Smartwatch User Authentication by Sensing Tapping Rhythms and Using One-Class DBSCAN

. 2021 Apr 2;21(7):2456. doi: 10.3390/s21072456

Algorithm 1 One-Class DBSCAN

Input:

D: The dimension of the vector.

m: The size of the training data.

{ $x^{(1)}, x^{(2)}, \dots, x^{(m)}$ }: Training dataset

$ϵ$ : The parameter of One-Class DBSCAN, which means that the distance is $ϵ$ .

$M i n P t s$ : The parameter of One-Class DBSCAN, which is the minimum number of data vectors within the distance $ϵ$ required to form a core object.

Function:

1:
for $i = 1, 2, \dots, m$ do
2:
for $j = 1, 2, \dots, D$ do
3:
$x_{j}^{(i)} = x_{j}^{(i)} / \sum_{k}^{D} x_{k}^{(i)}$
4:
end for
5:
end for
6:
Initialize the set of core objects $Ω = \emptyset$
7:
for $i = 1, 2, \dots, m$ do
8:
$N_{ϵ} (x^{(i)}) = \emptyset$
9:
for $j = 1, 2, \dots, m$ do
10:
$d i s = ‖ x^{(i)} - x^{(j)} ‖_{2}$
11:
if $d i s \leq ϵ$ then
12:
$N_{ϵ} (x^{(i)}) = N_{ϵ} (x^{(i)}) \cup {x^{(j)}}$
13:
end if
14:
end for
15:
if $∣ N_{ϵ} (x^{(i)}) ∣ \geq M i n P t s$ then
16:
$Ω = Ω \cup {x^{(i)}}$
17:
end if
18:
end for
19:
if $Ω = \emptyset$ then
20:
Initialize vector v
21:
for $j = 1, 2, \dots, D$ do
22:
$v_{j} = \frac{1}{m} \sum_{k}^{m} x_{j}^{(k)}$
23:
end for
24:
$Ω$ = {v}
25:
end if

Output:

$Ω$ : The set of core objects