Lecture 16: Unsupervised Learning

Applied Machine Learning

Volodymyr Kuleshov
Cornell Tech

Part 1: What is Unsupervised Learning?

Let's start by understanding what is unsupervised learning at a high level, starting with a dataset and an algorithm.

Unsupervised Learning

We have a dataset without labels. Our goal is to learn something interesting about the structure of the data:

• Clusters hidden in the dataset.
• Outliers: particularly unusual and/or interesting datapoints.
• Useful signal hidden in noise, e.g. human speech over a noisy phone.

Components of Unsupervised Learning

At a high level, an unsupervised machine learning problem has the following structure:

$$ \text{Dataset} + \text{Algorithm} \to \text{Unsupervised Model} $$

The unsupervised model describes interesting structure in the data. For instance, it can identify interesting hidden clusters.

An Unsupervised Learning Dataset

As a first example of an unsupervised learning dataset, we will use our Iris flower example, but we will discard the labels.

We start by loading this dataset.

# import standard machine learning libraries
import numpy as np
import pandas as pd
from sklearn import datasets

# Load the Iris dataset
iris = datasets.load_iris()

print(iris.DESCR)

.. _iris_dataset:

Iris plants dataset
--------------------

**Data Set Characteristics:**

    :Number of Instances: 150 (50 in each of three classes)
    :Number of Attributes: 4 numeric, predictive attributes and the class
    :Attribute Information:
        - sepal length in cm
        - sepal width in cm
        - petal length in cm
        - petal width in cm
        - class:
                - Iris-Setosa
                - Iris-Versicolour
                - Iris-Virginica
                
    :Summary Statistics:

    ============== ==== ==== ======= ===== ====================
                    Min  Max   Mean    SD   Class Correlation
    ============== ==== ==== ======= ===== ====================
    sepal length:   4.3  7.9   5.84   0.83    0.7826
    sepal width:    2.0  4.4   3.05   0.43   -0.4194
    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)
    petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)
    ============== ==== ==== ======= ===== ====================

    :Missing Attribute Values: None
    :Class Distribution: 33.3% for each of 3 classes.
    :Creator: R.A. Fisher
    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)
    :Date: July, 1988

The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken
from Fisher's paper. Note that it's the same as in R, but not as in the UCI
Machine Learning Repository, which has two wrong data points.

This is perhaps the best known database to be found in the
pattern recognition literature.  Fisher's paper is a classic in the field and
is referenced frequently to this day.  (See Duda & Hart, for example.)  The
data set contains 3 classes of 50 instances each, where each class refers to a
type of iris plant.  One class is linearly separable from the other 2; the
latter are NOT linearly separable from each other.

.. topic:: References

   - Fisher, R.A. "The use of multiple measurements in taxonomic problems"
     Annual Eugenics, 7, Part II, 179-188 (1936); also in "Contributions to
     Mathematical Statistics" (John Wiley, NY, 1950).
   - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.
     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.
   - Dasarathy, B.V. (1980) "Nosing Around the Neighborhood: A New System
     Structure and Classification Rule for Recognition in Partially Exposed
     Environments".  IEEE Transactions on Pattern Analysis and Machine
     Intelligence, Vol. PAMI-2, No. 1, 67-71.
   - Gates, G.W. (1972) "The Reduced Nearest Neighbor Rule".  IEEE Transactions
     on Information Theory, May 1972, 431-433.
   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al"s AUTOCLASS II
     conceptual clustering system finds 3 classes in the data.
   - Many, many more ...

We can visualize this dataset in 2D. Note that we are no longer using label information.

from matplotlib import pyplot as plt
plt.rcParams['figure.figsize'] = [12, 4]

# Visualize the Iris flower dataset
plt.scatter(iris.data[:,0], iris.data[:,1], alpha=0.5)
plt.ylabel("Sepal width (cm)")
plt.xlabel("Sepal length (cm)")
plt.title("Dataset of Iris flowers")

Text(0.5, 1.0, 'Dataset of Iris flowers')

An Unsupervised Learning Algorithm

We can use this dataset as input to a popular unsupervised learning algorithm, $K$-means.

• The algorithm seeks to find $K$ hidden clusters in the data.
• Each cluster is characterized by its centroid (its mean).
• The clusters reveal interesting structure in the data.

# fit K-Means with K=3
from sklearn import cluster
model = cluster.KMeans(n_clusters=3)
model.fit(iris.data[:,[0,1]])

KMeans(n_clusters=3)

Running $K$-means on this dataset identifies three clusters.

# display the clusters in 2D
plt.scatter(iris.data[:,0], iris.data[:,1], alpha=0.5)
plt.scatter(model.cluster_centers_[:,0], model.cluster_centers_[:,1], marker='D', c='r', s=100)
plt.ylabel("Sepal width (cm)")
plt.xlabel("Sepal length (cm)")
plt.title("Dataset of Iris flowers")
plt.legend(['Datapoints', 'Probability peaks'])

<matplotlib.legend.Legend at 0x1231df4a8>

These clusters correspond to the three types of flowers found in the dataset, which we obtain from the labels.

p1 = plt.scatter(iris.data[:,0], iris.data[:,1], alpha=1, c=iris.target, cmap='Paired')
plt.scatter(model.cluster_centers_[:,0], model.cluster_centers_[:,1], marker='D', c='r', s=100)
plt.ylabel("Sepal width (cm)")
plt.xlabel("Sepal length (cm)")
plt.title("Dataset of Iris flowers")
plt.legend(handles=p1.legend_elements()[0], labels=['Iris Setosa', 'Iris Versicolour', 'Iris Virginica'])

<matplotlib.legend.Legend at 0x123247fd0>

Applications of Unsupervised Learning

Unsupervised learning has numerous applications:

• Visualization: identifying and making accessible useful hidden structure in the data.
• Anomaly detection: identifying factory components that are likely to break soon.
• Signal denoising: extracting human speech from a noisy recording.

Application: Discovering Structure in Digits

Unsupervised learning can discover structure in digits without any labels.

Application: DNA Analysis

Dimensionality reduction applied to DNA reveal the geography of European countries: