◆◆ The first tree is parent 1, which represents 10 yt = x 1 - log a x 2 k . (5) UFO structure containing one output stream (i.e., referring to Figure 1, m = 1). If a data set contains n predictors {x 1, x 2, f, x n}, the approximated response can be mathematically expressed as ◆◆ The second tree, parent 2, represents -1 yt = x 2 $ cos ^ x 21 - 5 h. (6) yt = f (x 1, x 2, f, x k - 1, x k, x k + 1, f, x n - 1, x n) (9) and by using the vector notation ◆◆ The third tree is a child of the genetic crossover opera- tion, representing yt = x 1 - log c yt = f (X ) ; X = [x 1, x 2, g, x n]. (10) cos ^ x 12 - 5 h m. (7) x2 ◆◆ The fourth tree is a child of the subtree mutation oper- Now, suppose that yt is decomposed into v functions: f / { f1, f2, f, f j - 1, f j, f j + 1, f, fv - 1, fv}. (11) ation, and it represents 10 yt = x 4 $ x 5 - log a x 2 k. (8) Although the UFO and classical SR share the same aim to automatically build linear and nonlinear mathematical equations, they are totally different. There are some difficulties to practically applying SR techniques in real-world applications. A detailed discussion about the major differences between these two ML computing systems is given in [2]. The UFO The UFO is a new multipurpose ML computing system that explains everything as pure mathematical equations. It can act like SR to build simple and highly complicated linear/nonlinear equations. Also, it can be used in applications such as function simplification, function complication, dimension reduction, dimension expansion, and highdimensional function visualization. The UFO has a built-in selection process for features and analytic functions, which enables it to remove unwanted variables and terms from a final model. To help convey how this innovative computing system works, Figure 4 describes the basic x1 B1 x2 x3 f j (X ) = f j ^a 0, j 9 1, j a 1, j $ x b1 9 2, j a 2, j $ x b2 9 3, j a 3, j $ x b3 9 4, j g 9 n, j a n, j $ x bn h, 1, j g1 g2 g j (X ) = w j $ 6 f j (X )@c = w j $ 6 f j (x 1, x 2, f, x n)@c = w j $ 6 f j ^a 0, j 9 1, j a 1, j $ x b1 9 2, j a 2, j $ x b2 9 3, j a 3, j $ x b3 9 4, j g 9 n, j a n, j $ x bn h@c , j j 1, j 3, j 2, j n, j j (13) where c j is the " external exponent " assigned to f j locatmax ed in B j, where c j ! [c min j , c j ], and w j is the " external B0 Bv gv (x1, x2, ... , xn) g1 g2 g3 g1 g2 g3 g1 g2 g3 ... gv -1 Figure 4. The UFO mechanism with only one output stream [2]. 16 (12) n, j where 9 k, j is the kth " universal arithmetic operator " assigned to the kth predictor (x k) of the jth block (B j); it could be +, -, ×, or ' . In addition, a 0, j is the " in-- max a k, j is the kth tercept " of B j, where a 0, j ! [a 0min , j , a 0, j ]; " internal weight " assigned to x k located in B j, where max a k, j ! [a min k, j , a k, j ]; and b k, j is the kth " internal exponent " max assigned to x k located in B j, where b k, j ! [b min k, j , b k, j ]. If each f j has an exponent (cj) and the result is multiplied by a weight (w j), the following more general function can be attained: g2 (x1, x2, ... , xn) g3 (x1, x2, ... , xn) g1 (x1, x2, ... , xn) 2, j 3, j xn B3 B2 The interaction between {x 1, x 2, f, x n} in each jth analytic function can be modeled in many ways. The basic approach is mathematically expressed as follows: IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE Apri l 2021 ... gv w0 y (x1, x2, ... , xn) "

IEEE Systems, Man and Cybernetics Magazine - April 2021 - Cover1

IEEE Systems, Man and Cybernetics Magazine - April 2021 - Cover2

IEEE Systems, Man and Cybernetics Magazine - April 2021 - contents

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 2

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 3

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 4

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 5

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 6

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 7

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 8

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 9

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 10

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 11

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 12

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 13

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 14

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 15

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 16

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 17

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 18

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 19

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 20

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 21

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 22

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 23

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 24

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 25

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 26

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 27

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 28

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 29

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 30

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 31

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 32

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 33

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 34

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 35

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 36

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 37

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 38

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 39

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 40

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 41

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 42

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 43

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 44

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 45

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 46

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 47

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 48

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 49

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 50

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 51

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 52

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 53

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 54

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 55

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 56

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 57

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 58

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 59

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 60

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 61

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 62

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 63

IEEE Systems, Man and Cybernetics Magazine - April 2021 - 64

IEEE Systems, Man and Cybernetics Magazine - April 2021 - Cover3

IEEE Systems, Man and Cybernetics Magazine - April 2021 - Cover4

https://www.nxtbook.com/nxtbooks/ieee/smc_202301

https://www.nxtbook.com/nxtbooks/ieee/smc_202210

https://www.nxtbook.com/nxtbooks/ieee/smc_202207

https://www.nxtbook.com/nxtbooks/ieee/smc_202204

https://www.nxtbook.com/nxtbooks/ieee/smc_202201

https://www.nxtbook.com/nxtbooks/ieee/smc_202110

https://www.nxtbook.com/nxtbooks/ieee/smc_202107

https://www.nxtbook.com/nxtbooks/ieee/smc_202104

https://www.nxtbook.com/nxtbooks/ieee/smc_202101

https://www.nxtbook.com/nxtbooks/ieee/smc_202010

https://www.nxtbook.com/nxtbooks/ieee/smc_202007

https://www.nxtbook.com/nxtbooks/ieee/smc_202004

https://www.nxtbook.com/nxtbooks/ieee/smc_202001

https://www.nxtbook.com/nxtbooks/ieee/smc_201910

https://www.nxtbook.com/nxtbooks/ieee/smc_201907

https://www.nxtbook.com/nxtbooks/ieee/smc_201904

https://www.nxtbook.com/nxtbooks/ieee/smc_201901

https://www.nxtbook.com/nxtbooks/ieee/smc_201810

https://www.nxtbook.com/nxtbooks/ieee/smc_201807

https://www.nxtbook.com/nxtbooks/ieee/smc_201804

https://www.nxtbook.com/nxtbooks/ieee/smc_201801

https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_1017

https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0717

https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0417

https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0117

https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_1016

https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0716

https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0416

https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0116

https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_1015

https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0715

https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0415

https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0115

https://www.nxtbookmedia.com