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Compared to fully-continuous HMMs, semi-continuous HMMs are more compact in size, require less data to train well and result in comparable recognition performance with much faster decoding speeds. Nevertheless, the use of semi-continuous HMMs in large vocabulary speech recognition systems has declined considerably in recent years. A significant factor that has contributed this is that systems that use semi-continuous HMMs cannot be easily adapted to new acoustic (environmental or speaker) conditions. While maximum likelihood (ML) adaptation techniques have been very successful for continuous density HMMs, these have not worked to a usable degree for semi-continuous HMMs. This paper presents a new framework for supervised and unsupervised ML adaptation of semi-continuous HMMs, built upon the paradigm of probabilistic latent semantic analysis. Experiments with a specific implementation developed under this framework demonstrate its effectiveness.