This notebook was originally put together by [Jake Vanderplas](http://www.vanderplas.com) for PyCon 2014. [Peter Prettenhofer](https://github.com/pprett) adapted it for PyCon Ukraine 2014. Source and license info is on [GitHub](https://github.com/pprett/sklearn_pycon2014/).
Here is where we start diving into the field of machine learning.
By the end of this section you will
In addition, we will go over several basic tools within scikit-learn which can be used to accomplish the above tasks.
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%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
Machine Learning (ML) is about building programs with tunable parameters (typically an array of floating point values) that are adjusted automatically so as to improve their behavior by adapting to previously seen data.
In most ML applications, the data is in a 2D array of shape [n_samples x n_features],
where the number of features is the same for each object, and each feature column refers
to a related piece of information about each sample.
Machine learning can be broken into two broad regimes: supervised learning and unsupervised learning. We’ll introduce these concepts here, and discuss them in more detail below.
Every algorithm is exposed in scikit-learn via an ''Estimator'' object. For instance a linear regression is:
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from sklearn.linear_model import LinearRegression
Estimator parameters: All the parameters of an estimator can be set when it is instantiated:
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model = LinearRegression(normalize=True)
print model.normalize
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print model
Estimated parameters: When data is fitted with an estimator, parameters are estimated from the data at hand. All the estimated parameters are attributes of the estimator object ending by an underscore:
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x = np.array([0, 1, 2])
y = np.array([0, 1, 2])
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plt.plot(x, y, marker='o');
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X = x[:, np.newaxis] # The input data for sklearn is 2D: (samples == 3 x features == 1)
X
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model.fit(X, y)
model.coef_
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In Supervised Learning, we have a dataset consisting of both features and labels. The task is to construct an estimator which is able to predict the label of an object given the set of features. A relatively simple example is predicting the species of iris given a set of measurements of its flower. This is a relatively simple task. Some more complicated examples are:
What these tasks have in common is that there is one or more unknown quantities associated with the object which needs to be determined from other observed quantities.
Supervised learning is further broken down into two categories, classification and regression. In classification, the label is discrete, while in regression, the label is continuous. For example, in astronomy, the task of determining whether an object is a star, a galaxy, or a quasar is a classification problem: the label is from three distinct categories. On the other hand, we might wish to estimate the age of an object based on such observations: this would be a regression problem, because the label (age) is a continuous quantity.
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from sklearn import neighbors, datasets
iris = datasets.load_iris()
X, y = iris.data, iris.target
knn = neighbors.KNeighborsClassifier(n_neighbors=1)
knn.fit(X, y)
# What kind of iris has 3cm x 5cm sepal and 4cm x 2cm petal?
print iris.target_names[knn.predict([[3, 5, 4, 2]])]
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# A plot of the sepal space and the prediction of the KNN
from fig_code import plot_iris_classification
plot_iris_classification(neighbors.KNeighborsClassifier, n_neighbors=3)
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from sklearn.svm import SVC
unknown_iris = [[3, 5, 4, 2]]
# Use SVC to train and predict the species of the unknown iris...
Classification algorithms can be analyzed by the nature of the decision boundaries they can induce. The overview below shows some popular classification techniques and what kind of decision surface they induce on certain syntetic datasets.
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# Create some simple data
np.random.seed(0)
X = np.random.random(size=(20, 1))
y = 3 * X.squeeze() + 2 + np.random.normal(size=20)
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# Fit a linear regression to it
from sklearn.linear_model import LinearRegression
model = LinearRegression(fit_intercept=True)
model.fit(X, y)
print "Model coefficient: %.5f, and intercept: %.5f" % (model.coef_, model.intercept_)
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# Plot the data and the model prediction
X_test = np.linspace(0, 1, 100)[:, np.newaxis]
y_test = model.predict(X_test)
import pylab as pl
plt.plot(X.squeeze(), y, 'o')
plt.plot(X_test.squeeze(), y_test);
Unsupervised Learning addresses a different sort of problem. Here the data has no labels, and we are interested in finding similarities between the objects in question and discover patterns or latent structure in the data. Unsupervised learning comprises tasks such as dimensionality reduction, clustering, and density estimation. For example, in the iris data discussed above, we can used unsupervised methods to determine combinations of the measurements which best display the structure of the data. As we’ll see below, such a projection of the data can be used to visualize the four-dimensional dataset in two dimensions. Some more involved unsupervised learning problems are:
Sometimes the two may even be combined: e.g. Unsupervised learning can be used to find useful features in high dimensional data, and then these features can be used within a supervised framework.
