Pattern Recognition

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Pattern Recognition
April 19, 2007 Suggested Reading Horn Chapter 14
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Class and Label
A Class is a particular pattern that one wants
to detect from the input data. For example,
circles, squares, ellipses, etc. The set of
classes defines the scope of the pattern
recognition problem. A labeling (of a data point)
is the assignment of the data point to one of the
known classes.
Joe
John
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Extract meaningful measurements from data points
to form feature vectors.
The association data point ?? its feature
vector
Allows us to work directly with vectors in vector
space (mathematically tractable)
Second important ingredient How to compare
features, i.e., we need (good) metrics.
For face recognition, each pixel intensity can be
considered as one measurement.
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Typically, this provides us with a collection of
vectors in some high dimensional vector space.
L2 norm between two vectors
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Unsupervised Learning Problem Unlabeled data are
given.
Supervised Learning Problem Labeled training
data are given
who is this?
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Test sample
Decision boundary
Generalization of the training data to unseen
data. A classifier is an algorithm that, given
labeled training data, assigns a test data a
class.
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Xi, j are training data such that i indexes the
class and j, the class member.
A sample x is assigned class k, if (for all i, j)
Advantage Easy to understand and implement.
Drawbacks Need to store all training samples
and compute all pairwise distances (expensive for
high dimensional data).
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Each class is now represented by its
centroid. Each test data point is tested against
only the centroids.
A sample x is assigned class k, if (for all i)
Good for data such that each class form a nice
round cluster. Connection with Gaussisan
distribution
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Data from each class from a linear subspace
Example 1 Face images under different lighting
conditions
Assume lambertian reflectance for the faces
(e.g., ignoring the oily forehead, etc). The data
are close to a small dimensional subspace.
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Each class can now be represented to a linear
subspace (instead of just its centroid) and the
test data is tested against subspaces.
Widely used in face recognition and other pattern
classification problems.