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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

In this paper, we propose a non-parametric clustering method to recognize the number of human motions using features which are obtained from a single microelectromechanical system (MEMS) accelerometer. Since the number of human motions under consideration is not known

Human motion recognition (HMR) is an important topic currently being researched due to its large number of applications in tracking, personal navigation, health care, personal life log, surveillance, and sports, among other things. Human motion recognition [

In the health care domain, motions of patients are monitored via wearable sensors. This is useful for three reasons: (1) to keep track of the movements performed by a patient during the medical examination period, (2) to reduce the number of patient visits to medical facilities, and (3) automated motions retrieval and management to facilitate the documentation of a patient's history.

Two main technologies being currently used for motion recognition are body-mounted sensors (accelerometers) [

In the literature regarding the features, most studies incorporated fast Fourier transform (FFT) [

Methodologies investigated to this point follow heuristic classifiers, Gaussian mixture models (GMM) [

In this paper, we propose motion-dependent sensor metrics to identify human motion. Sensors produce a set of unique signal metrics for various human motions. A signal metric is a component of the sensor readings, such as acceleration in the

Selected features are independent of the sensor device, but only dependent of a particular motion.

It is an observation-based detection system that does not require any protocol or any active coordination among devices.

Unsupervised clustering is used without any prior knowledge about the number of clusters.

Our contributions in this study are as follows:

We propose a non-parametric human motion recognition technique that can detect and recognize an unbounded number of motions (clusters). By unbounded, we mean that the number of clusters (activities) is not fixed. Our techniques can automatically cluster those motions without any prior information.

The accuracy of the motion detection ranges from 97% to 99% with an unknown number of clusters.

We compute the Kullback–Leibler divergence (KLD) for newly detected motion using already recognized motions. This enables the system to draw inferences regarding the newly detected motions and cluster them.

The proposed cluster algorithm collects no prior information about the number of motions, and achieves higher accuracy in detecting the number of clusters compared to the conventional method.

The rest of the paper is organized as follows: Section 2 presents current literature describing various motion recognition techniques. Section 3 presents the system model and feature space with an explanation of each feature. Section 4 presents the non-parametric inference and Section 5 explains the non-parametric inference for motion recognition. Section 6 presents the experimental setup, Section 7 demonstrates experimental results, and Section 8 concludes this paper.

In this section, we review recently developed approaches in the motion recognition domain. Khan

Adil

Ling

Rodrigo

Slyper

Ravi

Practically, human motions are dynamic in that the number of motions varies with time. For example, a person at a particular moment is standing with friend, then after some time he or she starts walking. He or she may then start cycling and during cycling he or she may fall. The flow of different motions performed by a person can fluctuate over time and vary by individual, making it very likely that a motion recognition system will encounter unfamiliar motions. In other words, the number of motions shows non-parametric behavior. Therefore, a flexible system that can incorporate the time varying behavior of human motions, instead of relying on a fixed number of motions, is needed. In this paper, we propose a non-parametric Bayesian technique that is flexible enough to accommodate the detection and clustering of newly observed motions in order to account for the dynamic and unexpected nature of human motions that vary with time.

System architecture and feature space for the proposed non-parametric human motion recognition will be described in the next section.

The architecture of the proposed system for human motion recognition is illustrated in

While recording real-time data from a MEMS sensor, the output includes noise. It is important to remove this noise before extracting the features from the sensor output. This component tends to remove signal outliers by filtering the signal. The feature space for motion recognition is described in the following subsection, and infinite Gaussian modeling and non-parametric Bayesian inference modeling are discussed in detail in the following sections. The Gibbs sampler results in clusters, where each cluster corresponds to a particular human motion. The clusters obtained from the Gibbs sampler are further mapped to a particular recognized human motion.

In this section, we introduce the features used in the proposed motion recognition system. To distinguish among different motions, we need to identify unique features that govern various human motions. These features can be extracted from the readings taken by the MEMS sensor attached to the human body. We used an inertial MEMS sensor system (SD777) with a three-axis accelerometer and a single-axis gyroscope. The inertial MEMS sensor (SD777) is a device that measures its own acceleration as a four-dimensional (4D) vector. This 4D vector includes two measurement ranges for the gyroscope, ±100 °/s and ±300 °/s, and one measurement range accelerometer (three axes) from ±1 g to ±5 g. The acceleration can be defined as the rate of change of speed, (^{2}). The acceleration corresponding to each axis can be recorded by a sensor mounted on the subject's chest, as shown in

For data collection, we placed the accelerometer device on the chest of the subject. We obtained a 4D data set from the accelerometer, consisting of the acceleration on three axes and one gyroscope reading. We propose using the following features for human motion recognition: (1) cumulative sum of a gyroscope's angular speed, tilt angle

The tilt angle refers to the tilt of a body in space. The tilt angle can be defined as the angle between the _{x}_{y}_{z}_{x}_{y}_{z}

The cumulative sum of the tilt angle,

Most dynamic gaits (walk, run, fall) produce similar signal amplitude readings for the acceleration in the _{x}_{y}_{z}

The autocorrelation of a signal measures the similarity between observations as a function of the time separation between them. The goal is to identify a repeating pattern in the time-domain signal. Let _{i}

The clusters are modeled as the distribution of a unique hyper-parameter set. Each parameter set represents a unique cluster. The cluster may refer to a particular human motion with a unique hyper-parameter set.

