In [ ]:
%load_ext watermark
%watermark -d -u -a 'Andreas Mueller, Kyle Kastner, Sebastian Raschka' -v -p numpy,scipy,matplotlib
The use of watermark (above) is optional, and we use it to keep track of the changes while developing the tutorial material. (You can install this IPython extension via "pip install watermark". For more information, please see: https://github.com/rasbt/watermark).
Machine learning is about fitting models to data; for that reason, we'll start by discussing how data can be represented in order to be understood by the computer. Along with this, we'll build on our matplotlib examples from the previous section and show some examples of how to visualize data.
Data in scikit-learn, with very few exceptions, is assumed to be stored as a
two-dimensional array, of shape [n_samples, n_features]. Many algorithms also accept scipy.sparse matrices of the same shape.
The number of features must be fixed in advance. However it can be very high dimensional
(e.g. millions of features) with most of them being "zeros" for a given sample. This is a case
where scipy.sparse matrices can be useful, in that they are
much more memory-efficient than NumPy arrays.
As we recall from the previous section (or Jupyter notebook), we represent samples (data points or instances) as rows in the data array, and we store the corresponding features, the "dimensions," as columns.
As an example of a simple dataset, we're going to take a look at the iris data stored by scikit-learn. The data consists of measurements of three different iris flower species. There are three different species of iris in this particular dataset as illustrated below:
Iris Setosa
Iris Versicolor
Iris Virginica
Let's assume that we are interested in categorizing new observations; we want to predict whether unknown flowers are Iris-Setosa, Iris-Versicolor, or Iris-Virginica flowers, respectively. Based on what we've discussed in the previous section, how would we construct such a dataset?*
Remember: we need a 2D array of size [n_samples x n_features].
What would the n_samples refer to?
What might the n_features refer to?
Remember that there must be a fixed number of features for each sample, and feature number j must be a similar kind of quantity for each sample.
For future experiments with machine learning algorithms, we recommend you to bookmark the UCI machine learning repository, which hosts many of the commonly used datasets that are useful for benchmarking machine learning algorithms -- a very popular resource for machine learning practioners and researchers. Conveniently, some of these datasets are already included in scikit-learn so that we can skip the tedious parts of downloading, reading, parsing, and cleaning these text/CSV files. You can find a list of available datasets in scikit-learn at: http://scikit-learn.org/stable/datasets/#toy-datasets.
For example, scikit-learn has a very straightforward set of data on these iris species. The data consist of the following:
Features in the Iris dataset:
Target classes to predict:
(Image: "Petal-sepal". Licensed under CC BY-SA 3.0 via Wikimedia Commons - https://commons.wikimedia.org/wiki/File:Petal-sepal.jpg#/media/File:Petal-sepal.jpg)
scikit-learn embeds a copy of the iris CSV file along with a helper function to load it into numpy arrays:
In [ ]:
from sklearn.datasets import load_iris
iris = load_iris()
The resulting dataset is a Bunch object: you can see what's available using
the method keys():
In [ ]:
iris.keys()
The features of each sample flower are stored in the data attribute of the dataset:
In [ ]:
n_samples, n_features = iris.data.shape
print('Number of samples:', n_samples)
print('Number of features:', n_features)
# the sepal length, sepal width, petal length and petal width of the first sample (first flower)
print(iris.data[0])
The information about the class of each sample is stored in the target attribute of the dataset:
In [ ]:
print(iris.data.shape)
print(iris.target.shape)
In [ ]:
print(iris.target)
In [ ]:
import numpy as np
np.bincount(iris.target)
Using the NumPy's bincount function (above), we can see that the classes are distributed uniformly in this dataset - there are 50 flowers from each species, where
These class names are stored in the last attribute, namely target_names:
In [ ]:
print(iris.target_names)
This data is four dimensional, but we can visualize one or two of the dimensions at a time using a simple histogram or scatter-plot. Again, we'll start by enabling matplotlib inline mode:
In [ ]:
%matplotlib inline
import matplotlib.pyplot as plt
In [ ]:
x_index = 3
colors = ['blue', 'red', 'green']
for label, color in zip(range(len(iris.target_names)), colors):
plt.hist(iris.data[iris.target==label, x_index],
label=iris.target_names[label],
color=color)
plt.xlabel(iris.feature_names[x_index])
plt.legend(loc='upper right')
plt.show()
In [ ]:
x_index = 3
y_index = 0
colors = ['blue', 'red', 'green']
for label, color in zip(range(len(iris.target_names)), colors):
plt.scatter(iris.data[iris.target==label, x_index],
iris.data[iris.target==label, y_index],
label=iris.target_names[label],
c=color)
plt.xlabel(iris.feature_names[x_index])
plt.ylabel(iris.feature_names[y_index])
plt.legend(loc='upper left')
plt.show()
Change x_index and y_index in the above script
and find a combination of two parameters
which maximally separate the three classes.
