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An Unsupervised Approach for Automatic Activity Recognition based on Hidden Markov Model Regression
Dorra Trabelsi, Samer Mohammed, Faicel Chamroukhi, Latifa Oukhellou, Yacine Amirat
TL;DR
Limited and costly labelled data motivate unsupervised activity recognition from wearable acceleration. The paper proposes MHMMR, an HMM in a multiple regression context learned with EM from unlabelled data, and reports 91.4% mean correct classification while identifying transitions and stationary activities.
Problem
Collecting sufficient labelled data for varied free-living activities can be difficult and computationally expensive.
Method
MHMMR jointly segments multidimensional raw acceleration time series using activity-specific regression models whose switching is governed by a hidden Markov chain, with parameters learned unsupervised by EM.
Results
91.4% mean correct classification rate was achieved across observations, with both transitions and stationary activities identified.
Takeaways & Limitations
The approach provides unsupervised segmentation and classification of human activities while accounting for their temporal dependence.
Abstract
from arXiv · showhide
Using supervised machine learning approaches to recognize human activities from on-body wearable accelerometers generally requires a large amount of labelled data. When ground truth information is not available, too expensive, time consuming or difficult to collect, one has to rely on unsupervised approaches. This paper presents a new unsupervised approach for human activity recognition from raw acceleration data measured using inertial wearable sensors. The proposed method is based upon joint segmentation of multidimensional time series using a Hidden Markov Model (HMM) in a multiple regression context. The model is learned in an unsupervised framework using the Expectation-Maximization (EM) algorithm where no activity labels are needed. The proposed method takes into account the sequential appearance of the data. It is therefore adapted for the temporal acceleration data to accurately detect the activities. It allows both segmentation and classification of the human activities. Experimental results are provided to demonstrate the efficiency of the proposed approach with respect to standard supervised and unsupervised classification approaches
I. INTRODUCTION
Population aging is increasing pressure on healthcare and independence, motivating wearable technologies for assistive services. Human activity recognition is a promising but still challenging application of these sensors.
- By 2050, the European Union population aged 65 and above is expected to grow by 70%, and the population over 80 by 170%.
- Wearable and ubiquitous technologies are emerging as solutions for health monitoring, well-being, and security services.
- Activity recognition has promising applications in security monitoring and human-machine interaction.
- Despite extensive prior work using video, wearable, environmental, and object sensors, activity recognition remains an open and challenging problem.
II. RELATED WORK ON HUMAN ACTIVITY RECOGNITION
Unsupervised activity recognition addresses the difficulty and expense of collecting sufficient labels for varied free-living activities. The paper proposes MHMMR, which combines multiple regression with an HMM to segment and classify sequential acceleration data without labels.
- Collecting sufficient labelled data for varied free-living activities can be difficult and computationally expensive.
- Unsupervised methods learn from unlabelled data through density estimation or clustering and can support exploratory analysis or later supervised classification.
- HMMs suit activity monitoring because acceleration measurements form sequential time series, while EM supports unsupervised HMM learning.
- MHMMR formulates recognition as joint segmentation of multidimensional time series, with each segment associated with an activity.
- Each MHMMR activity is represented by a regression model, and switching between activities is governed by a hidden Markov chain.
- The most likely activity sequence is estimated with Viterbi and evaluated against supervised and unsupervised techniques.
III. DATA COLLECTION
The study collected raw acceleration from three body-mounted sensors to represent upper- and lower-body activities. Six healthy subjects performed twelve activities and transitions, producing nine-dimensional time series.
- Sensors were placed on the chest, right thigh, and left ankle to capture predominantly upper- and lower-body activities.
- The placement was selected to reduce wearer constraint while maintaining comfort and secure attachment.
- Experiments involved six healthy subjects aged 25–30 years and weighing 55–70 kg.
- The protocol studied twelve activities and transitions, including stairs, sitting, lying, standing, and walking.
- Each of three sensors provided tri-axial acceleration, yielding nine acceleration signals recorded over time.
- These signals form nine-dimensional time series with regime changes corresponding to activity changes.
IV. SEGMENTATION WITH MULTIPLE HIDDEN MARKOV MODEL REGRESSION - MHMMR
The paper frames activity recognition as automatic segmentation of multidimensional acceleration time series into regimes, each treated as an activity. It motivates piecewise regression as a model for regime-changing data.
- Activity recognition is formulated as jointly segmenting multidimensional time series into regimes, with each segment treated as an activity.
- The acceleration data exhibit regime changes, motivating automatic partitioning into activity-specific segments.
- Piecewise regression partitions data into segments characterized by separate mean polynomial curves and variances.
- Piecewise models have been applied to regime-changing data in finance, engineering, economics, and bioinformatics.
A. General description of the Multiple Hidden Markov Model Regression
The Multiple Hidden Markov Model Regression represents multidimensional acceleration sequences with activity-specific regression models whose switching follows a hidden Markov chain. Its parameters are estimated unsupervised by EM, combining posterior state inference with weighted regression updates.
