hierarchical approaches to estimate energy expenditure using phone-based accelerometers

1242 IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS, VOL. 18, NO. 4, JULY 2014

Hierarchical Approaches to Estimate EnergyExpenditure Using Phone-Based Accelerometers

Harshvardhan Vathsangam, E. Todd Schroeder, and Gaurav S. Sukhatme

Abstract—Physical inactivity is linked with increase in risk ofcancer, heart disease, stroke, and diabetes. Walking is an easilyavailable activity to reduce sedentary time. Objective methods toaccurately assess energy expenditure from walking that is normal-ized to an individual would allow tailored interventions. Currenttechniques rely on normalization by weight scaling or fitting apolynomial function of weight and speed. Using the example ofsteady-state treadmill walking, we present a set of algorithms thatextend previous work to include an arbitrary number of anthro-pometric descriptors. We specifically focus on predicting energyexpenditure using movement measured by mobile phone-based ac-celerometers. The models tested include nearest neighbor models,weight-scaled models, a set of hierarchical linear models, multi-variate models, and speed-based approaches. These are comparedfor prediction accuracy as measured by normalized average rootmean-squared error across all participants. Nearest neighbor mod-els showed highest errors. Feature combinations correspondingto sedentary energy expenditure, sedentary heart rate, and sexalone resulted in errors that were higher than speed-based mod-els and nearest-neighbor models. Size-based features such as BMI,weight, and height produced lower errors. Hierarchical modelsperformed better than multivariate models when size-based fea-tures were used. We used the hierarchical linear model to de-termine the best individual feature to describe a person. Weightwas the best individual descriptor followed by height. We alsotest models for their ability to predict energy expenditure withlimited training data. Hierarchical models outperformed personalmodels when a low amount of training data were available. Speed-based models showed poor interpolation capability, whereas hier-archical models showed uniform interpolation capabilities acrossspeeds.

Index Terms—Accelerometer, energy expenditure, hierarchicalmodel, mobile phone, treadmill walking.

I. INTRODUCTION AND RELATED WORK

PHYSICAL inactivity is the fourth leading risk factor forpreventable deaths worldwide [1]. Lack of physical activity

increases the risk of cancer, heart disease, stroke, and diabetes,and shortens lifespan by 3–5 years [2]. Increasing evidence for

Manuscript received April 9, 2013; revised October 19, 2013; acceptedDecember 8, 2013. Date of publication January 2, 2014; date of current versionJune 30, 2014. This work was supported in part by the National Science Foun-dation (CCR-0120778) as part of the Center for Embedded Network Sensing.The work of H. Vathsangam was supported by the USC Annenberg Doctoralfellowship program.

H. Vathsangam and G. S. Sukhatme are with the Department of ComputerScience, University of Southern California, Los Angeles, CA 90089 USA(e-mail: [email protected]; [email protected]).

E. T. Schroeder is with the Division of Biokinesiology and Physical Ther-apy, Univ. of Southern California, Los Angeles, CA 90089 USA (e-mail:[email protected]).

Digital Object Identifier 10.1109/JBHI.2013.2297055

such negative effects has necessitated new research paradigms tointervene in sedentary behavior [3], [4]. Accurate and objectiveassessment of activities in free-living conditions is an importantcomponent of intervention measures.

A recommended intervention for sedentary lifestyles is to re-place time spent in sedentary activities with moderate-intensity,nonexercise activities [5]. Daily walking represents a relativelylow-impact yet accessible method of increasing physical activ-ity [6]. Walking is the most common moderate intensity, phys-ical activity reported among active adults [7]. One measure ofwalking intensity is the energy expended during walking [8].

Over the last two decades, accelerometers have emerged asviable tools to gather information about physical activity andenergy expenditure [9]. Mapping accelerometer data to energyexpenditure can be framed as a regression problem [10]–[12].Here, functions from accelerometer-based descriptors of move-ment to the energy expended as a result of that movementare learned. The recent literature has examined various tech-niques to determine this functional mapping [13]–[17]. Tradi-tional approaches focus on learning regression models from ac-celerometry “counts” to energy expended. Other approaches,utilize pattern recognition on custom-designed descriptorsof movement to apply activity-specific regression equations[18]–[23].

Rapidly increasing prevalence of accelerometers in mobilephones has enabled the capture of movement and energy ex-penditure information using the hardware already carried bymillions of people. Using cellphones to estimate energy expen-diture has primarily focused on first identifying the activity andevaluating metabolic equivalents (METs) based on the activ-ity. Ryu et al. [24] used activity recognition in combinationwith MET predictions to estimate energy expenditure. This wasfollowed by Lester et al. [25] where speed and position mea-surements were used in combination with ACSM speed-basedequations. Manohar et al. [26] demonstrated the feasibility of aphone-based accelerometer placed in a fixed location in predict-ing energy expenditure in a laboratory setting, using movement-based features. In addition to learning activity-specific models,accuracy of predictions could be further increased by account-ing for interpersonal differences in body types among people.Accounting for these differences is important when comparingthe performance of individuals of different body types or thesame individual over time.

Our study aims to extend earlier approaches by addressingthe problem of creating personalized models of energy expen-diture for a person using phone-based accelerometer data withminimal information about a person. We use a data-driven ap-proach, where we consolidate information from a representative

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VATHSANGAM et al.: HIERARCHICAL APPROACHES TO ESTIMATE ENERGY EXPENDITURE USING PHONE-BASED ACCELEROMETERS 1243

population to which that individual belongs, and then use thatinformation to generate a personalized model based on the per-son’s individual anthropometric descriptor. We use tri-axial ac-celerometer data captured from a mobile phone worn on theright iliac crest. We compare different techniques to generatepersonalized models with an experimental study focused onsteady-state treadmill walking. Our goal is to understand thetradeoffs involved between different techniques and transfer thatknowledge to overground walking in free-living settings.