Principle Component Analysis (PCA) is a dimension reduction technique that can find the combinations of variables that explain the most variance. Here we'll show an example of using PCA for visualization.
Consider the iris dataset. It cannot be visualized in a single 2D plot, as it has 4 features. We are going to extract 2 combinations of sepal and petal dimensions to visualize it:
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X, y = iris.data, iris.target
from sklearn.decomposition import PCA
pca = PCA(n_components=2)
pca.fit(X)
X_reduced = pca.transform(X)
print "Reduced dataset shape:", X_reduced.shape
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plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=y);
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print "Meaning of the 2 components:"
for component in pca.components_:
print " + ".join("%.2f x %s" % (value, name)
for value, name in zip(component, iris.feature_names))
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from sklearn.cluster import KMeans
k_means = KMeans(n_clusters=3, random_state=0)
k_means.fit(X_reduced)
y_pred = k_means.predict(X_reduced)
plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=y_pred);
Clustering algorithms mainly differ in the way they define this grouping. Some algorithms are based on the notion of distance (or similarity) while others are based on the notion of density (e.g. cluster members are connected via regions of high density).
Scikit-learn strives to have a uniform interface across all methods,
and we’ll see examples of these below. Given a scikit-learn estimator
object named model, the following methods are available:
model.fit() : fit training data. For supervised learning applications,
this accepts two arguments: the data X and the labels y (e.g. model.fit(X, y)).
For unsupervised learning applications, this accepts only a single argument,
the data X (e.g. model.fit(X)).model.predict() : given a trained model, predict the label of a new set of data.
This method accepts one argument, the new data X_new (e.g. model.predict(X_new)),
and returns the learned label for each object in the array.model.predict_proba() : For classification problems, some estimators also provide
this method, which returns the probability that a new observation has each categorical label.
In this case, the label with the highest probability is returned by model.predict().model.score() : for classification or regression problems, most (all?) estimators implement
a score method. Scores are between 0 and 1, with a larger score indicating a better fit.model.transform() : given an unsupervised model, transform new data into the new basis.
This also accepts one argument X_new, and returns the new representation of the data based
on the unsupervised model.model.fit_transform() : some estimators implement this method,
which more efficiently performs a fit and a transform on the same input data.An important piece of machine learning is model validation: that is, determining how well your model will generalize from the training data to future unlabeled data. Let's look at an example using the nearest neighbor classifier. This is a very simple classifier: it simply stores all training data, and for any unknown quantity, simply returns the label of the closest training point.
With the iris data, it very easily returns the correct prediction for each of the input points:
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from sklearn.neighbors import KNeighborsClassifier
X, y = iris.data, iris.target
clf = KNeighborsClassifier(n_neighbors=1)
clf.fit(X, y)
y_pred = clf.predict(X)
print(np.all(y == y_pred))
A more useful way to look at the results is to view the confusion matrix, or the matrix showing the frequency of inputs and outputs:
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from sklearn.metrics import confusion_matrix
print(confusion_matrix(y, y_pred))
For each class, all 50 training samples are correctly identified. But this does not mean that our model is perfect! In particular, such a model generalizes extremely poorly to new data. We can simulate this by splitting our data into a training set and a testing set. Scikit-learn contains some convenient routines to do this:
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from sklearn.cross_validation import train_test_split
Xtrain, Xtest, ytrain, ytest = train_test_split(X, y)
clf.fit(Xtrain, ytrain)
ypred = clf.predict(Xtest)
print(confusion_matrix(ytest, ypred))
This paints a better picture of the true performance of our classifier: apparently there is some confusion between the second and third species, which we might anticipate given what we've seen of the data above.
This is why it's extremely important to use a train/test split when evaluating your models. We'll go into more depth on model evaluation later in this tutorial.
To get a feel for how a classification task works, please run the svm_gui.py file available in the repository (use the command below). It will open an interactive window which allows you to click and add points and see how this affects the model.
What is the fewest number of points you can create that are not linearly separable (that is, for which a linear kernel fails to build a correct discriminative model)?
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# %run fig_code/svm_gui.py
# or, if this doesn't work, try
# !python fig_code/svm_gui.py
This is a flow chart created by scikit-learn super-contributor Andreas Mueller which gives a nice summary of which algorithms to choose in various situations. Keep it around as a handy reference!
Original source on the scikit-learn website