Pima Indians Diabetes Database Processing through

EBBM-Optimized UTM Model

Luigi Lella

, Ignazio Licata

and Christian Pristipino

ISEM, Ins. For Scientific Methodology, PA, Italy

Interventional and Emergency Cardiology Unit, San Filippo Neri – ASL Roma 1, Rome, Italy

Keywords: Artificial Intelligence, Data Mining, Computational Optimization.

Abstract: A new predictive model tested on the Pima Indians Diabetes Database is presented. This model represents a

particular subclass of A-Type Unorganized Turing machine (UTM), where the state is unique. It appears as

a simple combinational network of NAND gates (it is not the more generic sequential type described by

Turing, but it is enough to solve the examined predictive task). The optimal architecture of this network is

identified by the use of evolutionary algorithms, which are therefore used as computational optimization

algorithms. In particular, a classic genetic algorithm and an hybrid evolutionary-swarm algorithm that we

have called Evolutionary Bait Balls Model (EBBM) were tested for this purpose. The predictive model thus

defined, made it possible to achieve higher performances than those obtained with other classic predictive

models. The final combinational network of NAND gates obtained through our model has allowed us to

identify a simple Boolean rule to determine the existence of the risk of incurring diabetes mellitus.

1 INTRODUCTION

Pima Indians Diabetes Database is provided by the

National Institute of Diabetes and Digestive and

Kidney Diseases (Pima Indians Diabetes Database,

2021) (Rossi and Ahmed, 2021) (Pima Indians

Diabetes on Rishabh Nimje Github section, 2021).

The goal of the dataset is to predict diagnostically

whether or not a patient may develop diabetes, based

on certain diagnostic measurements included in the

dataset. Several constraints have been placed on

selecting these instances from a larger database.

Notably, all patients here are women of at least 21

years of Pima Indian descent.

The considered variables to make diabetes risk

predictions are the following: number of pregnancies

(pn), plasma glucose concentration (pgc) at 2 hours

in an oral glucose tolerance test, diastolic blood

pressure in mm Hg (dbp), the thickness of the skin

fold of the triceps in mm (tsft), 2 hour serum insulin

in mu U / ml (si), body mass index (bmi) calculated

as (weight in kg) / ((height in m) ^ 2) , diabetes

pedigree function (dpf), age.

The diabetes pedigree function provides some

insight into the history of diabetes mellitus in

relatives and the genetic relationship of those

relatives to the patient. This measure of genetic

influence allows us to have an estimate of the

hereditary risk that could be had with the onset of

diabetes mellitus.

This work intends to present the results of the

experimentation on the Pima Indians Diabetes

Database of a single state A-type model of

Unorganized Turing Machine (UTM) (Turing,

1948), consisting of a combinational network of

NAND gates whose optimal configuration is

identified by evolving a population of chromosomes

each of which represents the coding of a UTM

configuration.

UTM is generated “in a unsystematic and

random way” from a set of two-input NAND gates.

Turing chose a NAND gate because every other

logical operations can be accomplished by a set of

NAND units. A Turing A-type unorganised machine

can be considered “a kind of Boolean neural

network without a layered structure, due to the fact

that recurrent connections are allowed with no

constraints” (Teuscher and Sanchez, 2000).

We used at first a genetic algorithm (GA)

(Mitchell, 1996) to determine the best A-type

network configuration. GAs are used to find high

quality solutions in optimization and search

problems by relying on bioinspired operators of

384

Lella, L., Licata, I. and Pristipino, C.

Pima Indians Diabetes Database Processing through EBBM-Optimized UTM Model.

DOI: 10.5220/0010806500003123

In Proceedings of the 15th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2022) - Volume 5: HEALTHINF, pages 384-389

ISBN: 978-989-758-552-4; ISSN: 2184-4305

natural selection like mutation, crossover and

selection.

Then a hybrid evolutionary-swarm algorithm

was experimented, that we called Evolutionary Bait

Balls Model (EBBM), where the chromosomes are

considered as individuals members of a swarm. Each

of them is capable of carrying out just three

elementary operations (repulsion from one's

neighbor, attraction towards another particularly

performing individual, orientation with respect to

one's neighbor). The evolution of this population

leads to the appearance of emergent behaviors (the

state in which a sort of bubble is formed in which

most individuals tend to orient themselves with

respect to their neighbors), manifesting a kind of

collective intelligence.