The primary contributions of this paper are a detailed de-scription of the problem of normalizing energy expenditure pre-diction and an evaluation of six candidate techniques on a testpopulation of 34 individuals. This study expands on previouswork involving hierarchical linear modeling [16], [27] and pre-vious work in regression [16] by presenting a new learningalgorithm and comparing it with other hierarchical algorithms.A preliminary version of this study appeared in [28]. Our goal isto utilize data-driven approaches to obtain personalized modelsof energy prediction.

II. RELATED WORK

One principle that can be used to predict energy expended isthe idea of similarity of body types. For the same movement in-tensity, two individuals may expend different amounts of energydue to interpersonal differences in anthropometric characteris-tics such as height, weight, sex, and fitness [9]. Individuals whoare similar to each other might expend similar amounts of energyfor the same movement. One can capture such common traitsacross individuals by treating them as a part of a populationwhere each member has different anthropometric characteris-tics. Each of the member’s regression maps would be specificcases of a common population model. A person’s individualanthropometric characteristics would then be used to obtain apersonalized version of the population map.

One approach to account for interpersonal differences is bytreating all participants as one after normalization for size. Acommonly used normalization method is to scale by an expo-nent of each person’s weight or height [29]. All participants arereplaced by a single pseudoparticipant with scaled energy val-ues, and a regression equation is learned. Most common scalingcoefficients include a range from 0.6−1.0 [30], [31], the mostcommon being 0.67 [32] and 0.75 [33]. Different populationsrequire different scaling coefficients. Rogers et al. [33] andPearce et al. [34] showed that scaling coefficients vary acrossage groups and stages of development in individuals. Other ap-proaches have attempted to scale for fat-free mass in addition tobody weight [35]. With respect to weight-scaling approaches, itis important to note that weight or height may not represent acomplete description of a person for developing a personalizedenergy expenditure model. Waters et al. [36] showed that in ad-dition to weight, the effect of other anthropometric descriptorssuch as sex, stride length, gait style, and heart rate also have tobe incorporated.

Another approach is to explicitly model the energy expendedas a polynomial function of movement and weight. For ex-ample, Wyndham et al. [37] showed a linear dependence on

weight and a squared dependence on velocity. In the context ofaccelerometers, recent techniques have attempted to normalizeenergy expenditure using two-level dependences on movementand anthropometric characteristics. Chen and Sun [11] success-fully showed how a step-wise multiple linear regression model,where the lower level coefficients depend on accelerometer in-formation and the upper level model coefficients depend onheight and weight. Choi et al. implemented a two-level hier-archical approach [13]. We extend their work by developing aprobabilistic multilevel approach tested with frequency-basedfeatures captured from a phone-based accelerometer on a largerpopulation.

Heil [38] developed a multiple linear regression model us-ing accelerometer counts and anthropometric features as inputs.Rothney et al. [14] combined accelerometer count and anthro-pometric features in an artificial neural network model to predictenergy expenditure from accelerometer data. They showed hownonlinear functional mappings could be used to reduce inter-person variance. The issue with artificial neural networks isthe requirement of a large number of labeled examples in ac-celerometer data and computational complexity of the models.Also, with respect to the previous two approaches, potentiallymore accurate results could be obtained by moving away fromcount-based approaches. Recent approaches have used sophis-ticated techniques to incorporate anthropometric descriptors inregression models. Altini et al. showed how allometric scaling ofbody weight coefficients followed by clustering [39] or normal-izing by a cardiorespiratory fitness predicate [40] could be usedto increase prediction accuracies of energy expenditure using anecklace form factor. We extend this research by proposing analternative approach that uses a two-level probabilistic modelin a phone-based form factor. This model enforces similarityconstraints between individuals through an explicit error func-tion. We consider this model along with other techniques thatcan incorporate an arbitrary number of descriptors and evaluatethem for effectiveness in normalization.

III. ALGORITHMS

A. Definition of Terms

Our goal is to identify an accurate map from a movement cap-tured with phone-based accelerometers to the energy expendedas a result of that movement given a person’s anthropometriccharacteristics. We present a set of algorithms to define thismap using general terminology and then adopt the specific caseof treadmill walking to compare techniques. Consider a testpopulation consisting of P participants. For each participantp, we collect training data points in the form of input–outputpairs

(xnp

, ynp

)where np ∈ {1, 2, . . . Np} is the index of data

point for person, p, xnp= [ 1xnp ,1 . . . xnp ,D ]T ∈ R(D+1)×1 is

the (D + 1)-dimensional descriptor of movement and ynp∈ R

is the energy expended by person p for that movement. Letthere be Np data points collected for each person p. Thus foreach participant p, we have a dataset consisting of the energymatrix Yp = [ y1p

y2p. . . yNp

]T ∈ RNp ×1 and movement ma-

trix Xp =[xT

1pxT

2p. . .xT

Np

]T ∈ RNp ×(D+1) . We also record


Fig. 1. Graphical model describing the relationships of the personal model. Alinear relationship between the movement and energy expenditure is assumed.A Bayesian approach to modeling the relationship is adopted.

their corresponding anthropometric descriptor Physp . An an-thropometric descriptor can be measurements like a person’sheight, weight, BMI, gender, and heart rate when sedentaryor any nonlinear combination of elementary measurements.We denote Y = {Y1 ,Y2 , . . . ,YP }, X = {X1 ,X2 , . . . ,XP },PHYS = [PhysT

1 PhysT2 . . .PhysT

P ]T to be the completetraining data for all participants in the population.

