Mixture Hidden Markov Models Research Articles

Model selection for mixture hidden Markov models: an application to clickstream data

AbstractIn a clickstream analysis setting, Mixture Hidden Markov Models (MHMMs) can be used to examine categorical sequences assuming they evolve according to a mixture of latent Markov processes, each related to a different subpopulation. These models involve identifying both the number of subpopulations and hidden states. This study proposes a model selection criterion based on an integrated completed likelihood approach that accounts for the two latent classes in the model. We implemented a Monte Carlo simulation study to compare selection criteria performance. In scenarios characterised by categorical short length sequences, our proposed measure outperforms the most commonly used model selection criteria in identifying components and states. The paper presents a case study on clickstream data collected from the website of a company operating in the hospitality industry and modelled by an MHMM selected by the proposed score.

CopyMix: Mixture model based single-cell clustering and copy number profiling using variational inference

Investigating tumor heterogeneity using single-cell sequencing technologies is imperative to understand how tumors evolve since each cell subpopulation harbors a unique set of genomic features that yields a unique phenotype, which is bound to have clinical relevance. Clustering of cells based on copy number data obtained from single-cell DNA sequencing provides an opportunity to identify different tumor cell subpopulations. Accordingly, computational methods have emerged for single-cell copy number profiling and clustering; however, these two tasks have been handled sequentially by applying various ad-hoc pre- and post-processing steps; hence, a procedure vulnerable to introducing clustering artifacts. We avoid the clustering artifact issues in our method, CopyMix, a Variational Inference for a novel mixture model, by jointly inferring cell clusters and their underlying copy number profile. Our probabilistic graphical model is an improved version of the mixture of hidden Markov models, which is designed uniquely to infer single-cell copy number profiling and clustering. For the evaluation, we used likelihood-ratio test, CH index, Silhouette, V-measure, total variation scores. CopyMix performs well on both biological and simulated data. Our favorable results indicate a considerable potential to obtain clinical impact by using CopyMix in studies of cancer tumor heterogeneity.

DBHC: Discrete Bayesian HMM Clustering

Sequence data mining has become an increasingly popular research topic as the availability of data has grown rapidly over the past decades. Sequence clustering is a type of method within this field that is in high demand in the industry, but the sequence clustering problem is non-trivial and, as opposed to static cluster analysis, interpreting clusters of sequences is often difficult. Using Hidden Markov Models (HMMs), we propose the Discrete Bayesian HMM Clustering (DBHC) algorithm, an approach to clustering discrete sequences by extending a proven method for continuous sequences. The proposed algorithm is completely self-contained as it incorporates both the search for the number of clusters and the search for the number of hidden states in each cluster model in the parameter inference. We provide a working example and a simulation study to explain and showcase the capabilities of the DBHC algorithm. A case study illustrates how the hidden states in a mixture of HMMs can aid the interpretation task of a sequence cluster analysis. We conclude that the algorithm works well as it provides well-interpretable clusters for the considered application.

Finite mixture of hidden Markov models for tensor-variate time series data

Finite mixture of hidden Markov models for tensor-variate time series data

How CSCL roles emerge, persist, transition, and evolve over time: A four-year longitudinal study

A prevailing trend in CSCL literature has been the study of students' participatory roles. The majority of existing studies examine a single collaborative task or, at most, a complete course. This study aims to investigate the presence —or the lack thereof— of a more enduring disposition that drives student participation patterns across courses. Based on data from a 4-year program where 329 students used CSCL to collaborate in 10 successive courses (amounting up to 84,597 interactions), we identify the emerging roles using centrality measures and latent profile analysis (LPA) and trace the unfolding of roles over the entire duration of the program. Thereafter, we use Mixture Hidden Markov Models (MHMM) —methods that are particularly useful in detecting “latent traits” in longitudinal data— to identify how students' roles, transition, persist or evolve over time. Relevant covariates were also examined to explain students’ membership of different trajectories. We identified three different roles (leader, mediator, isolate) at the course level. At the program level, we found three distinct trajectories: an intense trajectory with mostly leaders, a fluctuating trajectory with mostly mediators, and a wallowing-in-the-mire trajectory with mostly isolates. Our results show that roles re-emerge consistently regardless of the task or the course over extended periods of time and in a predictable manner. For instance, isolates “assumed” such a role in almost all of their courses over four years.

