Topological Dynamic Bayesian Networks

The objective of this research is to embed topology within the dynamic Bayesian network (DBN) formalism. This extension of a DBN (that encodes statistical or causal relationships) to a topological DBN (TDBN) allows continuous mappings (e.g., topological homeomorphisms), topological relations (e.g.,...

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Bibliographic Details
Main Author: Bouchaffra, Djamel
Format: Conference Proceeding
Language:English
Subjects:
Aging
Alpha-Shapes
Discrete wavelet transforms
Dynamic Bayesian Networks
Face
Face Identification Across Ages
Hidden Markov models
Network Embedding
Shape
Topology
Training
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Description
Summary:The objective of this research is to embed topology within the dynamic Bayesian network (DBN) formalism. This extension of a DBN (that encodes statistical or causal relationships) to a topological DBN (TDBN) allows continuous mappings (e.g., topological homeomorphisms), topological relations (e.g., homotopy equivalences) and invariance properties (e.g., surface genus, compactness) to be exploited. The mission of TDBN is not limited only to classify objects but to reveal how these objects are topologically related as well. Because TDBN formalism uses geometric constructors that project a discrete space onto a continuous space, it is well suited to identify objects that undergo smooth deformation. Experimental results in face identification across ages represent conclusive evidence that the fusion of statistics and topology embodied by the TDBN concept holds promise. The TDBN formalism outperformed the DBN approach in facial identification across ages.
ISSN:1051-4651
2831-7475
DOI:10.1109/ICPR.2010.226