This exercise is a preview of dimensionality reduction, which we'll see later.
In [ ]:
import pandas as pd
iris_df = pd.DataFrame(iris.data, columns=iris.feature_names)
pd.tools.plotting.scatter_matrix(iris_df, figsize=(8, 8));
Scikit-learn makes available a host of datasets for testing learning algorithms. They come in three flavors:
sklearn.datasets.load_*sklearn.datasets.fetch_*sklearn.datasets.make_*You can explore the available dataset loaders, fetchers, and generators using IPython's
tab-completion functionality. After importing the datasets submodule from sklearn,
type
datasets.load_<TAB>
or
datasets.fetch_<TAB>
or
datasets.make_<TAB>
to see a list of available functions.
In [ ]:
from sklearn import datasets
The data downloaded using the fetch_ scripts are stored locally,
within a subdirectory of your home directory.
You can use the following to determine where it is:
In [ ]:
from sklearn.datasets import get_data_home
get_data_home()
Be warned: many of these datasets are quite large, and can take a long time to download!
If you start a download within the IPython notebook
and you want to kill it, you can use ipython's "kernel interrupt" feature, available in the menu or using
the shortcut Ctrl-m i.
You can press Ctrl-m h for a list of all ipython keyboard shortcuts.
Now we'll take a look at another dataset, one where we have to put a bit more thought into how to represent the data. We can explore the data in a similar manner as above:
In [ ]:
from sklearn.datasets import load_digits
digits = load_digits()
In [ ]:
digits.keys()
In [ ]:
n_samples, n_features = digits.data.shape
print((n_samples, n_features))
In [ ]:
print(digits.data[0])
print(digits.target)
The target here is just the digit represented by the data. The data is an array of length 64... but what does this data mean?
There's a clue in the fact that we have two versions of the data array:
data and images. Let's take a look at them:
In [ ]:
print(digits.data.shape)
print(digits.images.shape)
We can see that they're related by a simple reshaping:
In [ ]:
import numpy as np
print(np.all(digits.images.reshape((1797, 64)) == digits.data))
Let's visualize the data. It's little bit more involved than the simple scatter-plot we used above, but we can do it rather quickly.
In [ ]:
# set up the figure
fig = plt.figure(figsize=(6, 6)) # figure size in inches
fig.subplots_adjust(left=0, right=1, bottom=0, top=1, hspace=0.05, wspace=0.05)
# plot the digits: each image is 8x8 pixels
for i in range(64):
ax = fig.add_subplot(8, 8, i + 1, xticks=[], yticks=[])
ax.imshow(digits.images[i], cmap=plt.cm.binary, interpolation='nearest')
# label the image with the target value
ax.text(0, 7, str(digits.target[i]))
We see now what the features mean. Each feature is a real-valued quantity representing the darkness of a pixel in an 8x8 image of a hand-written digit.
Even though each sample has data that is inherently two-dimensional, the data matrix flattens this 2D data into a single vector, which can be contained in one row of the data matrix.
One dataset often used as an example of a simple nonlinear dataset is the S-cure:
In [ ]:
from sklearn.datasets import make_s_curve
data, colors = make_s_curve(n_samples=1000)
print(data.shape)
print(colors.shape)
In [ ]:
from mpl_toolkits.mplot3d import Axes3D
ax = plt.axes(projection='3d')
ax.scatter(data[:, 0], data[:, 1], data[:, 2], c=colors)
ax.view_init(10, -60)
This example is typically used with an unsupervised learning method called Locally Linear Embedding. We'll explore unsupervised learning in detail later in the tutorial.
Here we'll take a moment for you to explore the datasets yourself. Later on we'll be using the Olivetti faces dataset. Take a moment to fetch the data (about 1.4MB), and visualize the faces. You can copy the code used to visualize the digits above, and modify it for this data.
In [ ]:
from sklearn.datasets import fetch_olivetti_faces
In [ ]:
# fetch the faces data
In [ ]:
# Use a script like above to plot the faces image data.
# hint: plt.cm.bone is a good colormap for this data
In [ ]:
# %load solutions/03A_faces_plot.py