- Model formulation: Each hidden state represents an activity and selects one polynomial regression model for the observed acceleration sequence.The state sequence controls switching between the K activity-specific models over time.
- Hidden dynamics: The hidden activity sequence is a first-order homogeneous Markov chain parameterized by the initial distribution π and transition matrix A.Conditional observations have Gaussian distributions with regression-dependent means and state-specific covariance structure.
- Model formulation: The multiple-regression formulation jointly models d-dimensional time series while one latent process governs all univariate components.The shared latent process enables simultaneous regime assignment across the time-series dimensions.
- Parameter estimation: EM estimates the model by alternating posterior-state calculations in the E-step with parameter maximization in the M-step.Posterior probabilities are computed using forward-backward procedures, then used to update the hidden-chain parameters and regression parameters.
- Parameter estimation: The M-step updates regression parameters through K weighted multiple polynomial regressions using posterior probabilities as weights.Covariance updates use a weighted multivariate Gaussian estimation procedure.
V. RESULTS AND DISCUSSIONS
The experiments evaluate whether MHMMR can segment and classify human activities directly from raw acceleration data without feature extraction. They also compare the approach with standard unsupervised and supervised classification methods.
- Evaluation design: The experiments target both segmentation and classification of human activity using MHMMR in an unsupervised learning framework.The study evaluates the proposed approach and compares it with established supervised and unsupervised classifiers.
- Evaluation design: Raw acceleration data are used directly without feature extraction, avoiding the additional computational cost that feature extraction may impose in real-time applications.The paper specifically notes feature extraction can be penalizing in real-time settings.
A. Performance evaluation
Using nine-dimensional acceleration data from three triaxial sensors, MHMMR produces segments that are treated as classified activities. The results are then compared with standard unsupervised and supervised approaches.
- Performance evaluation: MHMMR processes 9-dimensional acceleration data from three triaxial modules mounted on the chest, right thigh, and left ankle.The approach is applied to sequences containing twelve activities.
- Performance evaluation: Each obtained segment is considered an activity, so the segmentation output directly supplies the classification result.Expert activity labels provide ground truth for evaluating the obtained classes.
- Performance evaluation: The real-data MHMMR results are compared with standard unsupervised and supervised classification approaches.The paper presents the MHMMR results before the comparisons.
B. Classification performance of the MHMMR
MHMMR identifies latent activity sequences from nine-dimensional acceleration data and supports unsupervised segmentation of multiactivity sequences, with some confusion between walking and stair-climbing.
- MHMMR identifies a latent sequence of twelve activities from nine-dimensional acceleration data, using K=12 classes and regression order p=3.The data come from three triaxial accelerometers, and model parameters are estimated from the observations without using activity labels for training.
- The posterior probabilities represent the probability that each sample was generated by a regression model given the complete observation sequence.The posterior probabilities are plotted alongside acceleration data for the evaluated sequences.
- The method segments sequences containing standing, sitting, ground-sitting, and lying activities into corresponding activity classes.Figure 4 evaluates a seven-activity sequence spanning standing, sitting transitions, ground sitting, and lying.
- The method also segments a sequence containing standing, walking, stair ascent, and standing into three activity classes.Figure 5 reports the corresponding three-class segmentation sequence.
- 91.4% is the mean correct classification rate averaged over all observations, with transitions and stationary activities well identified.Static activities are easier to recognize than dynamic activities, while some confusion occurs between A11 and A12.
C. Comparison with unsupervised and supervised classification approaches
MHMMR outperforms the standard unsupervised classifiers evaluated while remaining label-free during training, but supervised classifiers achieve higher top classification rates using class labels.
- Unsupervised comparison: 91.4% is MHMMR’s classification rate, compared with 60%, 72%, and 84% for k-Means, GMM, and standard HMM, respectively.The paper attributes the weaker standard unsupervised results partly to their poorer suitability for longitudinal data.
- Training assumptions: MHMMR performs without labels, whereas the supervised approaches require a labelled collection of data for training.The paper presents this as a distinction between the proposed unsupervised approach and the supervised baselines.
- Error sources: Transition segments account for the main errors because their durations are much shorter than those of the activities.Ground-truth transition boundaries are also difficult to specify precisely using human expert labels.
VI. CONCLUSION AND FUTURE WORKS
The paper presents an unsupervised HMM regression approach that jointly segments multivariate acceleration time series and interprets hidden regimes as activities. It reports competitiveness with supervised approaches and identifies nonparametric modeling and rehabilitation applications as future directions.
- The proposed HMM regression model jointly segments multivariate human-activity time series from raw accelerometer data.Hidden Markov regimes are interpreted as activity classes.
- Unsupervised EM learning estimates model parameters from unlabelled examples by maximizing a likelihood criterion.The approach is intended to cluster large amounts of unlabelled acceleration data into activity groups.
- The method is competitive with well-known supervised classification approaches despite operating without activity labels.
- A future direction is a fully non-Bayesian nonparametric model that supports complex activities without fixing the number of activities.
- The approach could be applied in rehabilitation to recognize undesirable compensatory physical behaviours in stroke and injury patients.