A Mixture Hidden Markov Model to Mine Students’ University Curricula

In the context of higher education, the wide availability of data gathered by universities for administrative purposes or for recording the evolution of students’ learning processes makes novel data mining techniques particularly useful to tackle critical issues. In Italy, current academic regulations allow students to customize the chronological sequence of courses they have to attend to obtain the final degree. This leads to a variety of sequences of exams, with an average time taken to obtain the degree that may significantly differ from the time established by law. In this contribution, we propose a mixture hidden Markov model to classify students into groups that are homogenous in terms of university paths, with the aim of detecting bottlenecks in the academic career and improving students’ performance.

Response Patterns to Weekly Short Message Service Health Surveys Among Diverse Youth at High Risk for Acquiring HIV.

HIV researchers use short messaging service (SMS)-based surveys to monitor health behaviors more closely than what would be possible with in-person assessment. Benefits are tempered by nonresponse to completing surveys. Understanding response patterns and their associated study participant characteristics would guide more tailored use of SMS-based surveys for HIV studies. We examined response to weekly 7-item SMS surveys administered as part of an HIV prevention trial. Using Mixture hidden Markov models (MHMM), we identified the underlying response patterns shared by subgroups of participants over time and quantified the association between these response patterns and participant characteristics. Three underlying response patterns were identified; responders, responders with phone-related errors, and non-responders. Non-responders versus responders were more likely to be younger, male, cis-gender, Black and Latinx participants with histories of homelessness, incarceration, and social support service utilization. Responders with phone-related errors compared to non-responders were more likely to be Black, Latinx, female, students, and have a history of incarceration and social support service utilization. More nuanced results from MHMM analyses better inform what strategies to use for increasing SMS response rates, including assisting in securing phone ownership/service for responders with phone-related errors and identifying alternative strategies for non-responders. Actively collecting and monitoring non-delivery notification data available from SMS gateway service companies offers another opportunity to identify and connect with participants when they are willing but unable to respond during follow-up.

A COMPARATIVE RESEARCH ON G-HMM AND TSS TECHNOLOGIES FOR EYE MOVEMENT TRACKING ANALYSIS

Eye movement analysis provides a new way for disease screening, quantification and assessment. In order to track and analyze eye movement scanpaths under different conditions, this paper proposed the Gaussian mixture-Hidden Markov Model (G-HMM) modeling the eye movement scanpath during saccade, combing with the Time-Shifting Segmentation (TSS) method for model optimization, and also the Linear Discriminant Analysis (LDA) method was utilized to perform the recognition and evaluation tasks based on the multi-dimensional features. In the experiments, 800 real scene images of eye-movement sequences datasets were used, and the experimental results show that the G-HMM method has high specificity for free searching tasks and high sensitivity for prompt object search tasks, while TSS can strengthen the difference of eye movement characteristics, which is conducive to eye movement pattern recognition, especially for search tasks.

Multichannel mixture models for time-series analysis and classification of engagement with multiple health services: An application to psychology and physiotherapy utilization patterns after traffic accidents

BackgroundMotor vehicle accidents (MVA) represent a significant burden on health systems globally. Tens of thousands of people are injured in Australia every year and may experience significant disability. Associated economic costs are substantial. There is little literature on the health service utilization patterns of MVA patients. To fill this gap, this study has been designed to investigate temporal patterns of psychology and physiotherapy service utilization following transport-related injuries. MethodDe-identified compensation data was provided by the Australian Transport Accident Commission. Utilization of physiotherapy and psychology services was analysed. The datasets contained 788 psychology and 3115 physiotherapy claimants and 22,522 and 118,453 episodes of service utilization, respectively. 582 claimants used both services, and their data were preprocessed to generate multidimensional time series. Time series clustering was applied using a mixture of hidden Markov models to identify the main distinct patterns of service utilization. Combinations of hidden states and clusters were evaluated and optimized using the Bayesian information criterion and interpretability. Cluster membership was further investigated using static covariates and multinomial logistic regression, and classified using high-performing classifiers (extreme gradient boosting machine, random forest and support vector machine) with 5-fold cross-validation. ResultsFour clusters of claimants were obtained from the clustering of the time series of service utilization. Service volumes and costs increased progressively from clusters 1 to 4. Membership of cluster 1 was positively associated with nerve damage and negatively associated with severe ABI and spinal injuries. Cluster 3 was positively associated with severe ABI, brain/head injury and psychiatric injury. Cluster 4 was positively associated with internal injuries. The classifiers were capable of classifying cluster membership with moderate to strong performance (AUC: 0.62–0.96). ConclusionThe available time series of post-accident psychology and physiotherapy service utilization were coalesced into four clusters that were clearly distinct in terms of patterns of utilization. In addition, pre-treatment covariates allowed prediction of a claimant's post-accident service utilization with reasonable accuracy. Such results can be useful for a range of decision-making processes, including the design of interventions aimed at improving claimant care and recovery.

