## The MusArt Music-Retrieval System## Appendix 2: Finding the Best Target Using a Query Forward AlgorithmWilliam Birmingham, Bryon Pardo, Colin Meek, and Jonah Shifrin |

The Forward algorithm [1], given an HMM and an observation sequence, returns a value between 0 and 1, indicating the probability the HMM generated the observation sequence. Given a maximum path length, ## Selecting The Most Likely ModelLet there be an observation sequence (query), We have found that, in practice, the value returned by the Forward algorithm is negatively correlated with the number of states in the model. This is an effect of model topology and the probability distribution used to determine the starting state for a model. Many thematic models, such as that in Figure 3A, are essentially deterministic. For a deterministic model, the factors that determine the value returned by the Forward algorithm are the observation probabilities and the initial state distribution. We account for this by introducing a scaling factor that varies linearly with respect to the number of states in the model.
An individual scaling factor is found for each HMM in the set of models (themes), ## Reference[1] R. Durbin, S.E., A. Krogh, G. Mitchison, Biological Sequence Analysis: Probabilistic models of proteins and nucleic acids. 1998, Cambridge, UK: Cambridge University Press. ## Copyright© 2002 William Birmingham, Bryan Pardo, Colin Meek, and Jonah Shifrin. | |