Our goal is to determine a functional map: (xnp,Physp)

f→ ynpfor a person P + 1 and use this map to determine

energy expenditure, given an unseen example of their move-ment descriptor xnP + 1 and personal anthropometric descriptor,PhysP +1 . We adopt a statistical approach to this mapping, viz.,we collect examples of a number of people performing differ-ent kinds of movement and measure their energy expenditure.We build a model that indicates what the statistical distributionof energy expenditure, viz., p

(ynp

|xnp,Physp

)is given their

movement and anthropometric characteristics.

B. Personal Models

One approach is to develop a specific model for each per-son, where we simply train a separate model xnp

f→ ynp∀n ∈

[1, 2, . . . Np ] for each person p. Fig. 1 illustrates our approach.We consider the linear model mapping a movement descriptorto energy expenditure [16]:

ynp= wT

p xnp+ ε, ε ∼ N

(0, β−1

p

)

or ynp∼ N

(ynp

;wTp xnp

, β−1p

)

∀np ∈ {1, 2, . . . Np}generally, Yp = Xpwp + εI, ε ∼ N

(0, β−1

p

)

or Yp ∼ N(Yp ;Xpwp , β

−1p I

).

Here, each person’s wp = [wp,0 wp,1 . . . wp,D ]T ∈ R(D+1)×1

is a personal model parameter that describes how the movementdescriptors for person p map to energy expenditure. βp is anoise term which incorporates statistical noise in the mapping.We adopt a Bayesian approach by introducing a prior probabilitydistribution, p(wp) = N

(wp ;0, α−1

p I)

over the model param-eters wp , where αp is a hyperparameter. The optimal prediction

for a new data point is given by the predictive distribution:

p (y∗p |x∗p ,Yp , αp , βp) = N(mT

p x∗p , σ2p (x∗p)

)

σ2p (x∗p) = β−1

p + x∗pT Spx∗p

S−1p = αpI + βpXT

p Xp

mp = βpSpXTp Yp .

Learning the model amounts to learning{mNp

,SNp, αp , βp

}

for each person p. However, simultaneously learning of all theseparameters is not possible because of cyclical dependence. Weinstead adopt an iterative approach using EM algorithm 1.

Personal models perform well when used on data from thesame person. However, they have poor interpolation capabilityacross people because of differences in anthropometric descrip-tors. Hence, we present a set of modifications to the personalmodel to take anthropometric differences into account. In thisstudy, the personal model was used as the ground truth for thebest possible predictive capability that could be achieved perperson.

C. Multivariate Regression Models

A direction generalization of the the personal model acrossmultiple people is to consider a BLR model that uses bothanthropometric descriptors and movement descriptors as inputs.

Thus, the map(xnp

,Physp

) f→ ynpis:

ynp= wT

combined,p [xnpPhysp ] + ε

ε ∼ N(0, β−1

p

)


or ynp∼ N

(ynp

;wTcombined,px

′np

, β−1p

)

x′np

= [xnpPhysp ]

∀np ∈ {1, 2, . . . Np}generally, Yp = X′

pwcombined,p + εI

ε ∼ N(0, β−1

p

)

or Yp ∼ N(Yp ;X′

pwcombined,p , β−1p I

).

Training the parameters of the model amounts to a similarprocedure as in Section III-B. The multivariate model assumesthat each input component of the descriptor (which can be move-ment or anthropometric) is statistically independent of the othercomponents. One can introduce nonlinear combinations of thedescriptors to introduce nonlinear interdependences betweendescriptor variables. One issue with such models is how to de-termine the right set of nonlinear combinations.

D. Weight-Scaled Models

A commonly used technique to adjust for interperson dif-ferences is to scale the energy expended by the individualby an exponent of their weight, Weights . All participants arethen merged into a single pseudoparticipant with each orig-inal energy expended value ynp

replaced by a scaled valueynp ,scaled= yn p

Weights , s ∈ [0.1, 1.5]. The set of all energy val-

ues Yp are thus Y′p = [ y1p ,scaled y2p ,scaled . . . yNp ,scaled ]T ∈

RNp ×1 and movement descriptors Xp remain the same. Theoriginal problem

(xnp

,Physp

) f→ ynp∀np ∈ {1, 2, . . . Np} is

then recast as as personal regression model problemxnp

f ′→ ynp ,scaled . In contrast to the multivariate regression ap-

proach, this technique scales the output space before traininga regression model. A potential limitation with this approachis that it does not allow the incorporation of other anthropo-metric parameters or nonlinear combinations of anthropometricparameters.

E. Nearest-Neighbor Models

One approach to incorporate an arbitrary combination ofanthropometric parameters is to extend the personal modelapproach with nearest neighbor-based interpolation. Here, topredict energy expenditure for a person p, a personal modelsuch as in Section III-B is learned from a person p

′who

is “closest” in anthropometric similarity to person p. To de-rive a measure of closeness, given the anthropometric ma-trix, PHYS = [PhysT

1 PhysT2 . . .PhysT

P ]T , we calculatea space of reduced dimensionality using principal componentanalysis [41]. We first normalize the anthropometric matrix byensuring that each column (corresponding to an anthropometricdescriptor) has zero mean and unit variance. We then apply thePCA transform and preserve the first three dimensions (82% ofvariance preserved). Each point in this space corresponds to aperson p. In this reduced space, for a given person p, the datafrom the closest person p′ as measured by the Euclidean distance

Fig. 2. Graphical model showing the relationship between variables in a HLM.A two-level dependence is assumed. At the lower, intraperson level, a linear re-lationship between a person’s movement and energy consumption is formulated.At the higher, interperson level, the model parameters themselves are linearlydependent on the anthropometric descriptors and population parameter k.

were used to train a model. This model was then used to predictenergy expenditure using the input data for person p.