2 EBBM VS GA ALGORITHM

The first considered algorithm used to optimize the

configuration of the UTM network was a classic

model of genetic algorithm where elitism is also

used, that is, in each new generation the most

performing individual of the previous one is

preserved. Both the uniform crossover operator and

the mutation operator are used. First of all, with the

tournament selection strategy, the winners of two

tournaments involving 5 randomly chosen

individuals are identified. Their chromosomes are

crossed through uniform crossover (i.e. the

probability that the new individual acquires a gene

from parent i1 is exactly the same as that of

acquiring a gene from parent i2) corresponding to a

crossoverRate of 0.5. The new individual is subject

to mutation with probability equal to mutationRate.

Input: Array of individuals I to be

updated

Output: The position vectors (binary

vectors) of each individual in I will

be changed.



1: call function to alter the positions

of each individual

2: for all i ϵ I do

3: perform elitism;

4: i1 =

tournamentSelection(I,tournamentSize);

5: i2 =

tournamentSelection(I,tournamentSize);

6: perform crossover(i1,i2);

7: perform mutation(mutationRate);

8: end for



The original evolutionary model of the bait ball,

that inspired our EBBM, was developed by some

researchers who found that within the group of

fishes that try to escape from predators a

spontaneously generated nucleus constitutes what

they called "selfish herd" (Roberts, 2021) (Yang,

2018). This naming derives from the selfish herd

theory that individuals within the population attempt

to reduce their risk of predation by placing other

conspecifics between themselves and the predators.

Returning to the bait ball model, it is precisely this

"selfish" behavior adopted by individuals that leads

to the formation of the optimal collective

configuration. This configuration tends to persist

even when the inner core becomes less secure than

the outside. Paradoxically, the ball shape of the

group of individuals becomes even more regular in

these cases. On the other hand, by increasing the

level of insecurity of the center, the sphere

disintegrates and leads to the formation of many

groups of distinct individuals. Summarizing all these

are examples of optimal collective configurations

that emerge over time by defining simple rules that

individuals must respect, such as that of finding and

maintaining the safest position (or the one with the

highest fitness).

The EBBM ibrid evolutive-swarm algorithm,

that we tested as an alternative optimization

algorithm, was the following one.

Input: Array of individuals I to be

updated

Output: The position vectors (binary

vectors) of each individual in I will

be changed.

1: call function to alter the positions

of each individual

2: for all i ϵ I do

3: perform ZOR, ZOA, ZOO sets

calculations

4: if individual detected in ZOR then

5: perform repulsion (R)

6: else if individual detected in ZOO

then

7: perform orientation (O)

8: else if individual detected in ZOA

then

9: perform attraction (A)

10: end if

11: end for

Where ZOR is the Repulsion Zone: an individual

cannot occupy the position of another, that is, it

cannot be represented by the same binary vector. In

this case it assumes another position at random

(every single bit of the chromosome is changed with

Pima Indians Diabetes Database Processing through EBBM-Optimized UTM Model

385

probability repulsionRate). ZOA is the Zone of

Attraction: an individual tends to approach

individuals characterized by greater fitness (with

probability attractionRate each single bit of the

chromosome can assume the same value as the bit at

the same position of the best performing individual

in the ZOA set). ZOO is the Orientation Zone: an

individual tends to get closer, among the individuals

close to him, to the best performing one (with

probability orientationRate, every single bit of the

chromosome can assume the same value as the bit at

the same position of the best performing neighbor).

For each individual, to define ZOR, ZOA, ZOO sets

of other chromosomes, we introduced the

ZORrange, ZOArange and ZOOrange parameters

which represent the maximum number of different

bits between the considered chromosome and the

individual belonging to the chromosome ZOR, ZOA

and ZOO respectively.

3 TEST SET CODING CRITERIA

Pima Indian Diabetes Database (Pima Indians

Diabetes Database, 2021) (Rossi and Ahmed, 2021)

is a data set with 768 observations (i.e. 768 records)

and 9 variables. The target population consisted of

women who were at least 21 years old, of Pima

Indian heritage.

