IEEE Systems, Man and Cybernetics Magazine - April 2020 - 18

	13	 for t = 1 N do
l = )argmin 1 # i # k l " rm t ,
	14		
Zl = Zl , " t ,
	15		
	16	 end
	17	 Randomly select data near each distinguished point to obtain the n number of samples
	18	 n i = ^n #u Z iu/N h i = 1, 2,f, k l
	19	 Draw n i unique random indices from Z i to build sample Z il
i

kl

	20	 S d = ' Z il
i=1

	21	 % % Ensemble method to obtain a reliable iVAT image % %
	22	Generate Q , down-space data sets " S d,i ,Qi = 1 1 R q from S u 1 R p ^S d " S u h, using random matrices " Ti ,Qi = 1 ! R q # q,
  uS uu =uS du = n
	23	 Compute distance matrices  " D d,i ,Qi = 1 from  " S d,i ,Qi = 1
	24	 D n,d ! 0 (Initialize a n # n distance matrix)
	25	 for t = 1 Q do
W i = NormalizeRows ^D d,i h
	26		
Vi = 1/2 ^W i + W Ti h
	27		
	28		
D n, d = D n, d + V i
	29	 end
	30	 Apply VAT/iVAT on D n,d  returning D l )n,d , P, c
	31	 Choose the number of clusters k using image of D l )n,d
	32	 % % Clustering % %
	33	 Find indices u  of k largest values in MST cut magnitudes c
	34	 Form the aligned partition, U ) = " u 1 :u 2 - u 1 :f:u k - u k - 1 ,, U S = U )P , 1# i # k
	35	 Generate down-space data sets " Yi ,Qi = 1 1 R q using RP, uYiu = N
	36	 for each Yi do
	37		Consider sample Y (Si ) 1 R q and Yi - Y (Si ) 1 R q, where uY (Si )u = n, and uYi - Y (Si )u = N - n for each data point, yt ! Yi - Y (Si ) do
	38			 l = argmin i ! S " dist " yt, y i ,,
(i )
	39			 U yt = U l
	40		 end
	41	 end
(i )
	42	 U = Mode of labels for each data points U yt
u

d

d

d

i

d

d

d

Algorithm S23. Coclustering VAT (coVAT) [94].
Input : D - m # n rectangular dissimilarity matrix
Output: D ), Dt r , Dt c, and Dt r , c - reordered dissimilarity matrices
	 1	Build estimates of D r  and  D c  by interpreting the m rows and n columns of D  as the feature vector representing m row
  objects and n column objects, respectively
Dr D
E
	 2		
D r ,c = ; T
D Dc
	 3	Apply VAT to  D r ,c  generating permutation array Pr ,c = " P ^1h, P ^2h f, P ^m + nh,
	4	Initialize  rc = cc = 0;  RP = CP = 0
	 5	for t ! 1 to m + n  do
	 6		 if P ^ t h # m  then
	 7			 rc = rc + 1, rc  is row component
	 8			 RP ^rc h = P ^ t h, RP  are row indices
	 9		 else
	10			 cc = cc + 1, cc  is column component
	11			 CP ^cc h = P ^ t h - m, CP  are column indices
	12		 end
	13	 end
	14	 for p ! 1 to m do
	15		 for q ! 1 to n do
	16				 D )p,q = D RP ,CP
	17		 end
	18	 end
	19	 Create I ^D ) h
p

18	

q

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE Apri l 2020



IEEE Systems, Man and Cybernetics Magazine - April 2020

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