Mixture of hidden Markov models for accelerometer data

Motivated by the analysis of accelerometer data taken across a population of individuals, we introduce a specific finite mixture of hidden Markov models with particular characteristics that adapt well to the specific nature of this type of longitudinal data. Our model allows for the computation of statistics that characterize the physical activity of a subject (e.g., the mean time spent at different activity levels and the probability of the transition between two activity levels) without specifying the activity levels in advance but by estimating them from the data. In addition, this approach allows the heterogeneity of the population to be taken into account and subpopulations with homogeneous physical activity behavior to be defined. We prove that, under mild assumptions, this model implies that the probability of misclassifying a subject decreases at an exponential decay with the length of its measurement sequence. Model identifiability is also investigated. We also report a comprehensive suite of numerical simulations to support our theoretical findings. The method is motivated by and applied to the Physical Activity and Transit Survey.

HMM-GMM based Amazigh speech recognition system

This study presents conception and realisation of an automatic independent speech recognition system using hidden Markov model (HMM). The system recognises 33 letters in Amazigh language. System is found well performed and can identify the Amazigh spoken letters at 88, 44% recognition rate, which is well acceptable rate of accuracy for speech recognition. The tests were taken based on the HMM and Gaussian mixture distributions. Hidden Markov toolkit (HTK) has been used in implementation and test phases. The word error rate (WER) came initially to 29.41 and reduced to about 11.52% thanks to extensive testing and change of the recognition's parameters.

HMM-GMM based Amazigh speech recognition system

This study presents conception and realisation of an automatic independent speech recognition system using hidden Markov model (HMM). The system recognises 33 letters in Amazigh language. System is found well performed and can identify the Amazigh spoken letters at 88, 44% recognition rate, which is well acceptable rate of accuracy for speech recognition. The tests were taken based on the HMM and Gaussian mixture distributions. Hidden Markov toolkit (HTK) has been used in implementation and test phases. The word error rate (WER) came initially to 29.41 and reduced to about 11.52% thanks to extensive testing and change of the recognition's parameters.

Finite Mixtures of Hidden Markov Models for Longitudinal Responses Subject to Drop out

Drop out is a typical issue in longitudinal studies. When the missingness is non-ignorable, inference based on the observed data only may be biased. This paper is motivated by the Leiden 85+ study, a longitudinal study conducted to analyze the dynamics of cognitive functioning in the elderly. We account for dependence between longitudinal responses from the same subject using time-varying random effects associated with a heterogeneous hidden Markov chain. As several participants in the study drop out prematurely, we introduce a further random effect model to describe the missing data mechanism. The potential dependence between the random effects in the two equations (and, therefore, between the two processes) is introduced through a joint distribution specified via a latent structure approach. The application of the proposal to data from the Leiden 85+ study shows its effectiveness in modeling heterogeneous longitudinal patterns, possibly influenced by the missing data process. Results from a sensitivity analysis show the robustness of the estimates with respect to misspecification of the missing data mechanism. A simulation study provides evidence for the reliability of the inferential conclusions drawn from the analysis of the Leiden 85+ data.

Mixture Hidden Markov Models for Sequence Data: The seqHMM Package in R

Sequence analysis is being more and more widely used for the analysis of social sequences and other multivariate categorical time series data. However, it is often complex to describe, visualize, and compare large sequence data, especially when there are multiple parallel sequences per subject. Hidden (latent) Markov models (HMMs) are able to detect underlying latent structures and they can be used in various longitudinal settings: to account for measurement error, to detect unobservable states, or to compress information across several types of observations. Extending to mixture hidden Markov models (MHMMs) allows clustering data into homogeneous subsets, with or without external covariates. The seqHMM package in R is designed for the efficient modeling of sequences and other categorical time series data containing one or multiple subjects with one or multiple interdependent sequences using HMMs and MHMMs. Also other restricted variants of the MHMM can be fitted, e.g., latent class models, Markov models, mixture Markov models, or even ordinary multinomial regression models with suitable parameterization of the HMM. Good graphical presentations of data and models are useful during the whole analysis process from the first glimpse at the data to model fitting and presentation of results. The package provides easy options for plotting parallel sequence data, and proposes visualizing HMMs as directed graphs.

