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Nonsupervised sequential classification and recognition of patterns

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2 Author(s)

A Bayes approach to nonsupervised pattern recognition is given where n l -dimensional vector samples X_{1}, X_{2}, \cdots , X_{n} are received unclassified, i.e., any one of M pattern sources \omega _{1}, \omega _{2}, \cdots , \omega _{M} , with corresponding probabilities of occurrence Q_{1_{o}}, Q_{2_{o}} , \cdots , Q_{M_{o}} , caused each sample X_{s}, s=1,2, \cdots , n . The approach utilizes the fact that the cumulative distribution function (c.d.f.) of X_{s} is a mixture c.d.f., F(X_{s})= \sum _{i=1}^{M} F(X_{s}|\omega _{i}) Q_{i_{o}} . It is assumed that available a priori knowledge includes knowledge of M and the family {F(X_{s}|\omega _{i})} , where F(X_{s}|\omega _{i}) is characterized by a vector B_{i_{o}} . In general, B_{i_{o}} and Q_{i_{o}}, i = 1,2, \cdots , M are considered fixed but unknown, and conditional probability of error in deciding which source caused X_{n} is minimized. When the functional form of F(X_{s}|\omega _{i}) in terms of B_{i_{o}} is unknown, the family {F(X_{s}|\omega _{i})} is taken to be the family of multinomial c.d.f.'s--an application of the histogram concept to the nonsupervisory problem. Additional nonparameteric a priori knowledge about the family--such as F(X_{s}|\omega _{i}) is symmetrical, and/or F(X_{s}|\omega _{i}) differs from F(X_{s}|\omega _{j}) only by a translational vector--can be utilized in the Bayes solution.

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Information Theory, IEEE Transactions on  (Volume:12 ,  Issue: 3 )