Classification using scikit-learn¶
The goal of this tutorial is to introduce you to the scikit libraries for classification. We will also cover the topic of feature normalization, and evaluation.
import numpy as np
import scipy.sparse as sp_sparse
import matplotlib.pyplot as plt
import sklearn as sk
import sklearn.datasets as sk_data
import sklearn.metrics as metrics
from sklearn import preprocessing
import seaborn as sns
%matplotlib inline
Feature normalization¶
Python provides some functionality for normalizing and standardizing the data. Be careful though, some operations work only with dense data.
http://scikit-learn.org/stable/modules/preprocessing.html#preprocessing
Use the function preprocessing.scale to normalize by removing the mean and dividing by the standard deviation. This is done per feature, that is, per column of the dataset.
X = np.array([[ 1., -1., 2.],
[ 2., 0., 1.],
[ 0., 1., -1.]])
print("column means: ",X.mean(axis = 0))
print("column std: ",X.std(axis = 0))
X_scaled = preprocessing.scale(X)
print("after feature normalization")
print(X_scaled)
print("normalized column means: ",X_scaled.mean(axis=0))
print("normalized column std: ",X_scaled.var(axis = 0))
Feature normalization will not work with sparse data. In this case, the zeros are treated as values, so the sparse matrix will become non-sparse after normalization.
import scipy.sparse
cX = scipy.sparse.csc_matrix(X)
cX_scaled = preprocessing.scale(cX)
print(cX_scaled)
The same can be done with the StandardScaler from the preprocessing library of sklearn.
The function fit() computes the parameters for scaling, and transform() applies the scaling
from sklearn import preprocessing
std_scaler = preprocessing.StandardScaler()
std_scaler.fit(X)
print(std_scaler.mean_)
print(std_scaler.scale_)
X_std = std_scaler.transform(X)
print("scaled data:")
print(X_std)
The advantage is the we can now apply the transform to new data.
For example, we compute the parameters for the training data and we apply the scaling to the test data.
y = np.array([[2.,3.,1.],
[1.,2.,1.]])
print(std_scaler.transform(y))
The MinMaxScaler subbtracts from each column the minimum and then divides by the max-min.
min_max_scaler = preprocessing.MinMaxScaler()
X_minmax = min_max_scaler.fit_transform(X)
print(X_minmax)
print(min_max_scaler.transform(y))
The MaxAbsScaler divides with the maximum absolute value.
The MaxAbsScaler can work with sparse data, since it does not destroy the data sparseness. For the other datasets, removing the mean (or min) can destroy the sparseness of the data.
Sometimes we may choose to normalize only the non-zero values. This should be done manually.
max_abs_scaler = preprocessing.MaxAbsScaler()
X_maxabs = max_abs_scaler.fit_transform(X)
X_maxabs
# works with sparse data
cX_scaled = max_abs_scaler.transform(cX)
print(cX_scaled)
The normalize function normalizes the rows so that they become unit vectors in some norm that we specify. It can be applied to sparse matrices without destroying the sparsity.
#works with sparse data
X_normalized = preprocessing.normalize(X, norm='l2')
X_normalized
crX = scipy.sparse.csr_matrix(X)
crX_scaled = preprocessing.normalize(crX,norm='l1')
print(crX_scaled)
OneHotEncoder¶
The OneHotEncoder can be used for categorical data to transform them into binary, where for each attribute value we have 0 or 1 depending on whether this value appears in the feature vector. It works with numerical categorical values.
