Hierarchical Dirichlet Process Hidden Markov Model Research Articles

Extracting Overtaking Segments by Unsupervised Clustering and Predicting Nonmotorized Vehicle’s Trajectory

Interpretation of flexible cycling behavior has always been a tough task. It is meaningful to understand the overtaking behavior of cyclists for its threats to safety and its high frequency on shared roads. Advanced unsupervised nonparametric clustering methods are compared to distinguish the overtaking segments from the whole trajectory based on the cycling characteristics of nonmotorized two-wheelers, while the hierarchical Dirichlet process hidden Markov model (HDPHMM) outperforms the mixture model via the Dirichlet process (DP mixture model) and topic model via the hierarchical Dirichlet process (HDP topic model). HDPHMM clusters each record into different states and results in more continuous segments. Based on marked vehicle types, which state of clustering model represents the overtaking condition is deduced. The overtaking segments resulted from HDPHMM show the highest homogeneity in cycling features with actual overtaking behavior. Another practical task is to predict the overtaking trajectory and respond to overtaking behavior in advance. Comparing original trajectory and subdivided trajectory, it is found that training model with grouped data, which have homogeneous features, can improve prediction accuracy. With enough trainable samples, CNN + LSTM hybrid structure can achieve trajectory prediction with a mean absolute error of 3 cm. The segmentation produces trajectory segments with similar characteristics. The model is trained with overtaking trajectory segments. With tens of times less trainable data, the prediction on overtaking trajectory still keeps a mean absolute error of about 5 cm. Subdividing trajectory into segments with homogeneous features can improve the prediction accuracy and reduce the requirement of trainable data volume.

Variational Beta Process Hidden Markov Models with Shared Hidden States for Trajectory Recognition.

Hidden Markov model (HMM) is a vital model for trajectory recognition. As the number of hidden states in HMM is important and hard to be determined, many nonparametric methods like hierarchical Dirichlet process HMMs and Beta process HMMs (BP-HMMs) have been proposed to determine it automatically. Among these methods, the sampled BP-HMM models the shared information among different classes, which has been proved to be effective in several trajectory recognition scenes. However, the existing BP-HMM maintains a state transition probability matrix for each trajectory, which is inconvenient for classification. Furthermore, the approximate inference of the BP-HMM is based on sampling methods, which usually takes a long time to converge. To develop an efficient nonparametric sequential model that can capture cross-class shared information for trajectory recognition, we propose a novel variational BP-HMM model, in which the hidden states can be shared among different classes and each class chooses its own hidden states and maintains a unified transition probability matrix. In addition, we derive a variational inference method for the proposed model, which is more efficient than sampling-based methods. Experimental results on a synthetic dataset and two real-world datasets show that compared with the sampled BP-HMM and other related models, the variational BP-HMM has better performance in trajectory recognition.

Multistate Diagnosis and Prognosis of Lubricating Oil Degradation Using Sticky Hierarchical Dirichlet Process–Hidden Markov Model Framework

In this study, we present a state-based diagnostic and prognostic methodology for lubricating oil degradation based on a nonparametric Bayesian approach, i.e., sticky hierarchical Dirichlet process–hidden Markov model (HDP-HMM). An accurate health state-space assessment for diagnostics and prognostics has always been unobservable and hypothetical in the past. The lubrication condition monitoring (LCM) data is generally segregated as “healthy or unhealthy”, representing a binary state-based perspective to the problem. This two-state performance-based formulation poses limitations to the precision and accuracy of the diagnosis and prognosis for real data wherein there may be multiple states of discrete performance that are characteristic of the system functionality. In particular, the reversible and nonlinear time-series trends of degradation data increase the complexity of state-based modeling. We propose a multistate diagnostic and prognostic framework for LCM data in the wear-out phase (i.e., the unhealthy portion of degradation data), accounting for irregular oil replenishment and oil change effects (i.e., nonlinearity in the degradation signal). The LCM data is simulated for an elementary mechanical system with four components. The sticky HDP sets the prior for the HMM parameters. The unsupervised learning over infinite observations and emission reveals four discrete health states and helps estimate the associated state transition probabilities. The inferred state sequence provides information relating to the state dynamics, which provides further guidance to maintenance decision making. The decision making is further backed by prognostics based on the conditional reliability function and mean residual life estimation.

An HDP-HMM based approach for tool wear estimation and tool life prediction

Tool wear estimation and prediction are keys of maintenance decision-making for milling machine. Various discrete-state degradation models have been developed for tool wear estimation and prediction. However, previous research assume that the number of discrete wear states is fixed based on prior understanding of tool degradation process. To break this limitation, a data-driven approach based on Hierarchical Dirichlet process-Hidden Markov model (HDP-HMM) is proposed. The number of states, transition probability matrix and omission probability distribution of hidden Markov model (HMM) can be automatically updated using observation data through a hierarchical Dirichlet process (HDP). Compared with weighted HMM and Conventional HMM, experiments on real data from high-speed CNC milling machine cutters demonstrates that the proposed approach yielded greater accuracy on tool wear estimation and kept a high reliability in tool life prediction.

