IEEE Systems, Man and Cybernetics Magazine - April 2020 - 17

Algorithm S21. siVAT+ [78].
Input :
				
				
				
Output:

X = " x 1,f, x N , 1 R p -  High dimensional big data
k l -  Overestimate of true number of clusters
n -  Number of approximated samples
a -  A fraction of N, 0 1 a 1 1
D nl)# n - siVAT + reordered dissimilarity matrix

	 1	% % MMRS+  Sampling % %
	2	// Select the indices m  of kl  distinguished MM objects
	3	M = 4
	4	Randomly select the initial object, x m ! X
	5	M ! M , " x m ,
	 6	for i = 2 to kl do
	 7		 Randomly generate n s = ^aN h sized sample Y from X
	 8			 Y (i ) = " y (1i ),f, y n(i ) ,
0

0

s

	 9		Compute distance of each data point of sample Y (i ) to the closest element of existing M, z (i ) = ^min " r (mi) 1, r m(i ) 1,f, r (mi)1 ,,
min " r (mi) 2, r (mi) 2,f, r (mi)2 ,,f , min " r (mi ) n , r (mi ) n ,f, r m(i )n ,h = ^z 1(i ),f, z n(i )h
	10		
m i = )argmax 1 # j # n z (j i )   // Choose the farthest (- distinguished) object in Y (i )  from existing M
M ! M , " x (m ) ,   // Update M with new d
	11		
- istinguished object x (m ), where ^m i h =  index of y (mi) in X
	12	 end
	13	 // Group  n s  random objects in O  with its nearest distinguished object
	14	 Randomly generate n s  sized (intermediate) sample S int
	15	Compute w it -  distance of each distinguished object m i ! M to each data point  ! S int
	16	 Z 1 = Z 2 .... = Z k l = 4
	17	 for t = 1 to n s do
l = )argmin 1 # i # k l " w it ,
	18		
Zl = Zl , " t ,
	19		
	20	 end
	21	 // Randomly select data from S int near each distinguished point to obtain the n number of samples
	22	 n i = ^n #u Z iu/n sh i = 1, 2,f, k l
	23	Draw n i unique random indices from Z i to build sample Z il
1

1

2

1

i

s

2

s

i

s

2

i

s

s

i

i

i

kl

	24	 S = ' Z il
i =1

	25	%% Cluster Assessment %%
	26	 Compute  D n = dist ^x S, x S h
	27	 Apply VAT/iVAT on  D n ,  returning  D nl), P, c  (MST edge cuts)
	28	 Choose the number of clusters k using image of D nl)

Algorithm S22. Fast Ensemble siVAT (FensiVAT) [91].
Input :
				
				
				
				
Output:

X = " x 1,f, x N , 1 R p -  High dimensional big data
q -  down-space dimension
k l -  Overestimate of true number of clusters
n -  Number of approximated samples
Q -  number of random projections (RPs)
D nl)# n - FensiVAT reordered dissimilarity matrix

	 1	% % data set generation in down space % %
	 2	Generate down-space data sets Y 1 R N # q using Y = _ 1/ q i XT, where T ! R p # q is a random matrix
	 3	% % Near-MMRS Sampling: MMRS on Y % %
	4	Randomly select the first distinguished object x m
	 5	Distance of x m from N points, z = ^z 1,f z N h = " dist ^x m , x 1 h,f, dist ^x m , x N h, = ^rm 1,.... rm N h
	6	Calculate the distance of x m from N points, (rm 1,.... rm N )
	 7	for i = 1 to kl do
	 8		 z ! ^min " z 1, rm 1 ,,f, min " z N , rm N ,h
	 9		 m i = )argmax 1 # j # N z j
	10	 end
	11	 Group each object in O with its nearest distinguished object
	12	 Z 1 = Z 2 .... = Z k l = 4
0

0

0

j

i-1

j

0

0

0

j

i-1

	

Ap ri l 2020

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE	

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IEEE Systems, Man and Cybernetics Magazine - April 2020

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