1. Body Weight-Normalized Energy Expenditure
Estimation using Combined Activity and
Allometric Scaling Clustering
Marco Altini, Julien Penders, Oliver Amft

2. Physical Activity Monitoring
-> Energy Expenditure
- Basal Metabolic Rate (BMR)
- Diet Induced Thermogenesis (DIT)
- Physical Activity Energy Expenditure (PAEE)
BMR BMR
DIT
DIT
PAEE PAEEinactive active

3. time (minutes)
0 20 40 60
51015
time (minutes)
0 20 40 60
0.00.51.01.5
0 20 40 60
6080100120140
Walking biking Running Sedentary Household
MotionintensityEnergyExpenditure
EE
ACC
HeartRate
Time (minutes)
HR
Walking biking Running Sedentary Household
Walking biking Running Sedentary Household

4. Accelerometer
Features
Activity Recognition
Anthropometric
Characteristics (e.g. Body
Weight)
Activity 1 Model
Activity N Model
Energy
Expenditure
Heart Rate
Activity-Specific Energy Expenditure
Models – Tool#1

5. Energy Expenditure, Health and Body
Weight
- Quantify Energy Expenditure
- > Understand relation between Physical Activity
and Health (e.g. How much activity do we need?)
Need for Normalization

6. 50 60 70 80 90 100
1012141618
Running
Body Weight (kg)
EE(kcal/min)
r= 0.86 *
50 60 70 80 90 100
5.05.56.06.57.07.5
Biking
Body Weight (kg)
EE(kcal/min)
r= 0.29
50 60 70 80
3456
Walking
Body Weight
EE(kcal/min)
r= 0.72 *
50 60 70 80 90 100
9.09.510.010.511.011.5
Body Weight (kg)
EE(METs)
r= -0.48 *
50 60 70 80 90 100
4567
Body Weight (kg)
EE(METs) r= -0.81 *
50 60 70 80
2.53.03.54.04.5
Body Weight
EE(METs)
r= -0.08
How To Normalize?
50 60 70 80 90 100
1012141618
Running
Body Weight (kg)
EE(kcal/min)
r= 0.86 *
50 60 70 80 90 100
5.05.56.06.57.07.5
Biking
Body Weight (kg)
EE(kcal/min)
r= 0.29
50 60 70 80
3456
Walking
Body Weight
EE(kcal/min)
r= 0.72 *
50 60 70 80 90 100
9.09.510.010.511.011.5
Body Weight (kg)
EE(METs)
r= -0.48 *
50 60 70 80 90 100
4567
Body Weight (kg)
EE(METs) r= -0.81 *
50 60 70 80
2.53.03.54.04.5
Body Weight
EE(METs)
r= -0.08
Body Weight Body Weight

7. Allometric Modeling -Tool#2
-> Relationship between body size and physiology
Power law
– y = EE, x = BW, k = constant
– If β = 1, classic normalization
• No optimal single coefficient
– Coefficients are activity-dependent
y = k X
-β

8. Toolbox Summary
• Activity-Specific Energy Expenditure models
• Allometric modeling
-> Combined these methods to normalize EE
1. What allometric coefficients to use?
2. How to group activities taking into account:
• Activity recognition task
• Allometric coefficients

9. 9
O2
CO2
Indirect Calorimeter

10. 10
ECG Necklace
ACC
HR

11. 11
19 Subjects, 48 Activities
Household Sport

12. biking 60 rpm lev high
biking 60 rpm lev low
biking 60 rpm lev med
biking 80 rpm lev high
biking 80 rpm lev low
biking 80 rpm lev med
cleaning table
cleaning windows
cooking
folding clothes
lying
moving boxes
PC work
reading
running 10 km/h
running 7 km/h
running 8 km/h
running 9 km/h
sitting
sitting desk work
stacking groceries
standing
vacuuming
walk carrying 4 kg
walking 3 km/h
walking 3 km/h 10% inc
walking 3 km/h 5% inc
walking 4 km/h
walking 5 km/h
walking 5 km/h 10% inc
walking 5 km/h 5% inc
walking 6 km/h
walking self-paced
washing dishes
watch TV
writing
1) What Allometric Coefficients?

13. 2) How To Group Activities?
• Multi-Objective Optimization Problem
– Grouping 48 activities into clusters according to
two criteria:
• Activity-Specific allometric coefficients
• Practical Activity Recognition
-> Unsupervised Clustering
– Genetic Algorithm (optimal k-means clustering)
– Features: signal power, motion intensity, β

14. Clustering Output
-3 -2 -1 0 1 2
-1.5-1.0-0.50.00.51.01.52.0
-1
0
1
2
3
normalzied allometric coefficient
normalizedMI
normaizedPow
cluster 1
cluster 2
cluster 3
cluster 4
cluster 5
running
walking
biking
0.05
0.80
0.7
0.55
0.99

15. EE Algorithm Implementation
Accelerometer
Features (time and
frequency domain)
Activity Recognition
SVM, distinguishes 5
clusters of activities
Cluster 1 Model
Cluster 4 Model
Energy
Expenditure
Heart Rate
Cluster 2 Model
Cluster 3 Model
Cluster 5 Model
95.1%
accuracy
1.05 kcal/min
RMSE

16. Evaluation
sitting
EEkcal/min
0.00.40.81.2
walking 5 km/h
0123456
biking 80 rpm
02468
running 10 km/h
0246812
EEkcal/min/kg
0.00000.00100.00200.0030
0.00000.00100.0020
0.000.020.040.060.08
0.0000.0020.0040.006
subj 8 subj 18
EEkcal/min/BWb
0.000.050.100.15
subj 8 subj 18
0.000.040.080.12
subj 8 subj 18
01234
subj 8 subj 18
0.000.100.200.30
No Normalization
• Prevents comparisons between groups and
individuals
• Prevents comparison within individuals
undergoing weight changes

17. Evaluation
sitting
EEkcal/min
0.00.40.81.2
walking 5 km/h
0123456
biking 80 rpm
02468
running 10 km/h
0246812
EEkcal/min/kg
0.00000.00100.00200.0030
0.00000.00100.0020
0.000.020.040.060.08
0.0000.0020.0040.006
subj 8 subj 18
EEkcal/min/BWb
0.000.050.100.15
subj 8 subj 18
0.000.040.080.12
subj 8 subj 18
01234
subj 8 subj 18
0.000.100.200.30
Simple Ratio between EE and BW (e.g. kcal/kg)
• Overcorrects
• Doesn’t capture activity-dependence

18. Evaluation
sitting
EEkcal/min
0.00.40.81.2
walking 5 km/h
0123456
biking 80 rpm
02468
running 10 km/h
0246812
EEkcal/min/kg
0.00000.00100.00200.0030
0.00000.00100.0020
0.000.020.040.060.08
0.0000.0020.0040.006
subj 8 subj 18
EEkcal/min/BWb
0.000.050.100.15
subj 8 subj 18
0.000.040.080.12
subj 8 subj 18
01234
subj 8 subj 18
0.000.100.200.30

19. Summary and Conclusions
• Energy Expenditure
– Objective quantification of Physical Activity
• Normalization
– Allometric coefficients
– Activity recognition feasibility
• New Opportunities for
– Comparisons between groups and individuals
– Comparison within individuals undergoing weight
changes

20. Body Weight-Normalized Energy Expenditure
Estimation using Combined Activity and
Allometric Scaling Clustering
Marco Altini, Julien Penders, Oliver Amft
Thank You