CLASSIFICATION OF HUMAN PHYSICAL ACTIVITIES

FROM ON-BODY ACCELEROMETERS

A Markov Modeling Approach

Andrea Mannini and Angelo Maria Sabatini

Arts Lab, Scuola Superiore Sant’Anna, Piazza dei Martiri della Libertà, Pisa, Italy

Keywords: Human activity classification, Statistical pattern recognition, Accelerometers, Hidden Markov Models,

Human robot interaction, Machine learning.

Abstract: Several applications demanding the development of small networks of on-body sensors, such as motion

sensors, are currently investigated. Accelerometers are a popular choice as motion sensors: the reason is

partly in their capability of extracting information that can be used to automatically infer the physical

activity the human subject is involved, beside their role in feeding estimators of biomechanical parameters.

Automatic classification of human physical activities is highly attractive for pervasive computing systems,

whereas contextual awareness may ease the human-machine interaction, and in biomedicine, whereas

wearable sensor systems are proposed for long-term monitoring of physiological and biomechanical

parameters. This paper is concerned with the machine learning algorithms needed to perform the

classification task. Hidden Markov Model (HMM) classifiers are studied by contrasting them with Gaussian

Mixture Model (GMM) classifiers. HMMs incorporate the statistical information available on movement

dynamics into the classification process, without discarding the time history of previous outcomes, as

GMMs do. In this work, rather than considering them as models for single motor activities, we apply

HMMs as models suitable for sequences of chained activities. An example of the benefits of the statistical

leverage by HMMs is illustrated and discussed by analyzing a dataset of accelerometer time series.

1 INTRODUCTION

Many technical applications could greatly benefit

from the availability of systems that are capable of

automatically classifying specific physical activities

of human beings. In this paper, either static posture,

e.g., standing, or dynamic motion, e.g., walking is

included in the term physical activity. The sort of

contextual awareness coming from this knowledge

(Brézillon, 1999) may help improving the

performance of healthcare monitoring devices or

promoting the development of advanced human-

machine interfaces. In fact, the precise activity

performed by the subject helps defining the context

in which further estimation can be conducted.

Consider, for instance, the problem of estimating the

metabolic energy expenditure of a human subject by

indirect methods (Meijer et al., 1991): these methods

are reported to incur severe estimation errors in the

absence of any information about the particular

functional task the subject is actually involved

(Meijer et al., 1991 and Bouten et al., 1997). In

robotics, several applications which demand some

capability by the robot controller of recognizing the

user’s intent are, for instance, in the field of

rehabilitation engineering, where smart walking

support systems are developed to assist motor-

impaired persons and elderly in their efforts to stand

and to walk (Yu et al., 2003 and Chuy et al., 2007),

or to detect gait instabilities of the user (Sabatini et

al., 2002 and Hirata et al., 2008) and minimize the

risk of fall (Hirata et al., 2008).

In principle, the wearable sensors needed to elicit

the contextual information would be characterized

by low power consumption, small size and weight,

adequate metrological specifications. Micro

electromechanical systems (MEMS) motion sensors

appear well matched to these requirements. The

methods investigated in this paper revolve around

the processing of acceleration signals acquired from

small nets of MEMS accelerometers affixed to

selected points of the human body.

201

Mannini A. and Sabatini A..

CLASSIFICATION OF HUMAN PHYSICAL ACTIVITIES FROM ON-BODY ACCELEROMETERS - A Markov Modeling Approach.

DOI: 10.5220/0003151102010208

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2011), pages 201-208

ISBN: 978-989-8425-35-5

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

A major part of this paper consists of illustrating

and discussing an approach to classification of

human physical activities, which is based on using

Hidden Markov Models (HMMs). In principle, this

approach aims at exploiting the information

available on the movement dynamics, namely the

capability of recognizing activities performed at the

current time is related to the classification outcomes

provided in the past by the classifier. Accordingly,

we talk about sequential classifiers, which differ

from the so-called single-frame classifiers, in the

sense that the latter ones are interested to single

activity primitives, in other words elementary

activities are studied in isolation from the history of

previously detected activities (Allen et al., 2006;

Bao & Intille, 2004; Begg & Kamruzzaman, 2005;

Foerster et al., 1999; Karantonis et al., 2006; Mathie

et al., 2004; Ravi, 2005 and Van Laerhoven &

Cakmakci, 2000).

