List of notations

Abstract

Table 1: Notations and their meanings Notation Meaning C = {C1, C2, . . . , Cp} Classification problem with p class labels, Ck; (1≤ k ≤ p and 2≤ p) I = {I1, I2, . . . , In} Testing instance, It; (1 ≤ t ≤ n) rt = 〈R t , R 2 t , . . . , R p t 〉 Ground truth one-hot vector for It D = {D1, D2, . . . , DT } Stream training dataset,Di; (1 ≤ i ≤ T )Di ⊆ Dj if i < j L = {L1, L2, . . . , LT } Trained learners of a model forD, Li; (1 ≤ i ≤ T ) Ŷ = {Ŷ1, Ŷ2, . . . , ŶT } Prediction for I by L, Ŷi; (1 ≤ i ≤ T ) ξ = {SL1, SL2, . . . , SLm} Ensemble ofm component single learners, SLj ; (1 ≤ j ≤ m and 2 ≤ m) ξ̃ = {S̃L1, S̃L2, . . . , S̃Lm} The copy of ξ, ensemble ofm component single learners, S̃Lj ; (1 ≤ j ≤ m and 2 ≤ m) stj = 〈S tj , S 2 tj , . . . , S p tj〉 Prediction vector for It by SLj ; ∑p k=1 S k tj = 1 s̃tj = 〈S̃ tj , S̃ 2 tj , . . . , S̃ p tj〉 Prediction vector for It by S̃Lj ; ∑p k=1 S̃ k tj = 1 ot = 〈O t , O 2 t , . . . , O p t 〉 Centroid-point vector for It by ξ,O k t ; (1 ≤ k ≤ p) õt = 〈Õ t , Õ 2 t , . . . , Õ p t 〉 Centroid-point vector for It by ξ̃, Õ k t ; (1 ≤ k ≤ p) w = 〈W1,W2, . . . ,Wm〉 Weight vector for ξ,Wj ; (1 ≤ j ≤ m) w̃ = 〈W̃1, W̃2, . . . , W̃m〉 Weight vector for ξ̃, W̃j ; (1 ≤ j ≤ m) ζ = f(w, ξ) Combination learner for ξ and w ζ̃ = f(w̃, ξ̃) Combination learner for ξ̃ and w̃