Suppose we have _{1}, _{2}, _{3}, _{N}

The generative model is a model used to randomly generate observable data given hidden parameters. It specifies a joint distribution over observations and labels. Generative models serve two purposes in machine learning: (1) modeling data directly and (2) forming a conditional probability density function. GMM, HMM, naive Bayes (NB), and latent Dirichlet allocation are some examples of generative models. We intend to use the GMM for clustering data points, as the GMM is flexible and can be easily extended to the case in which the number of hidden clusters is unknown. Two models exist in the GMM literature: the finite Gaussian mixture model (FGMM) and the infinite Gaussian mixture model (IGMM). When the number of clusters is known

The Dirichlet distribution is a continuous multivariate distribution parameterized by the vector

The Dirichlet distribution of order K ≥ 2 with parameters _{1}, _{2}, …, _{k}^{K}^{−1} given by:
_{1}, _{2}, _{3}, …, _{k}_{−1} > 0 satisfying _{1} + _{2}, …, _{k}_{−1} < 1 [

A FGMM is a hidden variable probabilistic model based on weighted multivariate Gaussian random variables. The FGMM provides an accurate approximation for multi-modal probability density estimation and clusters data points if the hidden variables are interpreted as class labels. The FGMM assumes that all of the data points are generated from a finite number of Gaussians with unknown parameters.

Recall from the previous section that we know matrix _{1}, _{2}, _{3}, …, _{n}_{i}_{k}_{1}, _{2}, _{3}, …, _{N}_{k}_{k}_{k}_{k}_{i}_{i}_{i}_{k}

The hyper-parameters _{k}

The FGMM is effective when the number of labels is known, but in reality, we do not know how many clusters are in the mixture. Therefore, we need to have a flexible model that does not have a fixed prior θ ⃗. Therefore, θ⃗ follows the base distribution H⃗, which tends to give the model flexibility.

The problem becomes challenging when we do model selection for the FGMM. In our problem, if we have knowledge about the number of human motions, then we could apply the FGMM. However, there is no bound on the number of human motions; they may grow with time. Since it is not appropriate to use the FGMM, the IGMM is introduced in the next subsection for model selection.

The IGMM is an extension of the FGMM, where _{k}

where the Stick breaking follows beta distribution and is given as:
_{i}_{o}_{o}_{o}_{o}

Stick breaking process is used in the IGMM to model and imparts flexibility in terms of a variable number of clusters. In the stick breaking process, a stick of unit length is assumed, which can be represented as
_{1}, which corresponds to the weight. The same process is repeated for the remaining part of the stick (1 − _{1}). The countably infinite concept that we discussed in the previous subsection is realized here in the form of the Stick breaking process.

The IGMM fully models the problem under consideration, where the number of human motions is not known. Each type of motion forms a cluster with parameters _{k}_{k}_{k}_{k}

In this section, we focus on the non-parametric Bayesian inference model for motion recognition. We define the labels _{1}, _{2}, …, _{N}_{i}_{i}_{i} result from?

The IGMM is a generic model that can be extended by numerous approaches for parameter estimation described in the literature. For example, for parameter estimation, the following methods can be utilized with the IGMM for clustering: expectation maximization (EM), Markov chain Monte Carlo (MCMC), moment matching, spectral methods,

Recall that we are interested in the _{i}_{−1}, _{i}_{−}_{i}

In the context of FGMM, the number of clusters are fixed and assumed to be _{i}_{−i}_{N}_{+1}, then the probability of assigning this new data point to a cluster

_{N}_{+1} can be given by [_{k}

Now, we will relax the limit over the _{k}_{,−}_{i}

From _{k}

At this stage, we need Gibbs sampler to obtain the samples of _{−}_{i}_{i}_{i} = k_{−}_{i}_{i}_{k}_{k}

The integration is the marginal probability, where

Remember that our goal is to estimate the posterior distribution for the infinite Gaussian mixture model using the Gibbs sampler. Therefore, we have already chosen the inverse Wishart distribution which make it possible integrate out parameters _{k}_{k}_{k}_{k}

From [_{n}_{n}_{n}_{n}

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In Algorithm 1, input parameters are the measured data point from MEMS sensor, the number of sweep to monitor the convergence of algorithm, and hyper-parameters. The data model is estimated using the observed data and hyper-parameters. Algorithm 1 runs for the specified number of sweeps (steps) till convergence after initialization procedure. For example, the loop in the step 6 runs for 100 sweeps. The samples obtained for each data point from the conditional distribution are used to estimate the joint distribution of all variables. In Algorithm 1, priors are estimated and updated for each step in the Gibbs sampler. After repeated estimation and update process, the final posterior estimation can be obtained at the last step in Algorithm 1.