Multitaper Infinite Hidden Markov Model for EEG.

Electroencephalographam (EEG) monitoring of neural activity is widely used for identifying underlying brain states. For inference of brain states, researchers have often used Hidden Markov Models (HMM) with a fixed number of hidden states and an observation model linking the temporal dynamics embedded in EEG to the hidden states. The use of fixed states may be limiting, in that 1) pre-defined states might not capture the heterogeneous neural dynamics across individuals and 2) the oscillatory dynamics of the neural activity are not directly modeled. To this end, we use a Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM), which discovers the set of hidden states that best describes the EEG data, without a-priori specification of state number. In addition, we introduce an observation model based on classical asymptotic results of frequency domain properties of stationary time series, along with the description of the conditional distributions for Gibbs sampler inference. We then combine this with multitaper spectral estimation to reduce the variance of the spectral estimates. By applying our method to simulated data inspired by sleep EEG, we arrive at two main results: 1) the algorithm faithfully recovers the spectral characteristics of the true states, as well as the right number of states and 2) the incorporation of the multitaper framework produces a more stable estimate than traditional periodogram spectral estimates.

Dual Sticky Hierarchical Dirichlet Process Hidden Markov Model and Its Application to Natural Language Description of Motions.

In this paper, a new nonparametric Bayesian model called the dual sticky hierarchical Dirichlet process hidden Markov model (HDP-HMM) is proposed for mining activities from a collection of time series data such as trajectories. All the time series data are clustered. Each cluster of time series data, corresponding to a motion pattern, is modeled by an HMM. Our model postulates a set of HMMs that share a common set of states (topics in an analogy with topic models for document processing), but have unique transition distributions. The number of HMMs and the number of topics are both automatically determined. The sticky prior avoids redundant states and makes our HDP-HMM more effective to model multimodal observations. For the application to motion trajectory modeling, topics correspond to motion activities. The learnt topics are clustered into atomic activities which are assigned predicates. We propose a Bayesian inference method to decompose a given trajectory into a sequence of atomic activities. The sources and sinks in the scene are learnt by clustering endpoints (origins and destinations) of trajectories. The semantic motion regions are learnt using the points in trajectories. On combining the learnt sources and sinks, the learnt semantic motion regions, and the learnt sequence of atomic activities, the action represented by a trajectory can be described in natural language in as automatic a way as possible. The effectiveness of our dual sticky HDP-HMM is validated on several trajectory datasets. The effectiveness of the natural language descriptions for motions is demonstrated on the vehicle trajectories extracted from a traffic scene.

A Bayesian nonparametric approach for uncovering rat hippocampal population codes during spatial navigation

BackgroundRodent hippocampal population codes represent important spatial information about the environment during navigation. Computational methods have been developed to uncover the neural representation of spatial topology embedded in rodent hippocampal ensemble spike activity. New methodWe extend our previous work and propose a novel Bayesian nonparametric approach to infer rat hippocampal population codes during spatial navigation. To tackle the model selection problem, we leverage a Bayesian nonparametric model. Specifically, we apply a hierarchical Dirichlet process-hidden Markov model (HDP-HMM) using two Bayesian inference methods, one based on Markov chain Monte Carlo (MCMC) and the other based on variational Bayes (VB). ResultsThe effectiveness of our Bayesian approaches is demonstrated on recordings from a freely behaving rat navigating in an open field environment. Comparison with existing methodsThe HDP-HMM outperforms the finite-state HMM in both simulated and experimental data. For HPD-HMM, the MCMC-based inference with Hamiltonian Monte Carlo (HMC) hyperparameter sampling is flexible and efficient, and outperforms VB and MCMC approaches with hyperparameters set by empirical Bayes. ConclusionThe Bayesian nonparametric HDP-HMM method can efficiently perform model selection and identify model parameters, which can used for modeling latent-state neuronal population dynamics.

