Friday, November 22, 2013

The book I mentioned in my previous post also has a section on pattern recognition. Pattern recognition refers to the classification or description of objects or patterns. The patterns themselves can range from characters in an image of printed text to biological waveforms. The recognition involves indentifying the patterns and assigning labels for categories. We start with a set of training patterns. The main difference between pattern recognition and cluster analysis is the role of pattern class labels. In pattern recognition, we use the labels to formulate decision rules. In cluster analysis we use it to verify the results. Pattern recognition requires extrinsic information. In cluster analysis, we use only the data.
There are two basic paradigms to classify a pattern into one of K different classes. The first is a geometric or statistical approach.  In this approach, a pattern is represented in terms of d features and the pattern features are as independent from one another as possible. Then given training patterns for each pattern class, the objective is to separate the patterns belonging to different classes.
In statistical pattern recognition, the features are assumed to have a probability density function that is conditioned on the pattern class. A pattern vector x belonging to a class wj is a data point drawn from the conditional probability distribution P(x/wj) where j is one of the K different classes. Concepts from statistical decision theory and discriminant analysis are utilized to establish decision boundaries between the pattern classes.If the class conditional densities are known, then Bayes decision theory gives optimal decision rule. Since they are generally not known, a classifier is used based on the nature of the information available. A classifier requires a supervised or unsupervised learning In the supervised learning, if the form of class conditional densities are known, we use a parametric or non-parametric decision rules. In unsupervised learning, the density functions are estimated from training samples.  Here the labels one each training pattern represents the category to which the pattern belongs. The categories may be known beforehand or they may be unknown
When the number of pattern classes is unknown, it tries to find natural groupings in the data. In the tree representing these dichotomies in statistical pattern recognition algorithms, the problems get more difficult as we traverse from top to bottom and from left to right in the picture given below.
                                Prior Information
                                  -----------------
                                 |                       |
                          Complete    Incomplete
 (Bayes Decision Theory)               |
                                                        |
                                       --------------------------------
                                       |                                         |
                                 Supervised                Unsupervised
                                       |                                         |
                  ------------------------                       ---------------
                  |                               |                       |                    |
 Parameteric     Non-Parametric        Categories known   Categories Unknown
            |                        |                                    |                    |
----------------              --------------                    |                    |
|                   |                |               |                     |                    |
Optimal      Plugin   Density    Geometric   Mixture  Cluster analysis
rules        rules     estimation  Rules     resolving

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