An issue with nearest-neighbor-based approaches is that theyare sensitive to the metric space under consideration. Also,heuristics are required to determine the right set of nearestneighbors. They also do not take into account the quality ofdata available from the nearest neighbor. What is needed is anapproach that consolidates the information that takes advantageof data from all the people in a population simultaneously. Thenearest-neighbor model can arbitrarily be extended to K-nearestneighbors. We show the results of just a single nearest neighboras an illustration of the technique.

Note on the Nearest-Neighbor Metric: After transforming thedata into lower dimensional space, two clusters correspondingto men and women were seen. The third dimension separatedthese clusters into two planes. Therefore, rather than applyingthe Euclidean distance to the three-dimensional (3-D) space, agender-specific 2-D Euclidean distance metric was used. Forexample, if person p was a woman, only other women wereconsidered for determining the closest person.

F. Hierarchical Linear Models

Another technique to consolidate information across peo-ple is a a two-level approach with hierarchical linear models(HLMs) [42]. Hierarchical Linear Modeling has been success-fully used in various biological systems for joint modelingacross a population [43]. The principle behind hierarchical lin-ear modeling is that the population of participants is dividedinto separate subgroups, and an individual regression model islearned for each subgroup. Also, Fig. 2 illustrates our approach.As in Section III-B, we assume that each output energy value,ynp

is linearly dependent on input xnp. This can be expressed

as

ynp∼ N

(ynp

;wTp xnp

, β−1p

)

∀np ∈ {1, 2, . . . Np} .


For each participant, we are also given anthropometric descrip-tors determined by Physp and the complete set for all P peo-ple, PHY = {Physp}P

p=1 . We model top-down dependenceof each person’s model parameters,wp on their anthropomet-ric descriptors Physp and a “population parameter” k. Eachcomponent wp,l , l ∈ {0, 1, . . . D} of wp has the distribution:

wp,l ∼ N(wp,l ;PhysT

p kl , α−1p I

)

l ∈ {0, 1, . . . D} .

where αp is a noise term that incorporates noise in the map-ping from Physp to wp,m . Each wp in turn influences energypredictions ynp

for an input xnpas before. Fig. 2 illustrates

the graphical representation of the hierarchical linear regressionmodel. If there are M anthropometric parameters (including aconstant), then km ∈ RM ×1 . Thus, the overall parameter matrixk = [ k1 k2 . . . kD+1 ] is an M × (D + 1) matrix.

1) Training the Model: Training the hierarchical linear re-gression model is equivalent to learning individual wp ’s, theoverall parameter k, as well as the noise parameters {βp}P

p=1 ,{αp}P

p=1 . For this, one must maximize the log-likelihoodbrkfunction:

L =P∑

p=1

(Np

2logβp +

M

2logαp

−(

βp

2‖Yp − Xpwp‖2

+αp

2

M∑

l=1

∥∥wp,l − PhysT

p kl

∥∥2

))

.

The posterior distribution of wp given the dataset {X,Y} is:

Sp =(αpI + βpXT

p Xp

)−1

μp = Σ−1p

(βpXT

p Yp + αpmp

)

mp,l = PhysTp kl .

Once again, the appearance of cross terms in the differentialof this log-likelihood does not allow direct estimates of the pa-rameters and variables. So, we resort to an approximate methodusing the EM algorithm. Algorithm 2 describes the algorithmwe use to learn this model.

2) Inference: Given the model, we predict energy values fora new person P + 1 with anthropometric parameters given byPhysP +1 , using

wP +1,l ∼ N(wP +1;PhysT

P +1kl , α−1P +1

)

∀l ∈ {0, 1, 2, . . . D}ynP + 1 ∼ N

(ynP + 1 ;w

TP +1xnP + 1 , β

−1P +1

)

∀np+1 ∈ {1, 2, . . . NP +1} .

We set αP +1 and βP +1 to be the average of αp ’s and βp ’s overall people.

In this way, given a person’s anthropometric parameters, theHLM generates a personalized set of parameters wP +1 similarto what a personal model would produce. These can then be

used to predict energy expenditure for person P + 1 given theirmovement.

3) Note on Initialization: Since there are a large number ofmodel parameters and the EM algorithm is guaranteed onlyto converge to a local optimum, proper initialization is a key.Fortunately, we have an intuitively good initialization set foreach of these parameters as the estimates given by the indi-vidualized model algorithm. Using Bayesian Linear Regres-sion, we train P individual models and obtain estimates for{wp ∼ N (μp,Σp) , αp , βp}P

p=1 . We then use these models totrain a higher level Bayesian linear regression model mappingindividual wp,l’s to kl’s across people. We feed these initialestimates into our model.

4) Intuition and Comparison With Multivariate Models:HLMs and multivariate models are parametric regression ap-proaches that find the best functional fit given data. The mul-tivariate model tries to reduce the error function: βp

2 ‖Yp −X′

pwcombined,p‖2 + αp

2 ‖wcombined,p‖2 . This effectively findsa least-squared fit wcombined,p that is as small in magnitude aspossible (to prevent overfitting). Thus, multivariate models canbe expected to perform well when the data are noisy.