X = [[0,1,2],
[1,2,3],
[0,1,4]]
enc = preprocessing.OneHotEncoder(handle_unknown='ignore')
enc.fit(X)
enc.transform([[0,2,4],[1,1,2]]).toarray()
In this example every number in every column defines a separate feature
enc.categories_
We can also apply it selectively to some columns of the data
#works with sparse data
X = np.array([[0, 10, 45100],
[1, 20, 45221],
[0, 20, 45212]])
enc = preprocessing.OneHotEncoder(categorical_features=[2]) #only the third column is categorical
enc.fit(X)
enc.transform([[5,13,45212],[4,12,45221]]).toarray()
Feature Selection¶
Feature selection is about finding the best features for your classifier. This may be important if you do not have enough training data. The idea is to find metrics that either characterize the features by themselves, or with respect to the class we want to predict, or with respect to other features.
http://scikit-learn.org/stable/modules/feature_selection.html
The VarianceThreshold selection drops features whose variance is below some threshold. If we have binary features we can estimate the treshold exactly so as to guarantee a specific ratio of 0's and 1's
from sklearn.feature_selection import VarianceThreshold
X = [[0, 0, 1], [0, 1, 0], [1, 0, 0], [0, 1, 1], [0, 1, 0], [0, 1, 1]]
print(np.array(X))
sel = VarianceThreshold(threshold=(.8 * (1 - .8)))
sel.fit_transform(X)
A more sophisticated feature selection technique uses the chi-square test to determine if a feature and the class label are independent.
https://en.wikipedia.org/wiki/Chi-squared_test
In this case we keep the features with high chi-score and low p-value.
The features with the lowest scores and highest values are rejected.
The chi-square test is usually applied on categorical data.
from sklearn.datasets import load_iris
from sklearn.feature_selection import SelectKBest
from sklearn.feature_selection import chi2
iris = load_iris()
X, y = iris.data, iris.target
print(X.shape)
print('Features:')
print(X[1:10,:])
print('Labels:')
print(y[1:10])
sel = SelectKBest(chi2, k=2)
X_new = sel.fit_transform(X, y)
print('Selected Features:')
print(X_new[1:10])
print('Chi2 values')
print(sel.scores_)
c,p = sk.feature_selection.chi2(X, y)
print('Chi2 values')
print(c) #The chi-square value between X columns and y
print('p-values')
print(p) #The p-value for the test
Supervised Learning¶
Python has several classes and objects for implementing different supervised learning techniques such as Regression and Classification.
Regardless of the model being implemented, the following methods are implemented:
The method fit() takes the training data and labels/values, and trains the model
The method predict() takes as input the test data and applies the model.
Linear Regression¶
Linear Regression is implemented in the library sklearn.linear_model.LinearRegression: https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html
from sklearn.linear_model import LinearRegression
X = np.array([[1, 1], [1, 2], [2, 2], [2, 3]])
# y = 1 * x_0 + 2 * x_1 + 3
y = np.dot(X, np.array([1, 2])) + 3
reg = LinearRegression().fit(X, y)
reg.score(X, y)
#Obtain the function coefficients
print(reg.coef_)
#and the intercept
print(reg.intercept_)
#Predict for a new point
reg.predict(np.array([[3, 5]]))
Classification models¶
http://scikit-learn.org/stable/supervised_learning.html#supervised-learning
Python has classes and objects that implement the different classification techniques that we described in class.
Preparing the data¶
Load the iris dataset
from sklearn.datasets import load_iris
import sklearn.utils as utils
iris = load_iris()
print("sample of data")
print(iris.data[:5,:])
print("the class labels vector")
print(iris.target)
print("the names of the classes:",iris.target_names)
print(iris.feature_names)
Randomly shuffle the data. This is useful to know that the data is in random order
X, y = utils.shuffle(iris.data, iris.target, random_state=1) #shuffle the data
print(X.shape)
print(y.shape)
print(y)
Select a subset for training and a subset for testing
train_set_size = 100
X_train = X[:train_set_size] # selects first 100 rows (examples) for train set
y_train = y[:train_set_size]
X_test = X[train_set_size:] # selects from row 100 until the last one for test set
y_test = y[train_set_size:]
print(X_train.shape, y_train.shape)
print(X_test.shape, y_test.shape)
We can also use the train_test_split function of python for splitting the data into train and test sets. In this case you do not need the random shuffling (but it does not hurt).