Nowadays HMMs find applications in a large

number of recognition problems, including, but not

limited to, speech recognition (Rabiner, 1989), hand

gesture and sign language recognition (Liang &

Ouhyoung, 1995), controlling robotic tools by hand

gesture (Yang et al., 1997). Concerning the human

activity recognition, most studies on the application

of HMMs (Babu, 2002; Martìnez-Contreras, 2009)

are based on camera recordings, as shown by

Yamato (1992). These studies focus on the

validation of statistical models of each considered

activity. In a different way, our approach is based on

using lightweight wearable sensors and is oriented to

exploit HMMs at a higher level. In particular, their

use can be oriented towards modelling time relations

between elements of a sequence of activities. Few

applications of HMMs are reported in the literature

as for the problem of classifying human physical

activities from inertial sensors, probably because

HMMs are known potentially plagued by severe

difficulties of parameter estimation. In this paper we

propose a way of alleviating this difficulty by

adopting a supervised approach to classifier training.

This approach is feasible when the data available in

the training set are annotated.

2 MATERIALS AND METHODS

2.1 Datasets for Physical Activity

Classification

The present work is based on analyzing the dataset

of acceleration waveforms published by Bao &

Intille (2004), and disclosed to us by the authors.

Acceleration data, sampled at 76.25 Hz, are acquired

from five bi-axial accelerometers, located at the hip,

wrist, arm, ankle, and thigh. The original protocol is

based on testing 20 subjects, who are requested to

perform 20 activities. In this paper, we select the

seven activities shown in Figure 1, giving rise to a

reduced dataset, henceforth called seven-activity

dataset. These activities involve primarily the use of

the lower limbs; the rationale for their inclusion is

consistent with the most important item in our

current research agenda, namely the development of

a system for pedestrian navigation and gait

parameter estimation.

Since the research goal in Bao & Intille, (2004)

is exclusively to test single-frame classifiers, the

available data for each subject concern acceleration

time series that are known to correspond to each

activity primitive. Simulating a composite activity

by a single subject in our study (virtual experiment)

requires that one data frame is associated to each

state of the model. The associated data frame is

randomly sampled (with replacement) from the

maximum number N of frames available in the

reduced dataset for each primitive and subject (18 ≤

N ≤ 58). We assume that a sequence of elementary

activities, say, an activity at the motor sentence

level, can be modeled as a first-order Markov chain,

composed of a finite number Q of states S

; each

state accounts for an activity primitive, say, an

elementary activity at the motor word level. The

time evolution of a first-order Markov chain is

governed by the vector π of prior probabilities, and

the transition probability matrix (TPM) A. We opt

for a subject-specific training, i.e. a distinct classifier

is trained for each individual subject and we build a

Q-state model (π, A), so as to generate motor

sentences from the vocabulary of motor words

shown in Figure 1 (Q = 7).

Figure 1: Scheme of a sequential classification based on

HMMs.

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A number S = 20 of virtual experiments is

synthesized, each of which composed of T = 300

data frames. A subset of P virtual experiments is

included in the training set. The procedure of

synthesizing virtual experiments in the manner

described above implies the existence of clear-cut

borders between data frames associated to different

primitives, without unknown transients between

consecutive classifiable frames. This problem is

managed by manual data cropping in creating the

original dataset (Bao & Intille, 2004). Of course,

real-life composite activities would be more

complex and fuzzy, especially as for the postural

transitions between different activities. In the

attempt to get a more realistic picture of the HMM-

based sequential classifier performance, data frames

from the original dataset not included in the reduced

dataset are randomly interspersed in the tested data

sequences generated by the OMM, in variable

proportions, from null to 1:3 (max.). The resulting

garbage is managed in our system by the spurious

rejection algorithm described in Section 2.5.

