Fusion of Statistics and Topology

Preliminary Results of the Topological HMM's

2008-10-21T11:02:00.000-07:00

We have applied the concept of THMM's in: (i) biometrics, where the mission is to perform face and fingerprint identification; (ii) handwriting recognition; and (iii) bioinformatics, where the goal is to recognize protein 3 dimensional folds given the protein primary structure (amino acid sequence). The results reported are very encouraging in these 3 applications. We are currently exporting this machine learning paradigm to other areas in order to measure its large-scale significance.

absence of shape features in HMM's

2008-10-08T15:46:00.000-07:00

Hidden Markov models (HMM's) and their variants are powerful formalisms that can generate or recognize a sequence of symbols. However, besides their inability to capture long-range dependencies, their major shortcoming is that they have difficulty coping with topology. The shape features are not expressed in the HMM framework. In other words, the shape formed by the input visible observation sequence is not accounted for using HMM's.

fusion of statistics and topology

2008-10-08T15:40:00.000-07:00

One of the main challenges in statistical pattern recognition and machine learning is to devise formalisms that combine statistics with topology.