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Local Information Predictions

A similar latent variable model was constructed to test the fit of the local information content predictions to the data from Experiments 1 and 2 (see Figure 2). The outcome variables were coded in exactly the same manner as for the Run--Gap Model above. The predictor variables were calculated in terms of redundancy for features of a particular size.

Redundancy can be stated in terms of a ratio of entropies [1], and has been explored by Redlich [7] as an active mechanism in visual perception. In the case of segmentation, the quantity which needs to be calculated is a measure of local information content rather than redudancy. The measure of local information content which will be used here is simply 1 - R where R is redundancy.

Consider a repeating sequence of beats. If r is the number of contiguous repetitions with which a feature x of size s has previously occurred, then one possible measure of local surprise upon the reoccurrance of x is

whereas if x does not reoccur then

For each beat in the rhythmic sequence, three local measures of information content were calculated , , and . These three predictor variables have a value for each beat of each rhythmic sequence.

Figure 2: Path diagram of entropy prediction model where the predictors are: , entropy of features of length 1; , entropy of features of length 2; and , entropy of features of length 3.  

Steven M. Boker
Sun May 14 16:19:40 EDT 1995