At the time being, the wearable system ActiNav

is moving its first steps in our lab for applications in

the field of pedestrian navigation and smart

estimation of biomechanical parameters and it is

therefore a welcome addition to our opportunities to

test the developed algorithm. ActiNav revolves

around an ARMadeus Board (APF27). It is equipped

with an ARM9 based Freescale processor, having

128 MB of RAM, 256 MB of FLASH memory, and

a 200K-gates Xilinx FPGA. A custom printed circuit

board allows arming the APF27 with a 12-bit

Successive Approximation Register ADC (AD7490,

Analog Devices, Inc.). This converter operates up to

1 MSPS; moreover, since it is endowed with 16

analog channels, up-to-five tri-axis analog

accelerometers or gyros can be integrated in

ActiNav. The system with the main board

(100×84×16 mm) and different sensors connected is

shown in Figure 2. For the aim of this work a single

tri-axis accelerometer (ADXL325, Analog Devices,

Inc.) with FS = ±5 g is fastened on the right thigh of

a single tested subject. The acquired dataset is

limited to 20 sit-stand-walk sequences. This low-

complexity dataset allows us in testing the proposed

methods on a real sequential dataset that includes a

postural transition and the incipient locomotion

situation. These aspects are particularly relevant for

our studies in robotic walking aids for rehabilitation.

Accelerometer data, acquired at a sampling

frequency of 250 Hz, are labeled using the activity

class reported by the experimenter (supervised

approach). Henceforth, we refer to this reduced-

complexity dataset as the sit-stand-walk dataset, so

as to differentiate it from the seven-activity dataset.

Figure 2: The ActiNav board is shown with several

sensors connected to its input ports

2.2 Data Processing: Feature Vectors

The automatic classification of acceleration data

requires a pre-processing phase in which feature

variables with high information content are extracted

from the raw sensor data. The feature vectors are

computed from acceleration samples within sliding

windows with finite and constant width, henceforth

called data frames.

According to the indications reported in previous

works (Bao & Intille, 2004; Ravi et al., 2005), the

following feature variables are selected in this paper:

 DC component. This feature is helpful in

discriminating static postures; it is evaluated

by averaging the raw samples in each data

frame. One feature per data channel is

obtained.

 Energy. This feature is helpful in assessing the

motor act strength. It is evaluated as the sum

of squared spectrogram coefficients within

each data frame. The first coefficient that

includes information about the DC component

is excluded from the sum. One feature per data

channel is obtained.

 Entropy of spectrogram coefficients. This

feature is helpful in discriminating primitives

that differ in frequency domain complexity

(Bao & Intille, 2004). A kernel density

estimator is applied to spectrogram

coefficients for its determination. One feature

per data channel is obtained.

 Correlation coefficients between pair of

accelerometer signals. They are obtained by

computing the dot product of pairs of frame

vectors, normalized to their length, and are

helpful in discriminating activities that involve

motions of several body parts. A total of 55

coefficients can be computed in our

application.

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Before applying the classification algorithm, the

computed feature vectors are selected in order to

reduce the dimensionality of the problem. This is

required to limit the risk of bad parameter estimation

(Jain et al., 2000). In particular, we use the Pudil's

algorithm that is a sequential forward-backward

floating search (SFFS-SFBS) (Pudil, 1994); this

algorithm uses the Euclidean distances between each

pair of feature vectors of the same class in the

training set as a criterion for selection.

For the sit-stand-walk dataset we limit ourselves

to computing the DC components and the correlation

coefficients. Moreover, rather than applying the

Pudil’s feature selection approach, we prefer to

apply a feature extraction method (Jain et al., 2000).

Hence, a Principal Component Analysis (PCA) is

applied, in order to reduce the dimensionality from

nine (3 DC components + 6 Correlation coefficients)

to three.

2.3 Single-frame Classification

Although several single-frame classifiers can be

proposed, we consider here a particular technique

for single-frame classification, namely the Gaussian

Mixture Model (GMM) classifier. This approach is

reported by Allen et al. (2006) to achieve very

promising results. In particular, the authors discuss

the high adaptability of the classifier, a good feature

to analyze data from subjects that are not included in

the training set.

