IEEE Systems, Man and Cybernetics Magazine - April 2020 - 15
1 Input-Output: A, B, E, Pn + 1, d n + 1, Fn + 1, G, H
2 Pn + 1 = " Pn + 1,w 2 ,; d n + 1 = " d n + 1, z 2 ,; Fn + 1 = " Fn + 1,v 2 ,
3 G = " G, Pos ^w 2 h,
4 if w 2 = A 1 then
5 C = LongestSubsequence ^Pn, Pn + 1 h (algorithm S11)
6 B = Pn \C
7 while length ^H h 2 length ^B h do
8 delete H 1
9 end
10 E = Pn + 1 \ " n + 1 , \C
11 else
12 E = " E,w 2 ,
13 end
14 delete w 2 from A
Algorithm S14. Procedure M3.
Input : z 3 - minimum distance from G3
w 3 - closest point index from G3
v 3 - MST connection index from G3
1 Input-Output: A, B, E, Pn + 1, d n + 1, Fn + 1, G, H
2 Pn + 1 = " Pn + 1,w 3 ,; d n + 1 = " d n + 1, z 3 ,; Fn + 1 = " Fn + 1,v 3 ,
3 G = " G, Pos ^w 3 h,
4 if w 3 = A 1 then
5 C = LongestSubsequence ^Pn, Pn + 1 h (algorithm S11)
6 B = Pn \C
7 while length ^H h 2 length ^B h do
8 delete H 1
9 end
10 E = Pn + 1 \ " n + 1 , \C
11 else
12 E = " E,w 3 ,
13 end
Algorithm S16. Decremental VAT
(dec-VAT).
Input : D )n - n # n VAT reordered dissimilarity matrix for X n
Pn - VAT reordering indices of D )n
d n - MST cut magnitude order of D )n
Fn - MST connection indices of D )n
x p - point to remove
Output: D *n - 1 - ^n - 1h # ^n - 1 h VAT reordered dissimilarity
matrix for X n - 1
Pn - 1 - VAT reordering indices of D )n -1
d n - 1 - MST cut magnitude order of D )n -1
Fn - 1 - MST connection indices of D )n -1
1 Find the position i of x p in Pn
2 i = arg ^Pn = p h
3 Find the data points ^J h and their indices ^ I h in
Pn , that are connected to x p in the MST of D )n
4 I = arg ^Fn = i h; J = Pn
I
5 if J = 4 then
6 ^D )n - 1, Pn - 1, d n - 1, Fn - 1 h = LeafNodeRemove ^D )n, Pn,
d n, Fn, i h
(algorithm S17)
7 else
8 if i = Pn then
9 Pn - 1 = " Pn ,; d n - 1 = 4; Fn - 1 = " 1 ,
10 A = " Pn , Pn ,f, Pn ,
11 C = " Pn , Pn ,
12 B = Pn \C
13 E = 4
14 G = {2}
15 H = " Fn , Fn ,f, Fn ,
16 k = arg ^J = Pn h; delete J k
17 else
18 Pn - 1 = " Pn , Pn ,f, Pn ,; d n - 1 = " d n , d n ,f, d n ,;
Fn - 1 = " Fn , Fn ,f, Fn ,
19 A = " Pn , Pn ,f, Pn ,
20 C = " Pn , Pn ,f, Pn ,
21 B = Pn \C
22 E = 4
23 G = " 1, 2,f, i - 1 ,
24 H = " Fn , Fn ,f, Fn ,
25 end
1
2
3
4
1
2
3
Algorithm S15. Incremental iVAT
(inc-iVAT).
Input : D )n + 1 - ^n + 1h # ^n + 1 h inc-VAT reordered
-dissimilarity matrix for X n + 1
D nl) - n # n iVAT dissimilarity matrix for X n
i - insertion index of the new data point x n+1
in Pn + 1
Output: D nl)+ 1 - ^n + 1h # ^n + 1 h inc-iVAT dissimilarity
matrix for X n + 1
1 c = " 1, 2,f, i - 1 ,
2 D nl)+ 1 = D nl )
cc
cc
3 for r ! i to n + 1 do
4 j = argmin " D )n + 1 ,
4
n
2
1
2
1
i+1
i-1
2
i+1
1
14 delete w 3 from A
n
i+2
2
i+2
1
2
i-2
i-1
n
i
n
26 while A ! 4 do
27 if B 1 = J 1 then
28 ^A, B, E, Pn - 1, d n - 1, Fn - 1, G, H, J h =
SpecialInsert ^A, B, E, Pn - 1, d n - 1, Fn - 1, G, H, J,
D )n, Pn, d n, Fn h (algorithm S18)
29 else
30 ^A, B, E, Pn - 1, d n - 1, Fn - 1, G, H, h =
DecInsert ^A, B, E, Pn - 1, d n - 1, Fn - 1, G, H, D n) , Pn,
d n, Fn h
(algorithm S19)
31 end
32 end
33 D )n - 1 = D )n
34 end
G, G
rm
1 # m # r-1
)
)
n +1r j
n +1r j
5 D l = D
6 c = " 1, 2,f, r - 1 , \ " j ,
7 D nl)+1 = max {D n) + 1 , D nl)+1 }
8 D nl)+1 = D nl)+1
9 end
rc
rc
rj
jc
cr
Ap ri l 2020
IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE
15
IEEE Systems, Man and Cybernetics Magazine - April 2020
Table of Contents for the Digital Edition of IEEE Systems, Man and Cybernetics Magazine - April 2020
Contents
IEEE Systems, Man and Cybernetics Magazine - April 2020 - Cover1
IEEE Systems, Man and Cybernetics Magazine - April 2020 - Cover2
IEEE Systems, Man and Cybernetics Magazine - April 2020 - Contents
IEEE Systems, Man and Cybernetics Magazine - April 2020 - 2
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IEEE Systems, Man and Cybernetics Magazine - April 2020 - Cover3
IEEE Systems, Man and Cybernetics Magazine - April 2020 - Cover4
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