Fast computation

is necessary for the output densities of HMM states, because new density values need to be computed for every state when a new feature vector is fed to the system. Since the total density estimate is strongly dominated by the few Gaussians close to the sample, a good approximation can be obtained by using only the K best matching Gaussians of the total M in equation (20). Experiments to determine the relation between K and M for different HMMs are made in Publication 2. On situations of several candidates close to the sample, some of those K units can be replaced by other close-by candidates without a significant change in the total density value. These properties enable ways to generate some approximative K-best search methods (see the next section) without degrading much the modeling accuracy for codebooks smooth and dense around the sample vector as offered by the SOM training.