Analysis of healthcare service utilization after transport-related injuries by a mixture of hidden Markov models.

BackgroundTransport injuries commonly result in significant disease burden, leading to physical disability, mental health deterioration and reduced quality of life. Analyzing the patterns of healthcare service utilization after transport injuries can provide an insight into the health of the affected parties, allow improved health system resource planning, and provide a baseline against which any future system-level interventions can be evaluated. Therefore, this research aims to use time series of service utilization provided by a compensation agency to identify groups of claimants with similar utilization patterns, describe such patterns, and characterize the groups in terms of demographic, accident type and injury type.MethodsTo achieve this aim, we have proposed an analytical framework that utilizes latent variables to describe the utilization patterns over time and group the claimants into clusters based on their service utilization time series. To perform the clustering without dismissing the temporal dimension of the time series, we have used a well-established statistical approach known as the mixture of hidden Markov models (MHMM). Ensuing the clustering, we have applied multinomial logistic regression to provide a description of the clusters against demographic, injury and accident covariates.ResultsWe have tested our model with data on psychology service utilization from one of the main compensation agencies for transport accidents in Australia, and found that three clear clusters of service utilization can be evinced from the data. These three clusters correspond to claimants who have tended to use the services 1) only briefly after the accident; 2) for an intermediate period of time and in moderate amounts; and 3) for a sustained period of time, and intensely. The size of these clusters is approximately 67%, 27% and 6% of the number of claimants, respectively. The multinomial logistic regression analysis has showed that claimants who were 30 to 60-year-old at the time of accident, were witnesses, and who suffered a soft tissue injury were more likely to be part of the intermediate cluster than the majority cluster. Conversely, claimants who suffered more severe injuries such as a brain head injury or anon-limb fracture injury and who started their service utilization later were more likely to be part of the sustained cluster.ConclusionThis research has showed that clustering of service utilization time series is an effective approach for identifying the main user groups and utilization patterns of a healthcare service. In addition, using logistic regression to describe the clusters in terms of demographic, injury and accident covariates has helped identify the salient attributes of the claimants in each cluster. This finding is very important for the compensation agency and potentially other authorities as it provides a baseline to improve need understanding, resource planning and service provision.

A random coefficients mixture hidden Markov model for marketing research

The hidden Markov model (HMM) provides a framework to model the time-varying effects of marketing mix variables. When employed in a panel data context, it is important to properly account for unobserved heterogeneity across individuals. We propose a new random coefficients mixture HMM (RCMHMM) that allows for flexible patterns of unobserved heterogeneity in both the state-dependent and transition parameters. The RCMHMM nests all HMMs found in the marketing literature. Results of two simulation studies demonstrate that 1) averaging across a large number of different data generating processes, the RCMHMM outperforms all its nested versions using both in-sample and out-of-sample performance and 2) the RCMHMM is more robust than its nested versions when underlying model assumptions are violated. In addition, we apply the RCMHMM to an empirical application where we examine the effectiveness of in-game promotions in increasing the short-term demand for Major League Baseball (MLB) attendance. We find that the effectiveness of four promotional categories varies over the course of the season and across teams and that the RCMHMM performs best.

