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HSMM_codes_and_Related_literatures

HSMMs A hidden semi-Markov model (HSMM) is a statistical model. In this model, an observation sequence is assumed to be governed by an underlying semi-Markov process with unobserved (hidden) states. Each hidden state has a generally distributed duration, which is associated with the number of observations produced while in the state, and a probability distribution over the possible observations.

    Based on this model, the model parameters can be estimated/updated, the predicted, filtered, and smoothed probabilities of partial observation sequence can be determined, goodness of the observation sequence fitting to the model can be evaluated, and the best state sequence of the underlying semi-Markov process can be found. Due to those capabilities of the HSMM, it becomes one of the most important models in the area of artificial intelligence/machine learning.

    The first approach to HSMM was proposed by Ferguson (1980), which is partially included in the survey paper by Rabiner (1989). This approach is called the explicit duration HMM in contrast to the implicit duration of the HMM. It assumes that the state duration is generally distributed depending on the current state of the underlying semi-Markov process. It also assumes the conditional independence of outputs. Levinson (1986a) replaced the probability mass functions of duration with continuous probability density functions to form a continuously variable duration HMM. As Ferguson (1980) pointed out, an HSMM can be realized in the HMM framework in which both the state and its sojourn time since entering the state are taken as a complex HMM state. This idea was exploited in 1991 by a 2-vector HMM (Krishnamurthy et al., 1991) and a duration-dependent state transition model (Vaseghi, 1991). Since then, similar approaches were proposed in many applications. They are called in different names such as inhomogeneous HMM (Ramesh and Wilpon, 1992), nonstationary HMM (Sin and Kim, 1995), and triplet Markov chains (Pieczynski et al., 2002). These approaches, however, have the common problem of computational complexity in some applications. A more efficient algorithm was proposed in 2003 by Yu and Kobayashi (2003a), in which the forward-backward variables are defined using the notion of a state together with its remaining sojourn (or residual life) time. This makes the algorithm practical in many applications.

    The HSMM has been successfully applied in many areas. The most successful application is in speech recognition. The first application of HSMM in this area was made by Ferguson (1980). Since then, there have been more than one hundred such papers published in the literature. It is the application of HSMM in speech recognition that enriches the theory of HSMM and develops many algorithms for HSMM.

    Since the beginning of 1990s, the HSMM started being applied in many other areas. In this decade, the main application area of HSMMs is handwritten/printed text recognition (see, e.g., Chen et al., 1993a). Other application areas of HSMMs include electrocardiograph (ECG) (Thoraval et al., 1992), network traffic characterization (Leland et al., 1994), recognition of human genes in DNA (Kulp et al., 1996), language identification (Marcheret and Savic, 1997), ground target tracking (Ke and Llinas, 1999), document image comparison, and classification at the spatial layout level (Hu et al., 1999).

    From 2000 to 2009, the HSMM has been obtained more and more attentions from vast application areas. In this decade, the main applications are human activity recognition (see, e.g., Hongeng and Nevatia, 2003) and speech synthesis (see, e.g., Moore and Savic, 2004). Other application areas include change-point/end-point detection for semiconductor manufacturing (Ge and Smyth, 2000a), protein structure prediction (Schmidler et al., 2000), analysis of branching and flowering patterns in plants (Guedon et al., 2001), rain events time series model (Sansom and Thomson, 2001), brain functional MRI sequence analysis (Faisan et al., 2002), Internet traffic modelling (Yu et al., 2002), event recognition in videos (Hongeng and Nevatia, 2003), image segmentation (Lanchantin and Pieczynski, 2004), semantic learning for a mobile robot (Squire, 2004), anomaly detection for network security (Yu, 2005), symbolic plan recognition (Duong et al., 2005a), terrain modeling (Wellington et al., 2005), adaptive cumulative sum test for change detection in noninvasive mean blood pressure trend (Yang et al., 2006), equipment prognosis (Bechhoefer et al., 2006), financial time series modeling (Bulla and Bulla, 2006), remote sensing (Pieczynski, 2007), classification of music (Liu et al., 2008), and prediction of particulate matter in the air (Dong et al., 2009).

    In the recent years since 2010, the main application areas of HSMMs are equipment prognosis/diagnosis (see, e.g., Dong and Peng, 2011) and animal activity modeling (see, e.g., O'Connell et al., 2011). Other application areas include such as machine translation (Bansal et al., 2011), network performance (Wang et al., 2011), deep brain stimulation (Taghva, 2011), image recognition (Takahashi et al., 2010), icing load prognosis (Wu et al., 2014), irrigation behavior (Andriyas and McKee, 2014), dynamics of geyser (Langrock, 2012), anomaly detection of spacecraft (Tagawa et al., 2011), and prediction of earthquake (Beyreuther and Wassermann, 2011).

    The latest information, new developments, and emerging topics about HSMMs, including illustrated examples, with a more in-depth treatment and foundational approach in the understanding and application of HSMMs, can be found in Yu's recent book: "Hidden Semi-Markov Models: Theory, Algorithms and Applications" (1st Edition, 208 pages, Publisher: Elsevier, Nov. 2015, ISBN-10: 0128027673, ISBN-13: 978-0128027677.)

    The Matlab source codes for the forward-backward algorithms of HSMM are quite simple which can be found here. An R package for analyzing hidden semi-Markov models can be found in Bulla et al (2010).

    * Note: there are hundreds papers that use the HSMMs but do not contribute to the theory, modeling or algorithms of the HSMMs are not cited here.

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