset.

means = d.mean()[:-1].values.reshape(1, -1)
print(means)
pred = knn.predict(means)
target_mapping[pred[0]]

[[1.41272917e+01 1.92896485e+01 9.19690334e+01 6.54889104e+02
  9.63602812e-02 1.04340984e-01 8.87993158e-02 4.89191459e-02
  1.81161863e-01 6.27976098e-02 4.05172056e-01 1.21685343e+00
  2.86605923e+00 4.03370791e+01 7.04097891e-03 2.54781388e-02
  3.18937163e-02 1.17961371e-02 2.05422988e-02 3.79490387e-03
  1.62691898e+01 2.56772232e+01 1.07261213e+02 8.80583128e+02
  1.32368594e-01 2.54265044e-01 2.72188483e-01 1.14606223e-01
  2.90075571e-01 8.39458172e-02]]





'benign'

Optionally, visualize the accuracy using the plot below or something similar

def accuracy_plot():
    # 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]

    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()

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

    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)

    plt.tick_params(top=False, 
                    bottom=False, 
                    left=False, 
                    right=False, 
                    labelleft=False, 
                    labelbottom=True)

    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)

accuracy_plot()

<IPython.core.display.Javascript object>

The following data about the raw data used in this note.

d.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 569 entries, 0 to 568
Data columns (total 31 columns):
mean radius                569 non-null float64
mean texture               569 non-null float64
mean perimeter             569 non-null float64
mean area                  569 non-null float64
mean smoothness            569 non-null float64
mean compactness           569 non-null float64
mean concavity             569 non-null float64
mean concave points        569 non-null float64
mean symmetry              569 non-null float64
mean fractal dimension     569 non-null float64
radius error               569 non-null float64
texture error              569 non-null float64
perimeter error            569 non-null float64
area error                 569 non-null float64
smoothness error           569 non-null float64
compactness error          569 non-null float64
concavity error            569 non-null float64
concave points error       569 non-null float64
symmetry error             569 non-null float64
fractal dimension error    569 non-null float64
worst radius               569 non-null float64
worst texture              569 non-null float64
worst perimeter            569 non-null float64
worst area                 569 non-null float64
worst smoothness           569 non-null float64
worst compactness          569 non-null float64
worst concavity            569 non-null float64
worst concave points       569 non-null float64
worst symmetry             569 non-null float64
worst fractal dimension    569 non-null float64
target                     569 non-null int64
dtypes: float64(30), int64(1)
memory usage: 137.9 KB

The following text contains the description of the dataset used above. It is included with sklearn.

print(cancer.DESCR)

.. _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
        largest values) of these features were computed for each image,
        resulting in 30 features.  For instance, field 3 is Mean Radius, field
        13 is Radius SE, field 23 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.

These notes were taken from the Coursera course Applied Machine Learning in Python. The information is presented by Kevyn Collins-Thompson, PhD, an associate professor of Information and Computer Science at the University of Michigan.