Hidden Markov model (HMM) classifier design is considered for analysis of sequential data,
incorporating both labeled and unlabeled data for training; the balance between labeled and unlabeled
data is controlled by an allocation parameter lambda in [0, 1), where lambda = 0 corresponds to purely supervised
HMM learning (based only on the labeled data) and lambda = 1 corresponds to unsupervised HMM-based
clustering (based only on the unlabeled data). The associated estimation problem can typically be reduced
to solving a set of fixed point equations in the form of a “natural-parameter homotopy”. This paper
applies a homotopy method to track a continuous path of solutions, starting from a local supervised
solution (lambda = 0) to a local unsupervised solution (lambda = 1). The homotopy method is guaranteed to track
with probability one from lambda = 0 to lambda = 1 if the lambda = 0 solution is unique; this condition is not satisfied
for the HMM, since the maximum likelihood supervised solution (lambda = 0) is characterized by many local
optimal solutions. A modified form of the homotopy map for HMMs assures a track from lambda = 0 to
lambda = 1. Following this track leads to a formulation for selecting lambda in [0, 1) for a semi-supervised solution,
and it also provides a tool for selection from among multiple (local optimal) supervised solutions. The
results of applying the proposed method to measured and synthetic sequential data verify its robustness
and feasibility compared to the conventional EM approach for semi-supervised HMM training