For testing purposes, we decided to code the

training set of our models, consisting of 60% of the

available data with the same distribution of variable

values, in a binary format, according to the criteria

explained in table 1.

Table 1: Test set coding criteria.

Variable Coding Criteria

pn pn <= 5 code: 100; 6<= pn <= 10 code:

010;

n >= 11 code: 001

pgc pgc <= 103 code: 100; 104<= pgc <= 150

code: 010;

gc >= 151 code: 001

dbp dbp <= 52 code: 100; 53 <= dbp <= 80

code: 010; dbp >= 81 code: 001

tsft tsft <= 25 code: 100; 26 <= tsft <= 43 code:

010; tsft >= 44 code: 001

si si <= 291 code: 100; 292 <= si <= 568

code: 010; si >= 569 code: 001

bmi bmi <= 34 code: 100; 35 <= bmi <= 50

code: 010; bmi >= 51 code: 001

dpf dpf <= 776 code: 100; 777 <= dpf <= 1552

code: 010; d

f >= 1553 code: 001

age age <= 41 code: 100; 42 <= age <= 61

code: 010; a

e >= 62 code: 001

outcome risk of diabetes code: 1; no risk of diabetes

code: 0

In this way, the bit position is related to the

discretized value of the considered variable (that is

the discretized variable class), i.e. 100 stands for low

values of the considered variable, 010 stands for

medium values and 001 stands for high values. The

three intervals chosen for the discretization of each

variable where chosen subdividing the global

variation interval of the variable in three equal parts.

These bit sequences have been assembled to create

the encodings of the considered cases, which

consisted of 3*8+1=25 bits.

4 UTM MODELS TRAINING

Each possible UTM configuration, that corresponds to

a given chromosome, was also codified in a binary

form in the following way. The first 24 bits represent

all the choosable variables classes for the first input of

the NAND gates of the UTM model (first input

variable classes). For example a sequence starting

with “011 100 …” means that 6<= pn <= 10, pn >=

11, pgc <= 103 are chosen as possible input

conditions for input 1 of NAND gates. The following

24 bits represent all the choosable variables classes

for the second input of the NAND gates of the UTM

model (second input variable classes). The remaining

54 bits were used to codify the architecture of the 18

available NAND gates. Each NAND gate was

codified with three bits. If the value of the first bit is 1

the first input of the considered NAND gate is a first

input variable class, otherwise the first input is

connected with the output of the following NAND

gate. If the value of the second bit is 1 the second

input of the considered NAND gate is a second input

variable class, otherwise the first input is connected

with the output of another NAND gate. If the value of

the third bit is 1, this means that the inputs of the

considered NAND gates are short circuited and just

the first input has to be considered. In this way each

chromosome, representing a possible NAND network

configuration, is represented by 24+24+54=102 bits.

In order to represent a combinational NAND

network, when a chromosome is tested to evaluate

its fitness all the first input variable classes, all the

second input variable classes and all the 18 available

NAND gates are selected sequentially just one time.

The first NAND gate (NAND#1) of the 54 bits

sequence is the output gate of the network. If the

first bit of its code is 1, the input 1 of NAND#1 is

the first choosable first input class variable. If the

first bit of its code is 0, the input 1 of NAND#1 is

the output of NAND#2, whose code is represented

by the following three bits of the 54 bits sequence. If

HEALTHINF 2022 - 15th International Conference on Health Informatics

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the second bit of NAND#1 code is 1, the input 2 of

NAND#1 is the first choosable second input class

variable. If the second bit of NAND#1 is 1, the input

2 of NAND#1 is the output of NAND#3, whose

code is represented by the third triplet of bits within

the 54 bits sequence.

In evolutionary algorithms (including the hybrid

one of EBBM) it is important to adequately choose

the fitness function associated with each

chromosome. The codified configuration of network

represented by the chromosome was tested with the

training dataset, extracted following the criteria

explained in section 2. The fitness score of the

chromosome is the count of all the cases where the

output of the corresponding combinational NAND

network equals to the real output of the case (that is

the value of the 9

variable of the test set).

A population of 50 chromosomes, represented by

randomly chosen sequences of 102 bits, was evolved

for 100000 generations.

The chosen values for GA parameters were the

following: tournamentSize = 5, crossoverRate = 0.5,

mutationRate = 0.015.

