In this notebook, you will use SVM (Support Vector Machines) to build and train a model using human cell records, and classify cells to whether the samples are benign or malignant.
SVM works by mapping data to a high-dimensional feature space so that data points can be categorized, even when the data are not otherwise linearly separable. A separator between the categories is found, then the data is transformed in such a way that the separator could be drawn as a hyperplane. Following this, characteristics of new data can be used to predict the group to which a new record should belong.
import pandas as pd import pylab as pl import numpy as np import scipy.optimize as opt from sklearn import preprocessing from sklearn.model_selection import train_test_split %matplotlib inline import matplotlib.pyplot as plt
|UnifSize||Uniformity of cell size|
|UnifShape||Uniformity of cell shape|
|SingEpiSize||Single epithelial cell size|
|Class||Benign or malignant|
For the purposes of this example, we're using a dataset that has a relatively small number of predictors in each record. To download the data, we will use
!wget to download it from IBM Object Storage.
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#Click here and press Shift+Enter !wget -O cell_samples.csv https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/cell_samples.csv
--2019-04-15 14:35:56-- https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/cell_samples.csv Resolving s3-api.us-geo.objectstorage.softlayer.net (s3-api.us-geo.objectstorage.softlayer.net)... 126.96.36.199 Connecting to s3-api.us-geo.objectstorage.softlayer.net (s3-api.us-geo.objectstorage.softlayer.net)|188.8.131.52|:443... connected. HTTP request sent, awaiting response... 200 OK Length: 20675 (20K) [text/csv] Saving to: ‘cell_samples.csv’ cell_samples.csv 100%[=====================>] 20.19K --.-KB/s in 0.02s 2019-04-15 14:35:56 (844 KB/s) - ‘cell_samples.csv’ saved [20675/20675]
cell_df = pd.read_csv("cell_samples.csv") cell_df.head()
The ID field contains the patient identifiers. The characteristics of the cell samples from each patient are contained in fields Clump to Mit. The values are graded from 1 to 10, with 1 being the closest to benign.
The Class field contains the diagnosis, as confirmed by separate medical procedures, as to whether the samples are benign (value = 2) or malignant (value = 4).
Lets look at the distribution of the classes based on Clump thickness and Uniformity of cell size:
ax = cell_df[cell_df['Class'] == 4][0:50].plot(kind='scatter', x='Clump', y='UnifSize', color='DarkBlue', label='malignant'); cell_df[cell_df['Class'] == 2][0:50].plot(kind='scatter', x='Clump', y='UnifSize', color='Yellow', label='benign', ax=ax); plt.show()
Lets first look at columns data types:
ID int64 Clump int64 UnifSize int64 UnifShape int64 MargAdh int64 SingEpiSize int64 BareNuc object BlandChrom int64 NormNucl int64 Mit int64 Class int64 dtype: object
It looks like the BareNuc column includes some values that are not numerical. We can drop those rows:
cell_df = cell_df[pd.to_numeric(cell_df['BareNuc'], errors='coerce').notnull()] cell_df['BareNuc'] = cell_df['BareNuc'].astype('int') cell_df.dtypes
ID int64 Clump int64 UnifSize int64 UnifShape int64 MargAdh int64 SingEpiSize int64 BareNuc int64 BlandChrom int64 NormNucl int64 Mit int64 Class int64 dtype: object
feature_df = cell_df[['Clump', 'UnifSize', 'UnifShape', 'MargAdh', 'SingEpiSize', 'BareNuc', 'BlandChrom', 'NormNucl', 'Mit']] X = np.asarray(feature_df) X[0:5]
array([[ 5, 1, 1, 1, 2, 1, 3, 1, 1], [ 5, 4, 4, 5, 7, 10, 3, 2, 1], [ 3, 1, 1, 1, 2, 2, 3, 1, 1], [ 6, 8, 8, 1, 3, 4, 3, 7, 1], [ 4, 1, 1, 3, 2, 1, 3, 1, 1]])
We want the model to predict the value of Class (that is, benign (=2) or malignant (=4)). As this field can have one of only two possible values, we need to change its measurement level to reflect this.
cell_df['Class'] = cell_df['Class'].astype('int') y = np.asarray(cell_df['Class']) y [0:5]
array([2, 2, 2, 2, 2])
Okay, we split our dataset into train and test set:
X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.2, random_state=4) print ('Train set:', X_train.shape, y_train.shape) print ('Test set:', X_test.shape, y_test.shape)
Train set: (546, 9) (546,) Test set: (137, 9) (137,)
The SVM algorithm offers a choice of kernel functions for performing its processing. Basically, mapping data into a higher dimensional space is called kernelling. The mathematical function used for the transformation is known as the kernel function, and can be of different types, such as:
1.Linear 2.Polynomial 3.Radial basis function (RBF) 4.Sigmoid
Each of these functions has its characteristics, its pros and cons, and its equation, but as there's no easy way of knowing which function performs best with any given dataset, we usually choose different functions in turn and compare the results. Let's just use the default, RBF (Radial Basis Function) for this lab.
