Human Activity Dataset Generation - Smartphone-Based Human Activity Recognition - page 68

Table 4.5 List of measures for computing feature vectors
Function

Description Formulation

N i = 1 s i

1

¯ s =

Mean ( s ) Arithmetic mean

N i = 1 (

2

˃ = s i −¯ s )

Std ( s ) Standard deviation

median i s i ) Mad ( s ) Median absolute deviation − median j ( s j

Max ( s ) Largest values in array max i ( s i )

min i ( s i )

Min ( s ) Smallest value in array

E s − s
˃

3

Skewness ( s ) Frequency signal skewness

E ( s − s )

4

E (

2 2

Kurtosis ( s ) Frequency signal kurtosis

s −¯ s )

MaxfreqInd ( s ) Largest frequency component argmax i ( s i )

N i = 1 s i

1

Energy ( s ) Average sum of the squares

3 i = 1 j = 1 s i , j

1

Sma ( s 1 , s 2 , s 3 ) Signal magnitude area

i = 1 (

/ j = 1 s j Entropy ( s ) Signal entropy c i log ( c i )) , c i = s i

Iqr ( s ) Interquartile range Q3 ( s ) − Q1 ( s )

4

( s )

a =

( s , ) , a ∈ R

Autoregression 4th order burg autoregression

coefficients

arburg 4

/ C 1 , 1 C 2 , 2 Correlation ( s 1 , s 2 ) Pearson correlation

coefficient

C 1 , 2 , C = cov ( s 1 , s 2 )

i = 1 ( is i ) / j = 1 s j

MeanFreq ( s ) Frequency signal weighted

average

1 i = a s i

1

EnergyBand ( s , a , b ) Spectral energy of a

frequency band [ a

a − b +

, b ]

tan − 1

( [ s 1 , s 2 , s 3 ] × v , [ s 1 , s 2 , s 3 ] · v )

Angle ( s 1 , s 2 , s 3 ,v) Angle between triaxial signal

mean and vector

N signal vector length, Q Quartile

Features were normalized in order to lie within the [ − 1 , 1] range following this

formulation:

x min
x max −

x 0 −

x = 2

x min −

1 , (4.2)

where x 0 is the original vector of features and the x min and x max vectors respectively
contain the minimum and maximum values for each feature from the available data.
In order to ease the performance assessment, the dataset was randomly parti-
tioned into two independent sets, where 70% of the data were selected for training
and the remaining 30% for testing. This partition was done at the level of number
of people and not the number of samples in order to guarantee that samples from
both groups were completely independent. Moreover, the protocol of activities was