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

Function
Simplification/
Complication

Optimization
Modeling

Categorization/
Clustering

Dimension
Reduction/
Expansion

High-Dimensional
Problem
Visualization

Function
Approximation
UFO

e
yb

C

s

tic

rne

Pattern
Classification

Forecasting/
Prediction

Control
Systems

Figure 6. Possible UFO applications [2].

of computation-based cybernetic applications. It can
be used as an effective tool to find a suitable link and
to establish a correct translator between the input
and output variables in Figure 1. In other words, the
UFO can be considered a model builder for cybernetics. It can be used in linear/nonlinear control systems, opti m ization a lgor it h ms, LR / NLR , a nd
information and data science, which represent the
heart of cybernetics. Comparing the diagram in Figure 5 with the preceding UFO applications, Figure 6
links the UFO with cybernetics [2].

x1
x2

B1

B2

x3
x4

xn

B3

Bv

Figure 7. The UTU.
18	

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE Apri l 2021

UFO Extensions
Although the UFO can independently work to perform
many tasks, it can also be hybridized with other ML computing systems. There are numerous ways to achieve this.
One of them is to dismantle all the external universal
arithmetic operators (i.e., {V1, V2, f, Vv - 1}) to have no
direct connection between blocks; then, let the operators
transform the original predictors and change the problem
dimension by setting v ! n. This structure is called the
universal transformation unit (UTU), which appears in
Figure 7. This unit can be used as a basis to hybridize the
UFO with many ML/DL tools, including the following.
Universal Transformation-Based Regression
The per for ma nce of regression models could be
enhanced by transforming their predictors before being
sent to LR or NLR [10]. Thus, the proposed universal
transformation-based regression (UTR) is actually divided into two types:
1)	 UFO + LR: universal LR (ULR)
2)	 UFO + NLR: universal NLR (UNR).
The ULR structure is given in Figure 8. Because the
con nections between the v blocks are dismantled,
{V1, V1, f, Vv - 1} are not needed anymore. The block functions {g 1 (x), g 2 (X ), f, g v (X )} are used as transformed predictors in MLR. Thus, (3) becomes
	

yt = b 0 + b 1 g 1 + b 2 g 2 + g + b v g v. (18)



IEEE Systems, Man and Cybernetics Magazine - April 2021

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