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=0)
Decision Trees¶
http://scikit-learn.org/stable/modules/tree.html
Train and apply a decision tree classifier. The default score computed in the classifier object is the accuracy.
from sklearn import tree
dtree = tree.DecisionTreeClassifier()
dtree = dtree.fit(X_train, y_train)
print("classifier accuracy:",dtree.score(X_test,y_test))
y_pred = dtree.predict(X_test)
y_prob = dtree.predict_proba(X_test)
print("classifier predictions:",y_pred[:10])
print("ground truth labels :",y_test[:10])
print(y_prob[:10])
Compute some more metrics
print("accuracy:",metrics.accuracy_score(y_test,y_pred))
print("\nConfusion matrix")
print(metrics.confusion_matrix(y_test,y_pred))
print("\nPrecision Score per class")
print(metrics.precision_score(y_test,y_pred,average=None))
print("\nAverage Precision Score")
print(metrics.precision_score(y_test,y_pred,average='weighted'))
print("\nRecall Score per class")
print(metrics.recall_score(y_test,y_pred,average=None))
print("\nAverage Recall Score")
print(metrics.recall_score(y_test,y_pred,average='weighted'))
print("\nF1-score Score per class")
print(metrics.f1_score(y_test,y_pred,average=None))
print("\nAverage F1 Score")
print(metrics.f1_score(y_test,y_pred,average='weighted'))
Visualize the decision tree.
For this you will need to install the package python-graphviz
#conda install python-graphviz
import graphviz
print(iris.feature_names)
dot_data = tree.export_graphviz(dtree,out_file=None)
graph = graphviz.Source(dot_data)
graph
dtree2 = tree.DecisionTreeClassifier(max_depth=2)
dtree2 = dtree2.fit(X_train, y_train)
print(dtree2.score(X_test,y_test))
dot_data2 = tree.export_graphviz(dtree2,out_file=None)
graph2 = graphviz.Source(dot_data2)
graph2
k-NN Classification¶
from sklearn.neighbors import KNeighborsClassifier
knn = KNeighborsClassifier(n_neighbors=3)
knn.fit(X_train,y_train)
print("classifier score:", knn.score(X_test,y_test))
y_pred = knn.predict(X_test)
print("\naccuracy:",metrics.accuracy_score(y_test,y_pred))
print("\nConfusion matrix")
print(metrics.confusion_matrix(y_test,y_pred))
print("\nPrecision Score per class")
print(metrics.precision_score(y_test,y_pred,average=None))
print("\nAverage Precision Score")
print(metrics.precision_score(y_test,y_pred,average='weighted'))
print("\nRecall Score per class")
print(metrics.recall_score(y_test,y_pred,average=None))
print("\nAverage Recall Score")
print(metrics.recall_score(y_test,y_pred,average='weighted'))
print("\nF1-score Score per class")
print(metrics.f1_score(y_test,y_pred,average=None))
print("\nAverage F1 Score")
print(metrics.f1_score(y_test,y_pred,average='weighted'))
from sklearn import svm
#svm_clf = svm.LinearSVC()
#svm_clf = svm.SVC(kernel = 'poly')
svm_clf = svm.SVC()
svm_clf.fit(X_train,y_train)
print("classifier score:",svm_clf.score(X_test,y_test))
y_pred = svm_clf.predict(X_test)
print("\naccuracy:",metrics.accuracy_score(y_test,y_pred))
print("\nConfusion matrix")
print(metrics.confusion_matrix(y_test,y_pred))
print("\nPrecision Score per class")
print(metrics.precision_score(y_test,y_pred,average=None))
print("\nAverage Precision Score")
print(metrics.precision_score(y_test,y_pred,average='weighted'))
print("\nRecall Score per class")
print(metrics.recall_score(y_test,y_pred,average=None))
print("\nAverage Recall Score")
