On-Line Signature Verification Using Hidden Markov Models with Number of States Estimation from the Signature Duration

2007 ◽  
Author(s):  
J.M. Pascual-Gaspar ◽  
V. Cardenoso-Payo
Keyword(s):  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Signature Verification ◽  
On Line

scholarly journals Smooth On-Line Learning Algorithms for Hidden Markov Models

1994 ◽  
Vol 6 (2) ◽  
pp. 307-318 ◽  
Author(s):  
Pierre Baldi ◽  
Yves Chauvin
Keyword(s):  
Hidden Markov Models ◽  
Expectation Maximization ◽  
Markov Models ◽  
Learning Algorithm ◽  
Hidden Markov ◽  
Batch Mode ◽  
On Line ◽  
Maximization Algorithms ◽  
On Line Learning ◽  
Entropy Functions

A simple learning algorithm for Hidden Markov Models (HMMs) is presented together with a number of variations. Unlike other classical algorithms such as the Baum-Welch algorithm, the algorithms described are smooth and can be used on-line (after each example presentation) or in batch mode, with or without the usual Viterbi most likely path approximation. The algorithms have simple expressions that result from using a normalized-exponential representation for the HMM parameters. All the algorithms presented are proved to be exact or approximate gradient optimization algorithms with respect to likelihood, log-likelihood, or cross-entropy functions, and as such are usually convergent. These algorithms can also be casted in the more general EM (Expectation-Maximization) framework where they can be viewed as exact or approximate GEM (Generalized Expectation-Maximization) algorithms. The mathematical properties of the algorithms are derived in the appendix.

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