The chosen values for EBBM parameters were

the following: repulsionRate = 0.5, attractionRate =

0.1, orientationRate = 0.5, ZOArange = 100,

ZOOrange = 5, ZORrange = 0.

5 UTM MODELS TRAINING

Both GA-based and EBBM-based UTM models

were tested with the remaining 40% of the Pima

Indians Diabetes Database.

The performances of GA-based UTM and

EBBM-based UTM were compared with the

performances of other algorithms that were tested on

the same database (Pima Indians Diabetes on

Rishabh Nimje Github section, 2021). The test

results are shown in table 2.

Table 2: Prediction accuracy of different tested models.

Model Prediction accurac

EBBM-

ased UTM 76.04%

GA-

ased UTM 75.91%

ort Vector Classifie

74.68%

istic Re

ression 73.38%

XG Boost 72.73%

Random Forest 71.43%

Naïve Bayes 71.43%

K Nearest Nei

hbo

70.78%

Decision Tree

70.13%

Stochastic Gradient

Descent

51.3%

Both GA-based and EBBM-based UTM models

performed better than the other ones, but the best

results in terms of prediction accuracy were reached

by the EBBM-based UTM model.

Following the principles suggested by (Minati

and Licata, 2012), we demonstrated that the

collective behavior of individuals defined by our

EBBM model develops emerging phenomena over

time (for example the units tend to orient themselves

with neighboring ones rather than repel each other or

approach the safest positions).

We considered as mesoscopic state variables the

attraction state (A), the orientation state (O); and the

repulsion state (R) of the individuals. These

mesoscopic state variables take as values the number

of individuals who assume the related state over

time. The mesoscopic state O demonstrate a certain

degree of ergodicity (0.98), which was computed

according to the following formula:



=1 / [ 1 + ( X



% - Y



% )

] (1)

Where Y



% is the average percentage of time

spent by a single individual in state O and X



% is

the average percentage of individuals lying in the

same state.

We further trained and tested the EBBM-based

UTM model by the use of a filtered dataset where

records with missing data, i.e. not executed

observations corresponding to a value equals to 0,

were not taken into consideration. The number of

records dropped from 768 to 392.

Using a subset of 60% filtered samples for

training and the remaining 40% filtered samples for

testing we reached an accuracy of 80,1%. We

obtained 78 true positives, 26 false positives, 236

true negatives and 52 false negatives corresponding

to a sensitivity equal to 60,00%, a specificity equal

to 90,08% and a prevalence equal to 33,16%.

The resulting most performing network

configuration is represented in figure 1. The

chromosome is splitted in three parts representing

the first input variable classes, the second input

variable classes and the 18 NAND gates represented

by 18 triplets. All the picked up first input variable

classes, second input variable classes and NAND

gates are underlined. The first triplet of the 18

NAND gates represents the output gate which is

NAND#1. The second triplet of the 18 NAND gates

represents the NAND#2, whose output is chosen as

the first input of NAND#1. The third triplet of the 18

NAND gates represents the NAND#3, whose output

is chosen as the second input of NAND#1. The first

input 1 variable class picked up by NAND#2 is the

class variable in the third position that is pn>=11.

Pima Indians Diabetes Database Processing through EBBM-Optimized UTM Model

387

The first input 2 variable class picked up by

NAND#2 is the class variable in the eighth position

i.e. 53<=dbp<=80.

Figure 1: The best UTM combinational network

corresponding to the fittest chromosome.

This combinational network of NAND gates

corresponds to the following boolean rule:

IF(NOT(AND(NOT(AND(pn>=11;dbp>=53;dbp<=80));NOT(

AND(NOT(pgc<=103);NOT(AND(pgc>=104;pgc<=150;NOT(

AND(dbp>=81;AND(NOT(AND(tsft<=25;NOT(AND(tsft>=2

6;tsft<=43;NOT(AND(tsft>=44;dbp>=81))))));NOT(AN

D(NOT(AND(si<=291;NOT(AND(NOT(AND(NOT(AND(NOT(AN

D(si>=569;tsft<=25);tsft>=26;tsft<=43);si<=291);

dpf<=776);age<=41))))))))))))))))) THEN

OUTCOME=1

(2)

6 CONCLUSIONS

Nature has developed intelligent techniques to find a

solution to various types of problems, such as the

adaptation of species to environmental variations or

coordination between individuals operating within

populations. The study of these phenomena has

made it possible to develop intelligent systems

characterized by a high level of resilience (that is,

they still perform their function even in the presence

of local malfunctions) and adaptability to possible

changes in the environment in which they operate.

