Sequential Data Classification under Dynamic Emission

Abstract

Sequential data are ubiquitous and widely available in a range of applications in almost all areas. We aim at considering medical, metrological and motion capturing type applications in terms of sequential data analytics in general, and classification in particular. Two scenarios are considered. The first starts with a pass through the initial sequential data database, performing training/learning of set of classes–medical conditions of patients in case of the dynamic treatment regime problems. This learned procedure will be used during the automated classification of new patients. Before starting the next, second pass, we form a confusion matrix based on the learned classification algorithm, and we form a transition matrix, which can be obtained in two ways: by the original database and alternatively by the data classified by the trained algorithm. The second pass is designed to correct the original classification with help of an additional hidden Markov type model (HMM), based on the mentioned two matrices as transition and emission matrices. The database (set of trellises, the training set) has a lattice structure. A part of the trellis tracks end at the target class (important in dynamic treatment regime applications, sometime associated with the healthy class). The trained classification, applied to the training set, can change the set of tracks ending at the target class, which forms one of the performance indicators of this algorithm. The next scenario also is based on the HMM type model. If one takes a lattice track, treating it as a sequence of observations, then HMM can improve that sequence by generating a complementary sequence, similar to the sequence of Viterbi states of HMM. It can also change the set of tracks ending at the target class, which forms the next performance measure, this time for the HMM procedure. Convergence to the target class is characterized by the convergence of the degrees of the transition matrices to the simple special case of such matrices. Alternatively, by extracting the root of the convergent matrices, the corresponding characterization of the transition matrix can be obtained so that the convergence is guaranteed. This work is mostly methodological than innovative being a complementary part to our previous work on target class classification topics. In the experimental part of this work we considered a root-oriented directed acyclic graphs that correspond to the target class classification policy. On the model of this graphs, a random set of tracks is generated, forming a so-called synthetic training set, synthetic trellis.