HLMs can be considered a special case of multivariate mod-els where hierarchical constraints are imposed on the data. TheHLM tries to reduce the error function: βp

2 ‖Yp − Xpwp‖2 +


αp

2

∑Dl=0

∥∥wp,l − PhysT

p kl

∥∥2

. Similar to the multivariate case,it tries to find an individual least-squared fit wp so as to min-imize the “intraperson” error ‖Yp − Xpwp‖2 . But rather thantrying to find the smallest magnitude wp , it tries to find thewp that maintains interperson consistency. This is because eachcomponent of wp , wp,l has to simultaneously satisfy the con-

straint∥∥wp,l − PhysT

p kl

∥∥2

for the same kl across people. Thisintroduces nonlinear cross-dependences on the anthropometricparameters because of the interaction through parameter k. Thepopulation parameter k connects data from multiple individualsand consolidates information between individuals.

The predicted energy expenditure value for a person is aweighted combination of what the higher level predictions fromanthropometric descriptors (given by αpmp ) and what the indi-vidual participant’s movement descriptors (given by βpXT

p Yp ).The relative weightage of intraperson to interperson predictivecontributions is given by the ratio αp/βp . A smaller αp/βp

implies a greater dependence on “intraperson” parameters. Asmaller αp/βp implies a larger weightage to “interperson”parameters.

G. ACSM Speed-Based Models

In order to compare our approach with current state-of-the-art techniques, speed-based calorie predictions obtained fromthe ACSM Exercise Guidelines [44] were calculated on thecorresponding recorded speeds. The ACSM Exercise Guidelinesprovide a means to estimate calories expended from the speedof walk as

Energy(kcal/min) = ((13.4112 × Speed (m/h)) + 17.5)

× Weight (kg)/1000.

IV. EXPERIMENTAL EVALUATION

We applied the models described above in a case study todetermine energy expenditure from treadmill walking. Tread-mill walking was chosen because it allowed the easy capture ofrepeatable data of people walking at different speeds in steady-state conditions. This allowed us to focus on the relative meritsof each algorithm before generalizing to overground walking.

A. Population Characteristics

Data were collected on a total of 34 participants (25 male,9 female). All participants signed informed consent forms andthe study was approved by the Institutional Review Board ofthe University of Southern California. Fig. 3(a) describes par-ticipant statistics. All the models were developed using datafrom this population. Each participant’s height was measuredwith a wall-based height chart, and weight was measured withthe EatSmart Precision Digital weighing scale. Body mass in-dex was extracted from these measures. Average height was1.74 ± 0.07 m (minimum of 1.56 m and maximum of 1.85 m),average weight was 69.8 ± 7.6 kg (minimum of 55.9 kg andmaximum of 90.2 kg), average age was 26 ± 4 years (mini-mum of 18 years and maximum of 33 years), average BMI was23.0 ± 1.6 (minimum of 20.8 and a maximum of 27.2).

Fig. 3. Illustration of hardware, ground truth collection, and population statis-tics. (a) Characteristics of study population plotted as height versus weight withnormal and overweight regions shown. Men are shown as triangles and womenare shown as circles. (b) Each participant walked on a treadmill for three speeds.Triaxial accelerations were recorded with a phone on the right iliac crest. Energyexpenditure was measured with the Oxycon portable metabolic unit. (c) Inten-sity of movement was measured using the Y-axis periodogram of accelerometerdata for each 10-s epoch as it closely corresponded to energy expended. Thiscorresponded to Up–Down movement of the person and was robust to shift ofthe sensor. The average step-frequency of walking for each epoch was extractedusing the y-axis information and used as a movement descriptor.

B. Data Capture

Each participant p, wore a Galaxy Nexus S phone runningAndroid 2.3.3 on the right iliac crest with a belt holder torecord movement. Accelerometer data were captured with acustom-built smartphone app—Movement Trackr [45]. The apprecords triaxial accelerometer data at a set sampling rate. Forthe purpose of this study, the accelerometer settings were set at“Fastest” (50 Hz). A Butterworth bandpass filter with 3 dB cutoff


between 0.75 and 2.3 Hz was applied to the raw accelerome-ter data. Energy expenditure was measured using the OxyconMobile Metabolic unit from Carefusion. The unit was worn as abackpack fitted to the comfort of the participant. The metabolicunit reports participant V O2 and V CO2 and derived caloriedata at the frequency of every breath. Calories were estimatedusing the Weir equation [46].

The participant was asked to sit still and meditate for 5 min,while energy expenditure and heart rate data were collected atthe frequency of the every breath. These were averaged to obtainenergy expenditure when sedentary or sedentary energy expen-diture (SEE) and sedentary heart rate (SHR), respectively. Theparticipant then walked on a treadmill at three speeds—1.12,1.34, and 1.56 m/s (corresponding to 2.5, 3.0, and 3.5 m/h) for6 min per speed with 2 min of settling time between speedsto reach the steady state. Phone data were synchronized withmetabolic unit data in postprocessing. Data streams consistingof triaxial accelerometer and energy expenditure data that cor-responded to walking were segmented out. These were furthersegmented into separate steady-state walking subsections cor-responding to each speed.

C. Data Processing

For each sub-section, data were divided into 10 second inter-vals or epochs εnp

, np ∈ [1, Np ]. For each epoch, a 1024 pointperiodogram for the Y-axis was calculated from the accelerom-eter data. This corresponded to the up–down movement of theparticipant. The periodogram coefficients corresponding to fre-quencies greater than 2.5 Hz were discarded. The average stepfrequency for epoch εnp

was calculated by extracting the fre-quency corresponding to the highest magnitude in this domain.The extracted step frequency, step-frequency squared, and aconstant term were used as the descriptors of movement xnp

corresponding to epoch εnp, for that person p. The energy expen-

diture for that epoch ynpwas obtained by averaging metabolic

unit values for εnp. This was repeated for each epochs and the

complete input and output data {Xp ,Yp}were obtained for thatparticipant. The complete set of anthropometric descriptors forthis participant, Physp consisted of height, weight, BMI, SHRSEE.

