TOPICAL REVIEW A Review of Classification Algorithms for EEG-based Brain-Computer Interfaces <s> Hidden Markov Model <s> This tutorial provides an overview of the basic theory of hidden Markov models (HMMs) as originated by L.E. Baum and T. Petrie (1966) and gives practical details on methods of implementation of the theory along with a description of selected applications of the theory to distinct problems in speech recognition. Results from a number of original sources are combined to provide a single source of acquiring the background required to pursue further this area of research. The author first reviews the theory of discrete Markov chains and shows how the concept of hidden states, where the observation is a probabilistic function of the state, can be used effectively. The theory is illustrated with two simple examples, namely coin-tossing, and the classic balls-in-urns system. Three fundamental problems of HMMs are noted and several practical techniques for solving these problems are given. The various types of HMMs that have been studied, including ergodic as well as left-right models, are described. > <s> BIB001 </s> TOPICAL REVIEW A Review of Classification Algorithms for EEG-based Brain-Computer Interfaces <s> Hidden Markov Model <s> The information transfer rate, given in bits per trial, is used as an evaluation measurement in a brain-computer interface (BCI). Three subjects performed four motor-imagery (left hand, right hand, foot, and tongue) and one mental-calculation task. Classification of the EEG patterns is based on band power estimates and hidden Markov models. We propose a method that combines the EEG patterns based on separability into subsets of two, three, four, and five mental tasks. The information transfer rates of the BCI systems comprised of these subsets are reported. The achieved information transfer rates vary from 0.42 to 0.81 bits per trial and reveal that the upper limit of different mental tasks for a BCI system is three. In each subject, different combinations of three tasks resulted in the best performance. <s> BIB002 </s> TOPICAL REVIEW A Review of Classification Algorithms for EEG-based Brain-Computer Interfaces <s> Hidden Markov Model <s> We compare the use of two Markovian models, HMMs and IOHMMs, to discriminate between three mental tasks for brain computer interface systems using an asynchronous protocol. We show that IOHMMs outperform HMMs but that, probably due to the lack of any prior information on the state dynamics, no practical advantage in the use of these models over their static counterparts is obtained. <s> BIB003 </s> TOPICAL REVIEW A Review of Classification Algorithms for EEG-based Brain-Computer Interfaces <s> Hidden Markov Model <s> Mental task classification using brain signals, mostly electroencephalogram (EEG), is an approach to understand human brain functions. As EEG seems to be chaotic, it is important to verify the capability of probabilistic and statistical processing tools (such as HMM-based classifiers) in working with chaotic signals. At first, we study the performance of HMM's in classification of different classes of synthetically generated chaotic signals. Then performance of such classifiers in EEG-based mental task classification is studied. Results show good performance in both cases. <s> BIB004
Hidden Markov Models (HMM) are popular dynamic classifiers in the field of speech recognition BIB001 . An HMM is a kind of probabilistic automaton that can provide the probability of observing a given sequence of feature vectors BIB001 . Each state of the automaton can modelize the probability of observing a given feature vector. For BCI, these probabilities usually are Gaussian Mixture Models (GMM), e.g.,  . HMM are perfectly suitable algorithms for the classification of time series BIB001 . As EEG components used to drive BCI have specific time courses, HMM have been applied to the classification of temporal sequences of BCI features  [52] BIB002 and even to the classification of raw EEG BIB004 . HMM are not much widespread within the BCI community but these studies revealed that they were promising classifiers for BCI systems. Another kind of HMM which has been used to design BCI is the Input-Output HMM (IOHMM) BIB003 . IOHMM is not a generative classifier but a discriminative one.