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Forward Topology for Hidden Markov Models.
Inheritance Hierarchy

Online System Object
  Accord.Statistics.Models.Markov.Topology Forward

Namespace: Accord.Statistics.Models.Markov.Topology
Assembly: Accord.Statistics (in Accord.Statistics.dll) Version: (

public class Forward : ITopology

Forward topologies are commonly used to initialize models in which training sequences can be organized in samples, such as in the recognition of spoken words. In spoken word recognition, several examples of a single word can (and should) be used to train a single model, to achieve the most general model able to generalize over a great number of word samples.

Forward models can typically have a large number of states.


  • Alexander Schliep, "Learning Hidden Markov Model Topology".
  • Richard Hughey and Anders Krogh, "Hidden Markov models for sequence analysis: extension and analysis of the basic method", CABIOS 12(2):95-107, 1996. Available in:


In the following example, we will create a Forward-only discrete-density hidden Markov model.

// Create a new Forward-only hidden Markov model with 
// three forward-only states and four sequence symbols. 
var model = new HiddenMarkovModel(new Forward(3), 4);

// After creation, the state transition matrix for the model 
// should be given by: 
//       { 0.33, 0.33, 0.33 } 
//       { 0.00, 0.50, 0.50 } 
//       { 0.00, 0.00, 1.00 } 
// in which no backward transitions are allowed (have zero probability).
See Also