V. RESULTS AND DISCUSSION

A. Evaluation Methodology

We used a 1-of-K methodology to rank the predictive capa-bility of an algorithm. Given a population of P participants,each participant in turn was selected to test the algorithms. Foreach participant p, 60% of the data were randomly sampled astraining data, the remaining constituting test data. The personalmodel described in Section III-B was learned from this trainingdata and as a reference. Data from P − 1 participants were usedto train either a nearest-neighbor, weight-scaled, speed-basedmodel, multivariate model, or an HLM with a specific com-bination of anthropometric descriptors. Each combination ofanthropometric descriptors was a different hierarchical model.All models were used to predict energy expenditure on the test

data for participant P and the root-mean-squared (RMS) errorfor each model was calculated. This was repeated with dif-ferent randomly sampled data over 20 iterations and the errorcalculated each time. This represented performance per partic-ipant. The mean of the root-mean-squared error was calculatedacross all iterations. This error represented the performance ofeach algorithm for participant p. This error was divided by themedian energy expenditure value of the test data to obtain anormalized error. This was done to provide a percentage-likemetric to determine algorithm performance. This was repeatedfor each participant in the population and the errors were av-eraged across all participants to obtain the normalized averageroot-mean-squared error (ARMSE).

B. Dependence on Anthropometric Descriptors

Given five anthropometric descriptors, we evaluated algo-rithm performance with all possible combinations of descriptorsresulting in 63 different hierarchical and multivariate modelseach. When using anthropometric descriptors we also consid-ered squared and cross terms up to quadratic. This was basedon the intuition that a nonlinear functional dependence on an-thropometric descriptors could be approximated by a Taylorseries. We used personal regression and speed-based models forreference. The order of introduction of descriptors was SEE,SHR, BMI, Weight, and Height. Each descriptor combinationwas assigned a number corresponding to a binary encoding ofthat combination. For example, a number of 25 corresponded toa binary encoding of 10101 or SEE, BMI, and height.

Fig. 4(a) illustrates the variation of errors with different de-scriptor combinations as identified by the encoding along withnearest-neighbor, speed-based, and personal models for com-parison. The lowest errors were obtained when all the descrip-tors were used. Nearest-neighbor models showed highest errors.This could be to the lack of sufficient neighbors close enough toa particular participant due to a smaller population. With respectto the HLM, the earlier descriptor combinations correspond tousing SEE, SHR, and sex alone. These descriptor combinationsresulted in errors that were higher than multivariate, speed-basedmodels, and nearest neighbor models. Prior to introducing size-based features, multivariate models out-performed HLMs andwere more robust to error-scaling as measured by lower errors.Size-based descriptors were introduced from parameter number8. Once size-based descriptors such as BMI, weight, and heightwere introduced, the errors reduced and were more consistent.

Fig. 4(b) illustrates the relative performance of multivariatemodels and hierarchical linear models once size-based featureswere introduced. It can be seen that whenever weight was in-troduced, the hierarchical model outperformed the multivariatemodel (p < 0.1 per participant). The HLM is a more restrictedmodel than the multivariate model and is therefore more proneto overfitting. This is also why the multivariate models are morestable when descriptors such as gender are used, they treat theanthropometric descriptor as noise and reduce to a single re-gression model for all participants. However, given the rightanthropometric descriptors, the HLM is able to take advantageof the interparticipant consistency requirement to produce more


(a) (b)

Fig. 4. Relative performance of algorithms as measured by normalized average root mean-squared error (NARMSE). Lower is better. Individual descriptorscorresponded to parameters 1 (SEE), 2 (SHR), 4 (sex), 8 (BMI), 16 (Weight), and 32 (Height). Height and weight correspond to parameter 48. HLM descriptorscorresponding to SEE, SHR, and sex were poor anthropometric descriptors to derive a personal model from. Size-based descriptors such as weight, height, andBMI showed higher accuracy. Nearest-neighbor models showed the highest error followed by ACSM-based models. Hierarchical models performed better thanmultivariate models once size-based features werere introduced (p < 0.1 per participant). The dependence of hierarchical models on the right descriptor (weight)suggests a technique that uses weight as an entry-level feature to split populations before simpler regression models are applied. (a) Comparison of normalizationmodels. (b) Comparison of multivariate and hierarchical models for size-based features.

Fig. 5. Illustration of the performance of weight-scaled model compared withHLMs and personal models. The best HLM showed the same level of perfor-mance as weight-scaled models with an exponent 1.4. When evaluated on aper-person basis, the exponent showed a high variation (1.2 ± .6) indicatingthat a single weight scale is not appropriate across all users.

accurate results. The dependence of hierarchical models on theright descriptor (weight) also suggests a technique that usesweight as an entry-level filtering descriptor to split populationsbefore simpler regression models are applied.

Weight-scaled models were also compared. Fig. 5 illustratesthe variation of mean of errors with the weight exponent. Thebest HLM showed the same level of performance as weight-scaled models with an exponent 1.4. However, when evaluatedon a per-person basis, the exponent showed a high variation(1.2 ± .6) indicating that a single weight scale does not workequally well across all users. This needs further study. For theremainder of this paper, we neglect nearest-neighbor models forthe sake of brevity.