A Doubly Hierarchical Dirichlet Process Hidden Markov Model with a Non-Ergodic Structure

Nonparametric Bayesian models use a Bayesian framework to learn model complexity automatically from the data, eliminating the need for a complex model selection process. A Hierarchical Dirichlet Process Hidden Markov Model (HDPHMM) is the nonparametric Bayesian equivalent of a hidden Markov model (HMM), but is restricted to an ergodic topology that uses a Dirichlet Process Model to achieve a mixture distribution-like model. For applications involving ordered sequences (e.g., speech recognition), it is desirable to impose a left-to-right structure on the model. In this paper, we introduce a model based on HDPHMM that: 1) shares data points between states, 2) models non-ergodic structures, and 3) models non-emitting states. The first point is particularly important because Gaussian mixture models, which support such sharing, have been very effective at modeling modalities in a signal (e.g., speaker variability). Further, sharing data points allows models to be estimated more accurately, an important consideration for applications such as speech recognition in which some mixture components occur infrequently. We demonstrate that this new model produces a 20% relative reduction in error rate for phoneme classification and an 18% relative reduction on a speech recognition task on the TIMIT Corpus compared to a baseline system consisting of a parametric HMM.

Cooperative Spectrum Sensing With Data Mining of Multiple Users’ Historical Sensing Data

Under the case of exponentially growth of wireless services and the scarcity of spectrum resources, cognitive radio (CR) has been proposed to access licensed channels opportunistically, and thus improve spectrum utilization. In CR devices, accurate spectrum sensing is the prerequisite for opportunistic access. The current cooperative spectrum sensing still cannot effectively exploit the temporal correlations among sensing data, especially the correlations between the current sensing data and the historical data. This paper uses sticky hierarchical Dirichlet process-hidden Markov model to exploit the historical sensing data of multiple users, and classifies the historical sensing data into groups according to their latent spectrum states. The proposed spectrum sensing algorithm can fuse the historical sensing data into prior knowledge, which can be used to improve the accuracy in spectrum decision. Furthermore, a rejection process is proposed to filter out some sensing data with high uncertainty in classification, which guarantees the effectiveness of historical sensing data. The simulation results show that the proposed algorithm performs the best, compared with other three typical cooperative spectrum sensing algorithms, in terms of detection probability and false alarm probability. Specifically, when the false alarm probability is 0.2, the proposed algorithm has more than 10% and 60% detection probability improvement under channel signal-to-noise ratio as 0 and −5 dB, respectively.

Inertial Hidden Markov Models: Modeling Change in Multivariate Time Series

Faced with the problem of characterizing systematic changes in multivariate time series in an unsupervised manner, we derive and test two methods of regularizing hidden Markov models for this task. Regularization on state transitions provides smooth transitioning among states, such that the sequences are split into broad, contiguous segments. Our methods are compared with a recent hierarchical Dirichlet process hidden Markov model (HDP-HMM) and a baseline standard hidden Markov model, of which the former suffers from poor performance on moderate-dimensional data and sensitivity to parameter settings, while the latter suffers from rapid state transitioning, over-segmentation and poor performance on a segmentation task involving human activity accelerometer data from the UCI Repository. The regularized methods developed here are able to perfectly characterize change of behavior in the human activity data for roughly half of the real-data test cases, with accuracy of 94% and low variation of information. In contrast to the HDP-HMM, our methods provide simple, drop-in replacements for standard hidden Markov model update rules, allowing standard expectation maximization (EM) algorithms to be used for learning.

Action classification using a discriminative multilevel HDP-HMM

We classify human actions occurring in depth image sequences using features based on skeletal joint positions. The action classes are represented by a multi-level Hierarchical Dirichlet Process-Hidden Markov Model (HDP-HMM). The non-parametric HDP-HMM allows the inference of hidden states automatically from training data. The model parameters of each class are formulated as transformations from a shared base distribution, thus promoting the use of unlabelled examples during training and borrowing information across action classes. Further, the parameters are learnt in a discriminative way. We use a normalized gamma process representation of HDP and margin based likelihood functions for this purpose. We sample parameters from the complex posterior distribution induced by our discriminative likelihood function using elliptical slice sampling. Experiments with two different datasets show that action class models learnt using our technique produce good classification results.

An Improved Hierarchical Dirichlet Process-Hidden Markov Model and Its Application to Trajectory Modeling and Retrieval

In this paper, we propose a hierarchical Bayesian model, an improved hierarchical Dirichlet process-hidden Markov model (iHDP-HMM), for visual document analysis. The iHDP-HMM is capable of clustering visual documents and capturing the temporal correlations between the visual words within a visual document while identifying the number of document clusters and the number of visual topics adaptively. A Bayesian inference mechanism for the iHDP-HMM is developed to carry out likelihood evaluation, topic estimation, and cluster membership prediction. We apply the iHDP-HMM to simultaneously cluster motion trajectories and discover latent topics for trajectory words, based on the proposed method for constructing the trajectory word codebook. Then, an iHDP-HMM-based probabilistic trajectory retrieval framework is developed. The experimental results verify the clustering accuracy of the iHDP-HMM and trajectory retrieval accuracy of the proposed framework.

