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The problem of searching for patterns in data is a fundamental one and has a long and
successful history. For instance, the extensive astronomical observations of Tycho
Brahe in the 16th century allowed Johannes Kepler to discover the empirical laws of
planetary motion, which in turn provided a springboard for the development of classical mechanics. Similarly, the discovery of regularities in atomic spectra played a
key role in the development and verification of quantum physics in the early twentieth century. The field of pattern recognition is concerned with the automatic discovery of regularities in data through the use of computer algorithms and with the use of
these regularities to take actions such as classifying the data into different categories.
Consider the example of recognizing handwritten digits, illustrated in Figure 1.1.
Each digit corresponds to a 28×28 pixel image and so can be represented by a vector
x comprising 784 real numbers. The goal is to build a machine that will take such a
vector x as input and that will produce the identity of the digit 0,..., 9 as the output.
This is a nontrivial problem due to the wide variability of handwriting. It could be
1
2 1. INTRODUCTION
Figure 1.1 Examples of handwritten digits taken from US zip codes.
tackled using handcrafted rules or heuristics for distinguishing the digits based on
the shapes of the strokes, but in practice such an approach leads to a proliferation of
rules and of exceptions to the rules and so on, and invariably gives poor results.
Far better results can be obtained by adopting a machine learning approach in
which a large set of N digits {x1,..., xN } called a training set is used to tune the
parameters of an adaptive model. The categories of the digits in the training set
are known in advance, typically by inspecting them individually and handlabelling
them. We can express the category of a digit using target vector t, which represents
the identity of the corresponding digit. Suitable techniques for representing categories in terms of vectors will be discussed later. Note that there is one such target
vector t for each digit image x.
The result of running the machine learning algorithm can be expressed as a
function y(x) which takes a new digit image x as input and that generates an output
vector y, encoded in the same way as the target vectors. The precise form of the
function y(x) is determined during the training phase, also known as the learning
phase, on the basis of the training data. Once the model is trained it can then determine the identity of new digit images, which are said to comprise a test set. The
ability to categorize correctly new examples that differ from those used for training is known as generalization. In practical applications, the variability of the input
vectors will be such that the training data can comprise only a tiny fraction of all
possible input vectors, and so generalization is a central goal in pattern recognition.
For most practical applications, the original input variables are typically preprocessed to transform them into some new space of variables where, it is hoped, the
pattern recognition problem will be easier to solve. For instance, in the digit recognition problem, the images of the digits are typically translated and scaled so that each
digit is contained within a box of a fixed size. This greatly reduces the variability
within each digit class, because the location and scale of all the digits are now the
same, which makes it much easier for a subsequent pattern recognition algorithm
to distinguish between the different classes. This preprocessing stage is sometimes
also called feature extraction. Note that new test data must be preprocessed using
the same steps as the training data.
Preprocessing might also be performed in order to speed up computation. For
example, if the goal is realtime face detection in a highresolution video stream,
the computer must handle huge numbers of pixels per second, and presenting these
directly to a complex pattern recognition algorithm may be computationally infeasible. Instead, the aim is to find useful features that are fast to compute, and yet that
1. INTRODUCTION 3
also preserve useful discriminatory information enabling faces to be distinguished
from nonfaces. These features are then used as the inputs to the pattern recognition
algorithm. For instance, the average value of the image intensity over a rectangular
subregion can be evaluated extremely efficiently (Viola and Jones, 2004), and a set of
such features can prove very effective in fast face detection. Because the number of
such features is smaller than the number of pixels, this kind of preprocessing represents a form of dimensionality reduction. Care must be taken during preprocessing
because often information is discarded, and if this information is important to the
solution of the problem then the overall accuracy of the system can suffer.
Applications in which the training data comprises examples of the input vectors
along with their corresponding target vectors are known as supervised learning problems. Cases such as the digit recognition example, in which the aim is to assign each
input vector to one of a finite number of discrete categories, are called classification
problems. If the desired output consists of one or more continuous variables, then
the task is called regression. An example of a regression problem would be the prediction of the yield in a chemical manufacturing process in which the inputs consist
of the concentrations of reactants, the temperature, and the pressure.
In other pattern recognition problems, the training data consists of a set of input
vectors x without any corresponding target values. The goal in such unsupervised
learning problems may be to discover groups of similar examples within the data,
where it is called clustering, or to determine the distribution of data within the input
space, known as density estimation, or to project the data from a highdimensional
space down to two or three dimensions for the purpose of visualization.