The result we get from the collapsed Gibbs sampler is the indicators _{i}_{i}_{i}

In experiment, the MEMS accelerometer device was mounted to the chest of the individual as shown in _{x}_{x}

In this section, we will explain the hyper-parameters that are useful in carrying out the clustering procedure. Since we rely on the IGMM, we have to set the hyper-parameters in such a way that represents our actual true data set. The complexity of the Gibbs sampler grows significantly as the number of data points increases [

Since we have employed the generative model, we have to setup the following hyper-parameters, _{o}_{o}_{o}_{o}

The mean vector _{o}_{o}_{o}_{o}_{o}_{o}_{o}_{o}

The covariance matrix of the cluster depends on the following two hyper-parameters, _{o}_{o}_{o}_{o}_{o}_{o}_{o}

The Gibbs sampler results in a number of clusters that constitute the data set, as well as each data point's association with a particular cluster. We assume that the mean values of the features are available for all of the human motions. After clustering, we compare and then map the clusters to the human motion.

In this section, we present the performance analysis of the proposed motion detection technique, in addition to comparing our proposed technique with the parametric Fuzzy C-Means (FCM) [

In the K-means clustering algorithm, the _{1}, _{2}, …, _{N}_{i}_{1}, _{2}, …, _{K}

_{i}_{i}

The overall algorithm proceeds in two steps. Initially it is assumed that the initial means for the _{p}

The algorithm converges when there are no updates. The k-means in

Mean-shift is a non-parametric clustering algorithm [_{i}_{j}_{i}_{j}_{i}_{i}_{i}_{i} = θ⃗_{i}

The accuracy of the proposed non-parametric Bayesian inference can be evaluated using the following three metrics:

The hit rate for detecting the right number of human motions in the data set. The percentage is calculated for the correct number of human motions detected over the total number of trials performed.

The hit rate for each data point is realized by assigning every feature point to its correct cluster. It is the percentage of feature points assigned to its correct cluster over the total number of feature points.

The false alarm rate can be computed by counting the data points that are assigned to incorrect clusters.

In this subsection, we will show the efficacy of the proposed motion detection method against unforeseen motions. As discussed in the previous section, human motions vary with time and encountering new motions is anticipated. Moreover, the proposed HMR approach is robust in terms of new motion detection and recognition. For example, a person is walking and instantly falls due to some unavoidable cause. The person's fall is a new event that should be detected and recognized precisely. Therefore, we compared our proposed approach with a parametric Fuzzy C-Means clustering algorithm [_{i}_{k}_{i}

The algorithm also tend to minimize intra-cluster variance.

The accuracies of the proposed and FCM approaches are given in

In this subsection, we show the recognition accuracies for routine daily motions. We compare the proposed HMR technique with the K-means, and observe the performance gains in terms of the performance metric criteria discussed above. Since we used a generative model, we need to set the hyper-parameters in such a way that the hit rate is maximized with a minimum number of errors. Note that the clustering results are highly sensitive to the hyper-parameters. Therefore, the hyper-parameters must be set carefully in order to reduce the chance of cluster errors. We set the values of the hyper-parameters as _{o}_{o}_{o}_{o}_{o}

In the simulations, we compared the proposed approach with the K-Means clustering algorithm.

In this section, we compared the accuracy of the proposed approach with that of the K-Means approach with a varying Kullback–Leibler divergence value. The Kullback–Leibler divergence is the measure of the difference between two probability distributions.

In this section, we show how the clustering results are affected by varying the KLD for the proposed and K-Means clustering approaches. In

From the simulation results, it is apparent that the proposed collapsed Gibbs sampler converges to a stable state after a few iterations.

In this study, we proposed a non-parametric Bayesian approach for detecting and clustering various human motions. The proposed work exploits the motion-dependent signal features to model an available data set using the infinite Gaussian mixture model. The collapsed Gibbs sampler is utilized to classify the available data set into various human motions. The experimental results show that the proposed human motion recognition approach significantly outperforms methods including the Fuzzy-C Means, K-Means, and mean-shift approaches. The unsupervised nature of the proposed scheme relaxes the upper bound for the number of human motions under consideration. Therefore, the proposed approach can be extended to many other applications in which the number of underlying clusters is unknown.

System architecture with components and feature space for the proposed motion recognition.

The experimental setup for MEMS sensor: (

3D feature space with three human motions recognized.

Finite and Infinite Gaussian Mixture Models.

The acceleration (_{x}_{x}

Tilt angle signals for turning motions.

Unforeseen motion detection results by proposed (

Clustered results for the proposed algorithm (

Hit rate (

Clustering accuracy (

Convergence characteristics of the collapsed Gibbs sampler.

Performance metrics results for FCM and proposed HMR.

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( |
( |
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Walk | 100 | 66.67 | 100 | 0 |

Run | 100 | 0 | 100 | 0 |

Fall (new) | 0 | 100 | 99.33 | 0.67 |