Bayesian nonparametric hidden semi-Markov models

There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the ubiquitous Hidden Markov Model for learning from sequential and time-series data. However, in many settings the HDP-HMM's strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can extend the HDP-HMM to capture such structure by drawing upon explicit-duration semi-Markov modeling, which has been developed mainly in the parametric non-Bayesian setting, to allow construction of highly interpretable models that admit natural prior information on state durations. In this paper we introduce the explicit-duration Hierarchical Dirichlet Process Hidden semi-Markov Model (HDP-HSMM) and develop sampling algorithms for efficient posterior inference. The methods we introduce also provide new methods for sampling inference in the finite Bayesian HSMM. Our modular Gibbs sampling methods can be embedded in samplers for larger hierarchical Bayesian models, adding semi-Markov chain modeling as another tool in the Bayesian inference toolbox. We demonstrate the utility of the HDP-HSMM and our inference methods on both synthetic and real experiments.

A sticky HDP-HMM with application to speaker diarization

We consider the problem of speaker diarization, the problem of segmenting an audio recording of a meeting into temporal segments corresponding to individual speakers. The problem is rendered particularly difficult by the fact that we are not allowed to assume knowledge of the number of people participating in the meeting. To address this problem, we take a Bayesian nonparametric approach to speaker diarization that builds on the hierarchical Dirichlet process hidden Markov model (HDP-HMM) of Teh et al. [J. Amer. Statist. Assoc. 101 (2006) 1566–1581]. Although the basic HDP-HMM tends to over-segment the audio data—creating redundant states and rapidly switching among them—we describe an augmented HDP-HMM that provides effective control over the switching rate. We also show that this augmentation makes it possible to treat emission distributions nonparametrically. To scale the resulting architecture to realistic diarization problems, we develop a sampling algorithm that employs a truncated approximation of the Dirichlet process to jointly resample the full state sequence, greatly improving mixing rates. Working with a benchmark NIST data set, we show that our Bayesian nonparametric architecture yields state-of-the-art speaker diarization results.

Unsupervised Segmentation of Human Motion Data Using a Sticky Hierarchical Dirichlet Process-Hidden Markov Model and Minimal Description Length-Based Chunking Method for Imitation Learning

We propose an unsupervised motion segmentation method for enabling a robot to imitate and perform various unit motions by observing unsegmented human motion. Natural unsegmented human motion data contain various types of unit motions, such as 'waving good-bye', 'walking' and 'throwing a ball'. A robot has to segment the data and extract unit motions from the data to imitate the motions. In previous work, an ergodic hidden Markov model (HMM) was used to model unsegmented human motion. However, there are two main problems with the classical use of this model. (i) Setting an appropriate number of hidden states is difficult because how complex the motions contained in the learning data are and how many there are unknown. (ii) We did not have an effective chunking method that could chunk elemental motions into meaningful unit motions without being captured by local minima. To overcome these problems, we developed an unsupervised motion segmentation method for imitation learning using a sticky hierarchical Dirichlet process (HDP)-HMM, a nonparametric Bayesian model, and an unsupervised chunking method based on a Gibbs sampler and the minimal description length (MDL) principle of imitation learning of unsegmented human motion. We developed this chunking method to work with the sticky HDP-HMM and extract unit human motions. We conducted several experiments to evaluate this method. The proposed method could extract unit motions from unsegmented human motion data. The sticky HDP-HMM can be used to model unsegmented human motion more accurately than with a conventional HMM and simultaneously estimate the number of hidden states. We also evaluated the dependency of the HDP-HMM on the hyperparameters of the model.

The response of human nicotinic receptors in the hippocampus and cerebellum to cigarette smoking: Possible neuroprotective associates

Rodent hippocampal population codes represent important spatial information about the environment during navigation. Computational methods have been developed to uncover the neural representation of spatial topology embedded in rodent hippocampal ensemble spike activity.We extend our previous work and propose a novel Bayesian nonparametric approach to infer rat hippocampal population codes during spatial navigation. To tackle the model selection problem, we leverage a Bayesian nonparametric model. Specifically, we apply a hierarchical Dirichlet process-hidden Markov model (HDP-HMM) using two Bayesian inference methods, one based on Markov chain Monte Carlo (MCMC) and the other based on variational Bayes (VB).The effectiveness of our Bayesian approaches is demonstrated on recordings from a freely behaving rat navigating in an open field environment.The HDP-HMM outperforms the finite-state HMM in both simulated and experimental data. For HPD-HMM, the MCMC-based inference with Hamiltonian Monte Carlo (HMC) hyperparameter sampling is flexible and efficient, and outperforms VB and MCMC approaches with hyperparameters set by empirical Bayes.The Bayesian nonparametric HDP-HMM method can efficiently perform model selection and identify model parameters, which can used for modeling latent-state neuronal population dynamics.