Of course, other methods for single-frame

classification of human physical activity can be

chosen, and they may also outperform GMMs

(Mannini & Sabatini, 2010). Here, the GMM

classifier is selected as the single-frame classifier of

reference, in particular for its resemblance to the

structure of a cHMM. As a matter of fact, the

probability density of emissions of each state in a

cHMM is modeled as a Gaussian mixture.

The GMM classifier first performs a parametric

estimation of class-conditional probability density

functions p(x|w

), which assign the probabilities of

the feature vector x given its membership to the class

. During the training phase of a GMM classifier,

class-conditional probabilities are estimated on the

feature-space as Gaussian mixtures. Each feature

vector x is then classified in the class yielding the

highest value of p(x|w

2.4 cHMM-based Classification

In modeling sequences of human activities as first-

order Markov chains we propose that the prior and

transition probabilities that are associated to the

model are empirically determined by observing the

subject behavior. If the TPM and the state at the

current time are known, then the most likely state

that will follow is probabilistically determined.

However, each activity primitive can only be

observed through a set of raw sensor signals (the

measured time series from on-body accelerometers,

in the present case). In other terms, the states are

hidden and only a second-level process is actually

observable (emissions). The statistical model

including the pair (π, A) and the emission process is

an HMM. We opt for a continuous emissions

approach (continuous emissions densities HMM, aka

cHMM, Rabiner, 1989). The most common

approach to the problem of modeling continuous

emissions is parametric. In particular we consider

mixtures of M multivariate normal distributions

N(μ

,Σ

) that are specified by assigning the mean

value vectors µ

, the covariance matrices Σ

, and

the mixing parameters matrix C. The mixture is used

to model the emissions from each state in the chain.

An excellent reference source for HMMs and

algorithms for their learning and testing in a

recognition problem is in Rabiner (1989).

For our particular problem we consider a Q-state

cHMM as represented in Figure 1 (Q = 7). One of

the main problems may be in the high number of

parameters to be identified. In fact, a Gaussian

cHMM trained in a d-dimensional feature space,

with Q primitives to be classified and M components

for each mixture requires the specification of the

following parameters:

 π, prior probability vector, 1 × Q;

 A, transition probability matrix Q × Q;

 μ, set of mean value matrices, Q × M × d;

 Σ, set of covariance matrices, Q × M × d × d;

 C, set of mixing parameters, Q × M.

The approach to deal with the parameter

identification problem is to split the training phase

into two different steps: a first-level supervised

training phase is followed by a second-level training

phase, which is performed by running the Baum-

Welch algorithm (Rabiner, 1989). Indeed, the

particular problem we are facing with is typically

supervised. It is also known that an inaccurate

initialization of parameters could lead to suboptimal

results by using the Baum-Welch algorithm, due to

the presence of many local maxima in the

optimization surface (Rabiner, 1989). Accordingly,

the first level supervised training becomes the

proposed particular way for achieving a good

initialization of parameters entering the second

“traditional” phase.

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In order to simplify the estimation process, the

parameter set is divided into two main groups,

namely transition parameters (π, A) and emission

parameters (μ, Σ, C). This separation allows us to

train separately two parameter sets with reduced

size, yielding a relevant reduction of the overall size

of the training set. Transition parameters can be

estimated through an OMM. In fact, under

supervised conditions, activity labels from training

set sequences, which in our model correspond to

hidden states, are actually known. Emission

parameters can be estimated by running a GMM

classifier. The training process at the second level

exploits the values of the parameters estimated

during the training process at the first level, as initial

values for running the Baum-Welch algorithm.

In Figure 3 a conceptual scheme of the whole

sequential classification algorithm is depicted: thin

lines refers to parameters, bold lines represent data

frames.

Figure 3: Block diagram of the developed cHMM-based

sequential classifier.

2.5 Spurious Data Rejection

The introduced classification strategy allows us to

define a criterion for automatic rejection of spurious

feature vectors. If a threshold-based detector is

applied to estimated class-conditional probabilities

p(x|w

), it is straightforward to reject those feature

vectors the classification of which is believed too

uncertain, without introducing an additional model

for unknown data. In fact the probability p(x|w

) in

the cHMM refers to the probability of the feature

vector x of being the emission of the model state w

If, for any feature vector, the probabilities relative to

each state are below the threshold, the feature vector

itself can be marked as spurious and removed,

without affecting the cHMM operation. Low values

of p(x|w

) are typical when unknown activities are

hidden in the data presented to the classifier, or

when too much uncertainty affects them.