A New Threat Intelligence Scheme for Safeguarding Industry 4.0 Systems

Industry 4.0 represents the fourth phase of industry and manufacturing revolution, unique in that it provides Internet-connected smart systems, including automated factories, organizations, development on demand, and ‘just-in-time’ development. Industry 4.0 includes the integration of cyber-physical systems (CPSs), Internet of Things (IoT), cloud and fog computing paradigms for developing smart systems, smart homes, and smart cities. Given Industry 4.0 is comprised sensor fields, actuators, fog and cloud processing paradigms, and network systems, designing a secure architecture faces two major challenges: handling heterogeneous sources at scale and maintaining security over a large, disparate, data-driven system that interacts with the physical environment. This paper addresses these challenges by proposing a new threat intelligence scheme that models the dynamic interactions of industry 4.0 components including physical and network systems. The scheme consists of two components: a smart management module and a threat intelligence module. The smart data management module handles heterogeneous data sources, one of the foundational requirements for interacting with an Industry 4.0 system. This includes data to and from sensors, actuators, in addition to other forms of network traffic. The proposed threat intelligence technique is designed based on beta mixture-hidden Markov models (MHMMs) for discovering anomalous activities against both physical and network systems. The scheme is evaluated on two well-known datasets: the CPS dataset of sensors and actuators and the UNSW-NB15 dataset of network traffic. The results reveal that the proposed technique outperforms five peer mechanisms, suggesting its effectiveness as a viable deployment methodology in real-Industry 4.0 systems.

Secure computation of hidden Markov models and secure floating-point arithmetic in the malicious model

Hidden Markov model (HMM) is a popular statistical tool with a large number of applications in pattern recognition. In some of these applications, such as speaker recognition, the computation involves personal data that can identify individuals and must be protected. We thus treat the problem of designing privacy-preserving techniques for HMM and companion Gaussian mixture model computation suitable for use in speaker recognition and other applications. We provide secure solutions for both two-party and multi-party computation models and both semi-honest and malicious settings. In the two-party setting, the server does not have access in the clear to either the user-based HMM or user input (i.e., current observations) and thus the computation is based on threshold homomorphic encryption, while the multi-party setting uses threshold linear secret sharing as the underlying data protection mechanism. All solutions use floating-point arithmetic, which allows us to achieve high accuracy and provable security guarantees, while maintaining reasonable performance. A substantial part of this work is dedicated to building secure protocols for floating-point operations in the two-party setting, which are of independent interest.

Ensemble hidden Markov models with application to landmine detection

We introduce an ensemble learning method for temporal data that uses a mixture of hidden Markov models (HMM). We hypothesize that the data are generated by K models, each of which reflects a particular trend in the data. The proposed approach, called ensemble HMM (eHMM), is based on clustering within the log-likelihood space and has two main steps. First, one HMM is fit to each of the N individual training sequences. For each fitted model, we evaluate the log-likelihood of each sequence. This results in an N-by-N log-likelihood distance matrix that will be partitioned into K groups using a relational clustering algorithm. In the second step, we learn the parameters of one HMM per cluster. We propose using and optimizing various training approaches for the different K groups depending on their size and homogeneity. In particular, we investigate the maximum likelihood (ML), the minimum classification error (MCE), and the variational Bayesian (VB) training approaches. Finally, to test a new sequence, its likelihood is computed in all the models and a final confidence value is assigned by combining the models’ outputs using an artificial neural network. We propose both discrete and continuous versions of the eHMM. Our approach was evaluated on a real-world application for landmine detection using ground-penetrating radar (GPR). Results show that both the continuous and discrete eHMM can identify meaningful and coherent HMM mixture components that describe different properties of the data. Each HMM mixture component models a group of data that share common attributes. These attributes are reflected in the mixture model’s parameters. The results indicate that the proposed method outperforms the baseline HMM that uses one model for each class in the data.

Probabilistic sequence clustering with spectral learning

In this paper, we derive two novel learning algorithms for time series clustering; namely for learning mixtures of Markov Models and mixtures of Hidden Markov Models. Mixture models are special latent variable models that require the usage of local search heuristics such as Expectation Maximization (EM) algorithm, that can only provide locally optimal solutions. In contrast, we make use of the spectral learning algorithms, recently popularized in the machine learning community. Under mild assumptions, spectral learning algorithms are able to estimate the parameters in latent variable models by solving systems of equations via eigendecompositions of matrices or tensors of observable moments. As such, spectral methods can be viewed as an instance of the method of moments for parameter estimation, an alternative to maximum likelihood. The popularity stems from the fact that these methods provide a computationally cheap and local optima free alternative to EM. We conduct classification experiments on human action sequences extracted from videos, clustering experiments on motion capture data and network traffic data to illustrate the viability of our approach. We conclude that the spectral methods are a practical and useful alternative in terms of computational effort and solution quality to standard iterative techniques such as EM in several sequence clustering applications.