C. Best Individual Descriptor

We used the HLM to evaluate the best individual anthropo-metric descriptor to generate an accurate, personalized energymodel from movement to energy expenditure. For each par-ticipant, the ARMS errors of the HLM corresponding to eachdescriptor combination, were sorted in an ascending order and

Height Weight BMI Sex RHR REE15

20

25

30

35

40

45

50

Different Physiological Features

← A

vera

ge S

core

MeanMedian

Fig. 6. Average score across participants for each individual descriptor. De-scriptor combinations were ranked according to the ARMS errors that theyproduced and the ranking per descriptor was extracted and averaged across par-ticipants. Lower is better. Weight and height showed the lowest ranking, whilesex, SEE, and SHR showed the highest rankings. The effect of sex was absorbedby the weight and height since the population on average weighed less and wereshorter.

assigned a rank. For each error in this order, the descriptorscorresponding that error were awarded a score equal to the errorrank. For example, if weight and height appeared in the thirdlowest error, they both received a score of 3. This was calculatedfor each error in the ranking. The average of all scores awardedto each descriptor was calculated and represented the relativeperformance of that individual descriptor. This was repeatedfor each participant. The intuition behind this scheme is thatif the appearance of a particular descriptor results in the lowererrors, it will appear in the beginning of the sorted list moreoften. Hence, a lower score for an anthropometric descriptorimplies greater importance in personalizing a person’s energyexpenditure model.

Fig. 6 shows the comparative mean ranking (filled square)with standard deviation for each individual descriptor across allusers. Median is also shown for reference (cross). Weight andheight were the best individual descriptors with the lowest score.This indicates that size-based descriptors are the best descriptors


20 40 60 800.05

0.1

0.15

0.2

0.25

Percentage Training Data

Nor

mal

ized

RM

SE

(no

unit)

HLM MeanHLM MedianBLRMultivariate

(a) (b)

Fig. 7. Illustration of the predictive capability of each algorithm when limited training data were available. Lower is better. Hierarchical models performed aswell and in some cases were better than personal models. However, they were able to achieve this with no prior information about the participant other than theiranthropometric descriptors. (a) The hierarchical model performed better than the personal model when no or limited training data were available (p < 0.05 perparticipant). With more data, the personal model performed better. (b) The personal model showed the lowest error when predicting the intermediate speed of1.34 m/s. This shows that personal models show the best predictive capability when data from extreme values is available. ACSM speed-based models showedhighest RMS errors at higher speeds. Hierarchical models showed uniform predictive capability across all speeds.

to generate a model. Sex had the next highest score. This couldbe because women in our study were on average shorter andweighed less than men and this difference was absorbed in thesize based descriptors. Even though BMI is derived from heightand weight, it did not result in a lower score. This could bebecause even though BMI is calculated starting from weight, itscales weight based on height. This cancels out the differencesbetween people.

These results agree with the previous literature that shows thatin the context of weight-bearing activities such as walking, bodyweight is the main contributor to estimating energy expenditure.For example, given a very tall and thin person and a small andthin person, the tall person will consume much more energy.This is reflected by both body weight and height. Thus, the useof BMI is relevant in determining obesity rates, but is not a gooddescriptor in the context of predicting energy expenditure.Thiscould be because the relative contribution of weight and heightare mitigated by the mathematical transformation of BMI. SEEand SHR showed high scores indicating that rest-based descrip-tors are not good descriptors for generating a model.

D. Predictions With Reduced Training Data

We extended our study to examine the variation of predictivecapacity of each algorithm with reduced data. Fig. 7(a) describesthe performance of the hierarchical model versus the personalmodel (p < 0.05 per participant) with increasing training data.When small amount of training data were available, the hierar-chical model performed better than the personal model. How-ever, once more training data were available, the personal modelout-performed the hierarchical model. HLMs performed betterthan MLRs (p < 0.1 per participant).

A second experiment tested the ability of each algorithm inabsence of data corresponding to a particular speed. Instead ofrandomly sampling the data as described in Section V-A, weused training data corresponding to two out of three speeds andtrained a personal model with that data. All the general modelswere trained exactly as described before. Testing was done onthe third speed. This was repeated for all possible combinations

of speeds and the corresponding RMS error was calculated. Theresults are shown speed-wise in Fig. 7(b).

In the figure, each group represents RMS error when thatparticular speed was excluded from the training data. The in-terpolation capability of the individualized model was the bestwhen predicting the 1.34 m/s and poorest at 1.56 m/s. Intuitively,this can be understood as the best interpolation capability can beobtained when using training data from the extrema of speedsavailable. The second best error for personal models was ob-tained when higher speeds were used and tested on the lowestspeed. Hierarchical models showed lesser variance in predic-tive capability across speeds. This indicates that when trainingdata from either extreme is not available, it would be preferableto use HLMs. ACSM speed-based models showed increasinglyhigher errors with increasing speed indicating their unsuitabilityfor predicting energy expenditure at higher speeds.

It is important to note that in both these cases, the hierarchicalmodel does not have access to any person-specific training datafrom the participant. Despite this, the model performs compa-rably and in some cases out-performs a personal model that hasaccess to training data in all stages.