The threshold value can be optimized upon

assessment of the ROC curves; in Figure 4, the

specificity-sensibility curve, averaged over the 20

subjects, is reported for the data in the seven-activity

dataset. The threshold is settled in our application by

retaining the value when the sensibility of rejection

is slightly greater than the specificity.

Figure 4: ROC curve obtained for different threshold

values.

3 RESULTS

3.1 The seven-activity Dataset

After applying the Pudil's feature selection algorithm

to data, the number of features is reduced from 85 to

17, namely 4 DC components of accelerations and

13 correlation coefficients are retained. The training

set for the single-frame classifier is composed of K

frames per class and per subject. According to the

results of some preliminary testing, K = 7 turns out

to be a convenient choice. Testing is performed

using the remaining N–K frames available for each

subject.

The number of Gaussian components of the

mixture is taken M = 1, either in the GMM or the

cHMM-based classifiers. Indeed the experimental

evidence is in strong support of the assumption of

unimodal data distributions. Algorithm testing up to

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M = 5 indicates only marginal improvements over

the simpler choice M = 1 discussed in the following.

We consider the value K = 7 for the cHMM-based

classifier too. The effect of the number P of motor

sentences in the training set is then analyzed and

results are shown in Figure 5, either in the case that

the second-level training is performed or not,

yielding P = 5 as a reasonable value for sizing the

training set. A subject-specific training and test is

performed for both GMM and cHMM-based

classifiers. In Table 1 the classification accuracy is

reported for each tested subject.

As far as the algorithm for spurious data

rejection is concerned, the threshold is fixed so as to

achieve sensibility Se = 96.6% and specificity Sp =

90.8%. In Table 2 the classification accuracy in the

presence of spurious data and after their automatic

rejection is presented.

Figure 5: Classification accuracy vs. number of P motor

sentences in the training set. o: only first-level training is

applied; *: first-level training is followed by second-level

training.

3.2 The sit-stand-walk Dataset

This dataset is processed using the same sequential

classification methodology as for the seven-activity

dataset. However, the presence of a single subject

dataset requires a different validation method. A

leave-one-out approach is followed: 20 classifiers

are trained, and each time a single sequence is used

to validate the classifier. Classification results in

terms of recognition accuracy are reported in Table

3. As far as spurious data, there is no need to add

spurious data, as described before for the seven-

activity dataset. The spurious rejection algorithm is

now applied to tag data from the sit-stand-walk

dataset, whose reliability for classification is deemed

questionable. Of course, we expect to observe a

higher number of tagged data where activity

transitions take place. In Figure 6 the classifier

outcome and the spurious rejection effect are

reported.

Table 1: Recognition accuracies (percentage values) for

each subject and mean accuracy value over 20 subjects

(seven-activity dataset, before introducing spurious data).

Subject

GMM

cHMM

(First level only)

cHMM

(First and second level)

1 97.6 97.2 99.6

2 93.9 95.6 99.7

3 94.9 94.9 99.7

4 99.9 96.1 99.7

5 82.1 92.2 97.8

6 91.6 89.8 99.5

7 89.5 90.5 97.7

8 98.3 90.6 99.7

9 87.2 94.5 99.6

10 95.6 96.3 99.7

11 98.3 96.2 98.8

12 90.4 89.2 98.1

13 79.9 86.7 99.2

14 92.7 87.2 98.8

15 64.3 94.2 99.6

16 98.7 97.9 98.9

17 53.6 94.8 97.6

18 67.9 81.7 83.4

19 86.9 96.5 99.5

20 75.2 98.5 99.7

Mean 86.9 93.0 98.3

Table 2: Classification accuracy (mean percentage values)

in the presence of spurious data, seven-activity dataset.