Genetic algorithms (Mitchell, 1996) (and

evolutionary computation in general) draw

inspiration from the theory of natural evolution

according to which individuals able to adapt better

to their environment (with greater fitness) live

longer and produce more offspring. Their genetic

heritage is recombined (crossover) and passed on to

offspring with small random variations (mutation).

In this way the positive characteristics of the

individuals are combined, but also limited elements

of novelty are introduced into the genetic heritage.

Swarm intelligence algorithms emulate the

behavior of individuals operating within a

population. Each individual belonging to any genus

and species present in nature seems to behave

following a series of elementary rules that lead to an

organized population behavior aimed at achieving

objectives (for example, identifying the most

favorable conditions for survival) (Bouffanais,

2016). The interesting aspect of these biological

systems is that these behaviors arise (emerge)

autonomously, without the presence of a

coordinator/ supervisor. The study of these

behavioral models leads to the development of

algorithms that belong to the class called "swarm

intelligence".

These considerations lead us to develop an

“hybrid” algorithm with characteristics that can be

associated with both evolutionary algorithms and

swarm intelligence algorithms. The EBBM

algorithm allowed us to train a combinational UTM

network which reached the highest performances in

predicting the outcomes of Pima Indians Diabetes

Database with respect to other prediction models.

This model can be used, within the healthcare

sector, not only to develop expert systems for

diagnostic support, but also to define useful

guidelines for the preventive medicine. This model

opens also new perspectives in the field of

personalized medicine (Lella et al., 2019), given its

capability to reach the highest prediction accuracies

and to explain the used criteria to human experts.

We are also going to implement, by the use of the

same EBBM algorithm for the optimization of the

architectural configuration, a sequential network of

NAND gates in order to explore the full potentials of

Turing's unorganized A-type machine model.

REFERENCES

Bouffanais R. (2016). A Biologically Inspired Approach to

Collective Behaviours. In Design and Control of

Swarm Dynamics, Springer Briefs in Complexity.

Lella L., Licata I., Minati G., Pristipino C., De Belvis A.G.

(2019). Predictive AI Models for the Personalized

Medicine. In Proceedings of the 12th International

Joint Conference on Biomedical Engineering Systems

and Technologies, pp. 396-401.

Minati G., Licata I. (2012). Meta-Structural properties in

Collective Behaviours. In International Journal of

General Systems, pp. 1-23.

Mitchell M. (1996). An Introduction to Genetic

Algorithms. Cambridge, MA: MIT Press.

Pima Indians Diabetes Database download page,

https://networkrepository.com/pima-indians-

diabetes.php , last accessed 2021/09/30.

Pima Indians Diabetes Database on Rishabh Nimje Github

section, https://risx3.github.io/pima-diabetes/, last

accessed 2021/09/30.

HEALTHINF 2022 - 15th International Conference on Health Informatics

388

Roberts T.J.: Dynamical and computational structures

under the sea: modelling of fish motion,

http://studentnet.cs.manchester.ac.uk/resources/library/

3rd-year-projects/2016/timothy.roberts-2.pdf , last

accessed 2021/09/30.

Rossi R., Ahmed N.: The Network Data Repository with

Interactive Graph Analytics and Visualization,

https://networkrepository.com, last accessed

2021/09/30.

Teuscher C., Sanchez E. (2000). A Revival of Turing’s

Forgotten Connectionist Ideas: Exploring

Unorganized Machines. In Proceedings of the 6th

Neural Computation and Psychology Workshop,

NCPW6, University of Lige.

Turing A. (1948). Intelligent Machinery. In Collected

Works of A.M. Turing: Mechanical Intelligence.

Edited by D.C. Ince. Elsevier Science Publishers,

1992.

Yang W. (2018). When the Selfish Herd is Unsafe in the

Middle. In: The 22nd Asia Pacific Symposium on

Intelligent and Evolutionary Systems.

Pima Indians Diabetes Database Processing through EBBM-Optimized UTM Model

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