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Ergodic (fully-connected) Topology for Hidden Markov Models.
Inheritance Hierarchy

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

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

public class Ergodic : ITopology

Ergodic models are commonly used to represent models in which a single (large) sequence of observations is used for training (such as when a training sequence does not have well defined starting and ending points and can potentially be infinitely long).

Models starting with an ergodic transition-state topology typically have only a small 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 a second example, we will create an Ergodic (fully connected) discrete-density hidden Markov model with uniform probabilities.

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

// After creation, the state transition matrix for the model 
// should be given by: 
//       { 0.33, 0.33, 0.33 } 
//       { 0.33, 0.33, 0.33 } 
//       { 0.33, 0.33, 0.33 } 
// in which all state transitions are allowed.
See Also