We present a learning strategy for Hidden Markov Models that may be used to cluster handwriting sequences or to learn a character model by identifying its main writing styles. Our approach aims at learning both the structure and parameters of a Hidden Markov Model (HMM) from the data. A byproduct of this learning strategy is the ability to cluster signals and identify allograph. We provide experimental results on artificial data that demonstrate the possibility to learn from data HMM parameters and topology. For a given topology, our approach outperforms in some cases that we identify standard Maximum Likelihood learning scheme. We also apply our unsupervised learning scheme on on-line handwritten signals for allograph clustering as well as for learning HMM models for handwritten digit recognition.