print(metrics.recall_score(y_test,y_pred,average='weighted'))
print("\nF1-score Score per class")
print(metrics.f1_score(y_test,y_pred,average=None))
print("\nAverage F1 Score")
print(metrics.f1_score(y_test,y_pred,average='weighted'))
import sklearn.linear_model as linear_model
lr_clf = linear_model.LogisticRegression()
lr_clf.fit(X_train, y_train)
print("classifier score:",lr_clf.score(X_test,y_test))
y_pred = lr_clf.predict(X_test)
print("\naccuracy:",metrics.accuracy_score(y_test,y_pred))
print("\nConfusion matrix")
print(metrics.confusion_matrix(y_test,y_pred))
print("\nPrecision Score per class")
print(metrics.precision_score(y_test,y_pred,average=None))
print("\nAverage Precision Score")
print(metrics.precision_score(y_test,y_pred,average='weighted'))
print("\nRecall Score per class")
print(metrics.recall_score(y_test,y_pred,average=None))
print("\nAverage Recall Score")
print(metrics.recall_score(y_test,y_pred,average='weighted'))
print("\nF1-score Score per class")
print(metrics.f1_score(y_test,y_pred,average=None))
print("\nAverage F1 Score")
print(metrics.f1_score(y_test,y_pred,average='weighted'))
For Logistic Regression we can also obtain the probabilities for the different classes
probs = lr_clf.predict_proba(X_test)
print("Class Probabilities (first 10):")
print (probs[:10])
print(probs.argmax(axis = 1)[:10])
print(probs.max(axis = 1)[:10])
print(lr_clf.coef_)
Computing Scores¶
p,r,f,s = metrics.precision_recall_fscore_support(y_test,y_pred)
print(p)
print(r)
print(f)
report = metrics.classification_report(y_test,y_pred)
print(report)
#y_true = np.array([0, 0, 1, 1])
y_true = np.array(y_test)
print(y_true)
print(y_test)
y_true[y_true != 2] = 0
y_true[y_true==2] = 1
#y_scores = np.array([0.1, 0.4, 0.35, 0.8])
y_scores = probs[:,2]
precision, recall, thresholds = metrics.precision_recall_curve(y_true,y_scores)
plt.scatter(recall,precision)
print(recall)
print(precision)
print(thresholds)
fpr, tpr, ths = metrics.roc_curve(y_true,y_scores)
print(metrics.roc_auc_score(y_true,y_scores))
(Xtoy,y_toy)=sk_data.make_classification(n_samples=1000)
Xttrain = Xtoy[:800,:]
Xttest = Xtoy[800:,:]
yttrain = y_toy[:800]
yttest = y_toy[800:]
lr_clf.fit(Xttrain, yttrain)
#print(lr_clf.score(Xttest,yttest))
#y_tpred = lr_clf.predict(X_test)
tprobs = lr_clf.predict_proba(Xttest)
print (tprobs)
y_tscores = tprobs[:,1]
precision, recall, thresholds = metrics.precision_recall_curve(yttest,y_tscores)
plt.scatter(recall,precision)
k-fold cross validation¶
In k-fold cross validation the data is split into k equal parts, the k-1 are used for training and the last one for testing. k models are trained, each time leaving a different part for testing
https://scikit-learn.org/stable/modules/cross_validation.html
There are two methods for implementing k-fold cross-validation, under the library model selection: cross_val_score, and cross validate. The latter allows multiple metrics to be considered together.
import sklearn.model_selection as model_selection
scores = model_selection.cross_val_score(#lr_clf,
#svm_clf,
#knn,
dtree,
X,
y,
scoring='f1_weighted',
cv=5)
print (scores)
print (scores.mean())
scores = model_selection.cross_validate(#lr_clf,
#svm_clf,
#knn,
dtree,
X,
y,
scoring=['precision_weighted','recall_weighted'],
cv=3)
print (scores)
print (scores['test_precision_weighted'].mean(),scores['test_recall_weighted'].mean())