Implementation

Classification

accuracy, [%]

Without rejection of spurious data

72.1

With rejection of spurious data

95.7

Table 3: Classification accuracy (mean percentage values)

after and before spurious data rejection, sit-stand-walk

dataset.

Classifier

Classification

accuracy (%)

GMM 89.7

cHMM (First level only)

86.4

cHMM (First and second level)

96.0

cHMM (With spuria rejection)

99.2

4 DISCUSSIONS AND

CONCLUSIONS

Referring to the seven-activity dataset, the Pudil’s

feature selection scheme individuates a subset of

features that simply consist of gross postural

information (DC components) and movement

coordination information (correlation coefficients).

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Figure 6: Classification and spurious data rejection on a

sequence of the sit-stand-walk dataset.

Nonetheless, it is argued that energy and entropy

time-domain features would be highly valuable,

provided that we decide to investigate other

activities, e.g., those from the set studied in (Bao &

Intille, 2004) that are not considered in this paper.

Our decision to concentrate on a basic vocabulary of

activities is motivated by our ongoing work aimed at

developing a wearable sensor system for pedestrian

navigation and human locomotion rehabilitation.

The applicability of Markovian modeling to the

classification of human physical activities - the

subject of this paper - is demonstrated. In particular

we highlight the importance of exploiting the

statistical knowledge about the human motion

dynamics that can be “trapped” within the Markov

chain. The cHMM-based classifier, owing to the

exploitation of statistical information about the

activity dynamics it provides, systematically

outperforms the GMM classifier (the classification

accuracy, averaged across the pool of tested

subjects, raises from about 87% to 98%).

A subject-specific training is considered in this

work. Especially for the cHMM-based sequential

classifier indeed, this approach is more appropriate

than training a single net for a pool of subjects; this

is because of the high variability in how humans

perform a given physical activity.

The supervised training is pursued in this paper

with the idea to split the process of estimating the

parameters of the cHMM-based classifier into two

distinct levels. We can observe that considering only

the first-level training the accuracy of the cHMM-

based classifier performance goes down to about

93% from 98%, still superior to the performance of

the single-frame GMM classifier. Splitting the

training process in two distinct levels is helpful to

effectively cope with the size limitations of the

training set: P = 5 sequences lasting each just few

minutes are enough to yield a suitable training set in

the present application.

A final point is related to the proposed method

for managing spurious feature vectors. Most

published studies, including (Bao & Intille, 2004),

handle the problem of the fuzzy borders by manual

data cropping. Clearly this is neither useful nor

applicable if we look for a real-time system for

activity classification. In our approach, the whole

spurious rejection process is made automatic. When

up to one third of the whole feature vectors in the

data are spurious, the cHMM-based classifier

accuracy is limited to about 72% in the absence of

the proposed threshold-based detector. If the

threshold-based detector is actually implemented the

performance ramps up to about 96%.

Although being limited to three activities chained

in a fixed order, and lasting few seconds only, the

tests on the sit-stand-walk dataset show that the

proposed algorithm can be applied to data in which

transitions are not removed by data cropping. The

beneficial effect of the dynamic information of

HMMs respect to GMMs is confirmed and high

classification accuracy is obtained (> 95 %). This

capability encourages the application of the

proposed methods even for subjects that are affected

by pathologies. As it is shown in Figure 6, the

spurious rejection system is able to identify those

data that actually correspond to postural transitions,

whose classification would be troublesome. This

allows using the proposed methodology, without any

particular attention to how the dataset is labeled

during data acquisition.

In conclusion, a Markov modeling approach to

the design of a sequential human activity classifier

has been pursued. The requirements in terms of

dataset size are not prohibitive, owing to the

proposed subdivision of the training process into two

distinct levels. The supervised machine learning

algorithm also includes a very effective device for

rejecting spurious feature vectors, which turns out to

show high sensibility and specificity of detection.

Ongoing work will concern the extension of the

proposed algorithm in the ActiNav system for

applications in the field of pedestrian navigation,

human robot interaction and smart estimation of

biomechanical parameters.

ACKNOWLEDGEMENTS

The authors are indebted to Prof. Stephen S. Intille,

for allowing them to use his acceleration dataset for

the computer experiments in this paper.

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