Why Temporal Persistence of Biometric Features, as Assessed by the Intraclass Correlation Coefficient, Is So Valuable for Classification Performance

. 2020 Aug 14;20(16):4555. doi: 10.3390/s20164555

Algorithm 1 Creating Synthetic Features.

Input: N (subjects), K (features),

I C C_{T a r g e t}

Output: 3-dimensional (

N \times K \times 2

) feature matrix

X_{i j s}

with desired correlation structure
for

j = 1, \dots K

for

i = 1, \dots N

Set

X_{i j 1} = Z

where Z is a random standard normal deviate.
Set

X_{i j 2} = X_{i j 1}

for

j = 1, \dots K

for

i = 1, \dots N

for

s = 1, 2

Set

X_{i j s} = X_{i j s} + W

; where W is a random normal deviate with mean = 0 and
standard deviation =

\sqrt{(1 - I C C_{T a r g e t}) / I C C_{T a r g e t}}

For each feature j, treat

X_{i j s}

as a single vector of length

N \cdot S

and apply a z-score transform
to ensure mean = 0 and standard deviation = 1