from sklearn import svm clf = svm.SVC(kernel='rbf') clf.fit(X_train, y_train)
/home/jupyterlab/conda/lib/python3.6/site-packages/sklearn/svm/base.py:196: FutureWarning: The default value of gamma will change from 'auto' to 'scale' in version 0.22 to account better for unscaled features. Set gamma explicitly to 'auto' or 'scale' to avoid this warning. "avoid this warning.", FutureWarning)
SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0, decision_function_shape='ovr', degree=3, gamma='auto_deprecated', kernel='rbf', max_iter=-1, probability=False, random_state=None, shrinking=True, tol=0.001, verbose=False)
After being fitted, the model can then be used to predict new values:
yhat = clf.predict(X_test) yhat [0:5]
array([2, 4, 2, 4, 2])
from sklearn.metrics import classification_report, confusion_matrix import itertools
def plot_confusion_matrix(cm, classes, normalize=False, title='Confusion matrix', cmap=plt.cm.Blues): """ This function prints and plots the confusion matrix. Normalization can be applied by setting `normalize=True`. """ if normalize: cm = cm.astype('float') / cm.sum(axis=1)[:, np.newaxis] print("Normalized confusion matrix") else: print('Confusion matrix, without normalization') print(cm) plt.imshow(cm, interpolation='nearest', cmap=cmap) plt.title(title) plt.colorbar() tick_marks = np.arange(len(classes)) plt.xticks(tick_marks, classes, rotation=45) plt.yticks(tick_marks, classes) fmt = '.2f' if normalize else 'd' thresh = cm.max() / 2. for i, j in itertools.product(range(cm.shape), range(cm.shape)): plt.text(j, i, format(cm[i, j], fmt), horizontalalignment="center", color="white" if cm[i, j] > thresh else "black") plt.tight_layout() plt.ylabel('True label') plt.xlabel('Predicted label')
# Compute confusion matrix cnf_matrix = confusion_matrix(y_test, yhat, labels=[2,4]) np.set_printoptions(precision=2) print (classification_report(y_test, yhat)) # Plot non-normalized confusion matrix plt.figure() plot_confusion_matrix(cnf_matrix, classes=['Benign(2)','Malignant(4)'],normalize= False, title='Confusion matrix')
precision recall f1-score support 2 1.00 0.94 0.97 90 4 0.90 1.00 0.95 47 micro avg 0.96 0.96 0.96 137 macro avg 0.95 0.97 0.96 137 weighted avg 0.97 0.96 0.96 137 Confusion matrix, without normalization [[85 5] [ 0 47]]
You can also easily use the f1_score from sklearn library:
from sklearn.metrics import f1_score f1_score(y_test, yhat, average='weighted')
Lets try jaccard index for accuracy:
from sklearn.metrics import jaccard_similarity_score jaccard_similarity_score(y_test, yhat)
# write your code here clf2 = svm.SVC(kernel='linear') clf2.fit(X_train, y_train) yhat2 = clf2.predict(X_test) print("Avg F1-score: %.4f" % f1_score(y_test, yhat2, average='weighted')) print("Jaccard score: %.4f" % jaccard_similarity_score(y_test, yhat2))
Avg F1-score: 0.9639 Jaccard score: 0.9635
Double-click here for the solution.
IBM SPSS Modeler is a comprehensive analytics platform that has many machine learning algorithms. It has been designed to bring predictive intelligence to decisions made by individuals, by groups, by systems – by your enterprise as a whole. A free trial is available through this course, available here: SPSS Modeler
Also, you can use Watson Studio to run these notebooks faster with bigger datasets. Watson Studio is IBM's leading cloud solution for data scientists, built by data scientists. With Jupyter notebooks, RStudio, Apache Spark and popular libraries pre-packaged in the cloud, Watson Studio enables data scientists to collaborate on their projects without having to install anything. Join the fast-growing community of Watson Studio users today with a free account at Watson Studio
Saeed Aghabozorgi, PhD is a Data Scientist in IBM with a track record of developing enterprise level applications that substantially increases clients’ ability to turn data into actionable knowledge. He is a researcher in data mining field and expert in developing advanced analytic methods like machine learning and statistical modelling on large datasets.