VI. CONCLUSION

Accurate, objective, and personalized measures of energy ex-penditure due to walking would aid in interventions to promotemore physical activity. Phone-based accelerometers provide thecapability to determine such measurements under free-livingconditions. Mapping movement descriptors measured with ac-celerometers to energy expended can be framed as a regressionproblem. An issue with current regression techniques is howone can normalize regression maps to account for physical dif-ferences between individuals. This paper described a family ofregression techniques that normalize the data based on the prin-ciple of similarity between individuals. Our chief contributionsare summarized as:

Mathematical formulation of the problem of normaliza-tion: We cast the problem of normalization of regressionmaps in a mathematical framework and then described various


regression models using this framework. These includednearest-neighbor models, weight-scaled models, a set of HLMs,multivariate models, and speed-based approaches. The relativemerits and demerits of these approaches were also described.

Model comparison of algorithms: We performed a compara-tive analysis of the normalization capability of these algorithmstaking the example of treadmill walking on a population of34 participants. Given the population, nearest-neighbor modelsshowed highest errors. Descriptor combinations correspondingto SEE, SHR, and sex alone resulted in errors that were higherthan speed-based models and nearest-neighbor models. Size-based descriptors such as BMI, weight, and height producedlower errors. This indicates that among our chosen descriptorset, size-based descriptors such as weight and height were thebest available to generate personalized models. The best HLMshowed the same level of performance as weight-scaled modelswith an exponent 1.4. However, when evaluated on a per-personbasis, the same weight exponent could not be used. When com-paring HLMs and multivariate models, HLMs performed betteronce weight was introduced. This could be because the HLMwas able to take advantages of the dominance of weight as asimilarity measure in normalizing models and use it to generatebetter models. This also suggests a hierarchical approach whereweight is used as an initial feature before applying simpler linearmodels.

Evaluation of the best descriptor combination: We used theHLM to determine the best individual descriptor to describea person. Weight was the best individual descriptor followedby height. This agrees with the literature. Sex, SEE, and SHRshowed the highest rankings. The effect of sex was absorbed bythe weight and height since women in the population were onaverage shorter and lighter than men.

VII. FUTURE WORK

We plan to expand our work in a number of directions. Ourapproach uses mobile phone-based accelerometers to estimatemovement. In this study, we used the phone in a constrainedposition on the human body. This does not mimic the everydayusage of mobile phones. We aim to expand on this study toderive techniques that robustly estimate step frequency-basedmovement descriptors independent of location on the humanbody. We plan on extending state of the art techniques in this do-main [47]. Another limitation in our approach is that by choosingtreadmill walking as our example activity, we do not completelymimic walking under free-living conditions. In addition to de-veloping robust features, we will expand the validation of thealgorithms developed to free-living walking conditions. Doingso will allow us to implement a phone-based personalized en-ergy expenditure monitor for walking that is robust to locationand placement.

We also aim to expand our modeling capability by includingother contextual information such as walking up or down a slopeto further fine-tune our models. Another direct extension of ourstudy is to develop similar models for other kinds of activitiessuch as running, cycling, or general household tasks. For eachactivity, our goal is to derive the right movement and anthropo-metric descriptors to accurately model energy expenditure. We

also plan on combining these with robust classifiers of humanactivity.

We aim to expand the capability of the model to combine thebenefits of nearest-neighbor and hierarchical approaches. Weplan on replacing the upper linear layer with a kernelized re-gression layer. The intuition behind this approach is that peoplewith similar anthropometric traits will generate similar maps.The kernelized layer will allow us to directly operate in sim-ilarity space without explicitly modeling nonlinear functionsof anthropometric descriptors. We also plan on expanding theactivities tested and the use of other descriptors such as heartrate during movement. This will include a similar analysis forthe case of overground walking and also generalizing to anyperiodic activity.

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Harshvardhan Vathsangam received the B. Tech.degree in engineering physics from the Indian Insti-tute of Technology Madras, Chennai, India, in 2008,the M.S. and Ph.D. degrees in computer science fromthe University of Southern California, Los Angeles,CA, USA.

He is currently a Postdoctoral Research Associatewith the Robotic Embedded Systems Laboratory,Viterbi School of Engineering, University of South-ern California. He received the Annenberg GraduateFellowship. His research interests include the appli-

cation of statistical machine-learning techniques in sensing for healthcare.

E. Todd Schroeder received the B.S. degree in hu-man anthropometric characteristics from the Univer-sity of California at Davis, Davis, CA, USA, in 1992,the Ph.D. degree in biokinesiology from the Univer-sity of Southern California (Clinical Exercise anthro-pometric characteristics), Los Angeles, CA, in 2000.

He is currently an Associate Professor of ClinicalPhysical Therapy at the Division of Biokinesiologyand Physical Therapy, University of Southern Cal-ifornia. His primary research interest includes themechanisms whereby progressive resistance training

and testosterone treatment stimulate protein synthesis and improve muscle qual-ity in older persons. Additional research interests include understanding themechanisms (signals/factors) associated with eccentric resistance exercise thatinduces hypertrophic adaptations and the implications of such exercise in olderindividuals to optimize rehabilitation.

Gaurav S. Sukhatme received the B. Tech. degreein computer science and engineering from the IndianInstitute of Technology Bombay, Mumbai, India, andthe M.S. and Ph.D. degrees in computer science fromthe University of Southern California (USC), Los An-geles, CA, USA.

He is a Professor of computer science (joint ap-pointment in Electrical Engineering) at the USC. Heis the Codirector of the USC Robotics Research Labo-ratory and the director of the USC Robotic EmbeddedSystems Laboratory which he founded in 2000. He

received the NSF CAREER award and the Okawa foundation research award.He is the Editor-in-Chief of Autonomous Robots and has served as an AssociateEditor of the IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, the IEEETRANSACTIONS ON MOBILE COMPUTING, and on the editorial board of IEEEPERVASIVE COMPUTING.

hierarchical approaches to estimate energy expenditure using phone-based accelerometers

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