Homotopy-based semi-supervised hidden Markov tree for texture analysis

A semi-supervised hidden Markov tree (HMT) model is developed for texture analysis, incorporating both labeled and unlabeled data for training; the optimal balance between labeled and unlabeled data is estimated via the homotopy method. In traditional EM-based semi-supervised modeling, this balance is dictated by the relative size of labeled and unlabeled data, often leading to poor performance. Semi-supervised modeling may be viewed as a source allocation problem between labeled and unlabeled data, controlled by a parameter lambda is an element of [0, 1], where lambda = 0 and 1 correspond to the purely supervised HMT model and purely unsupervised HMT based clustering, respectively. We consider the homotopy method to track a path of fixed points starting from lambda = 0, with the optimal source allocation identified as a critical transition point where the solution is unsupported by the initial labeled data. Experimental results on real textures demonstrate the superiority of this method compared to the EM-based semi-supervised HMT training.