Competitive training in hidden Markov models

The use of hidden Markov models is placed in a connectionist framework, and an alternative approach to improving their ability to discriminate between classes is described. Using a network style of training, a measure of discrimination based on the a posteriori probability of state occupation is proposed, and the theory for its optimization using error back-propagation and gradient ascent is presented. The method is shown to be numerically well behaved, and results are presented which demonstrate that when using a simple threshold test on the probability of state occupation, the proposed optimization scheme leads to improved recognition performance.

On the relationship between hidden Markov Models and convex functional transforms for simulating scanning probe Microscopy

Models for simulating Scanning Probe Microscopy (SPM) may serve as a reference point for validating experimental data and practice. Generally, simulations use a microscopic model of the sample-probe interaction based on a first-principles approach, or a geometric model of macroscopic distortions due to the probe geometry. Examples of the latter include use of neural networks, the Legendre Transform, and dilation/erosion transforms from mathematical morphology. Dilation and the Legendre Transform fall within a general family of functional transforms, which distort a function by imposing a convex solution.In earlier work, the authors proposed a generalized approach to modeling SPM using a hidden Markov model, wherein both the sample-probe interaction and probe geometry may be taken into account. We present a discussion of the hidden Markov model and its relationship to these convex functional transforms for simulating and restoring SPM images.©2009 SPIE.