Human Activity Dataset Generation - Smartphone-Based Human Activity Recognition - page 67

Table 4.4 Time and
frequency domain signals
obtained from the smartphone
sensors

Name Time Frequency

Body acc 1 1

Gravity acc 1 0

Body acc jerk 1 1

Body angular speed 1 1

Body angular acc 1 0

Body acc magnitude 1 1

Gravity acc mag 1 0

Body acc jerk mag 1 1

Body angular speed mag 1 1

Body angular acc mag 1 1

• Signal Magnitude Area : this measure helps to identify periods of activity over

a triaxial signal in the time domain. It is defined as the sum of the absolute
value of all axis divided by the number of samples N in a signal window

(Karantonis et al. 2006 ).

• Entropy : this measure of uncertainty commonly used in Information Theory is

applied to the signal s in the frequency domain and gives an estimation of the
amount of information this provides. It is estimated using the normalized infor-
mation entropy of the magnitudes of this signal (Ho 2004 ).

• Interquartile range : this statistical measure calculates the difference between the

upper ( Q 3 ) and lower quartiles ( Q 1 ) of a ranked set of elements. These quartiles
are the points that divide the data by 25 and 75% respectively.

• Autoregression coefficients : are the coefficients found through the Burg's method

that fit an autoregressive model of the input s (Roth et al. 2003 ). This operation
is applied to the signal in the time domain and produces an output of 4 features
corresponding to the algorithm order such as in (Khan et al. 2010 ).

• Pearson correlation coefficient : measures the relationship between two signal

vectors s 1 and s 2 . This statistical measure is bounded between the interval [ 1]

and denotes either a positive or negative correlation when this value is close to 1 or
−

− 1 ,

1 respectively, and no correlation when it is close to 0. We apply this operation
to the time signals from pair of axis from the accelerometer or gyroscope.

•

Signal weighted average : this measure gives the average frequency of a signal s
considering that each point contributes in proportion to its magnitude.

• Spectral energy of a frequency band : this function returns an energymeasure in a

similar way to the energy function but only within an interval of the frequency

signal. We selected contiguous intervals starting from zero with three different
bandwidths (8, 16 and 24 points).

( s )

• Angle between vectors : this measure gives an estimation of the angle between

the mean value of a triaxial time signal and a another vector (e.g. to measure the
angle of the average acceleration with respect to the y axis [0 .Itisusefulfor

determining the average orientation of the smartphone in every activity window.

, 1 , 0] )