=Paper=
{{Paper
|id=Vol-3611/paper21
|storemode=property
|title=Iris database - Effectiveness of selected classifiers
|pdfUrl=https://ceur-ws.org/Vol-3611/paper21.pdf
|volume=Vol-3611
|authors=Paulina Hałatek,Katarzyna Wiltos,Mariusz Wróbel
|dblpUrl=https://dblp.org/rec/conf/ivus/HalatekWW22
}}
==Iris database - Effectiveness of selected classifiers==
https://ceur-ws.org/Vol-3611/paper21.pdf
Iris database - Effectiveness of selected classifiers
Paulina Hałatek1, Katarzyna Wiltos1 and Mariusz Wróbel1
1
Faculty of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44100 Gliwice, Poland
Abstract
Machine learning and artificial intelligence are crucial tools in the vast majority of different fields, but mainly in computer
science and technology. Classifiers play a vital role in this field, especially in predicting the class membership of a sample
under consideration. An example of the practical use of classifiers is the spam filter of email messages. The following paper
aims to determine the most efficient classifier from selected: kNN, Soft set, and Naive Bayes on Iris database. Different
versions of each of the classifiers have been considered. For kNN, the performance of various metrics was compared, for the
Soft set, two approaches for establishing intervals during the classification, and for Naive Bayes, the normal and triangular
distributions were compared. The most effective versions of the classifiers have been selected for the final comparison.
Keywords
Artificial intelligence, Iris, classifiers, kNN, Soft set, Naive Bayes
1. Introduction data analytics. In [1] was proposed a model of soft set to
approximate reasoning from input data. A model based
Artificial intelligence is an important aspect in today’s on kNN classifier for big data analytics was presented
world. It brings a communication between human and in [7]. In decision processes we also very often use
machine. Thanks to that we are able to teach our com- bayesian approaches which analyze probability of
puter how to process a given data and get a response possible situations. In [2] was presented an wildfire
from it. This is a called machine learning. risk assessment from data of remote sensing.
Machine learning is a field of study that uses diverse Transmission of sensor readings for classifiers is an
algorithms to make some analysis in the given data. That important topic, and there are many interesting models
can be for example: to support this process [5]. Classification model also
depends on the type of the input information. In [6] was
1. variety recognition, discussed how to use bayesian model for text
2. weather and disease prediction, classification. This kind of processes also need efficient
3. puzzle or sudoku solver, data aggregation to improve efficiency of the classifier
4. building a movie recommendation system. [3].
In our paper we are going to compare three classifiers:
This is actually a small fraction of the immeasurable pos-
kNN, Soft set, Naive Bayes and decide which of those is
sibilities in this field of study. Machine learning models
the most accurate and effective. We will be trying to use
are used to learn the patterns in data. Machine learning
different methods for each classifiers to determine the
algorithms can be used for example to gather information
most reliable results. Each of these classifiers is different
about data, split data for two parts and try to identify
in some aspects. But the thing which connects them is
unknown sample as a data element. The methods which
that all of theirs main purpose is to identify a given sam-
determine this, are called classifiers. We have various
ple by learning from a database using different types of
types of classifiers applicable to different task. In machine
identification. And in this paper we want to bring each
learning models neural networks based ideas are very
classifier closer in the meaning, we are going to explain
efficient in complex data analysis. In [4] was presented
each of those three classifiers, explain which techniques
how to use them in low-dimensional data feature learn-
of identification we were used and make overall conclu-
ing. The idea presented in [8] proposed neural network
sion which one is the best classifier.
for analytical purposes of data recorded form high-speed
train. There are also very efficient, however simple in We decided to use Iris data base to compare the accu-
construction, classifiers based on approaches sourced in racy of those classifiers and identify the most suitable.
IVUS 2022: 27th International Conference on Information 2. Iris database
Technology, May 12, 2022, Kaunas, Lithuania
$ paulhal456@student.polsl.pl (P. Hałatek); Before we started working on our base, we made sure
katawil756@student.polsl.pl (K. Wiltos);
mariwro279@student.polsl.pl (M. Wróbel)
that our Iris base didn’t have null or NaN values. We have
© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License created additional class called DataProcessing which
Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
helped us to shuffle, normalize and split database by di- 2.1. Normalization
viding it into 70% as a training set and 30% as a validation
For all classifiers we were normalizing a given database
set. As we can see, the setos class is significantly sepa-
by taking all values from a specific column, determining
rated from the rest of the classes. This will result in a
of the lowest and highest value in the specific column
high proportion of correctly recognized objects for this
and changing all values in the column according to the
class.
formula which is given below:
𝑜𝑙𝑑𝑉 𝑎𝑙𝑢𝑒[𝑥][𝑦] − 𝑚𝑖𝑛
𝑛𝑒𝑤𝑉 𝑎𝑙𝑢𝑒[𝑥][𝑦] = (1)
𝑚𝑎𝑥 − 𝑚𝑖𝑛
𝑥 a current row
𝑦 a current column
𝑚𝑖𝑛 a minimal value in the current column
𝑚𝑎𝑥 a maximal value in the current column
3. Methods
3.1. kNN
3.1.1. Formulas
In order to function properly, the kNN algorithm needs
functions that calculate the distance of the object for
which we are looking for a class to the objects of classes
Figure 1: Iris dataset graphs
already known to us. It is on the basis of this distance
that the kNN algorithm decides to which class a given
object may belong. There are many ways to calculate
distances, each with its pros and cons. When
calculating distances, we can, for example, use one of
the known metrics, e.g. Euclid:
𝑛
∑︁
||𝑥 − 𝑥𝑖 ||2 = (𝑥𝑗 − 𝑥𝑖𝑗 )2 (2)
𝑗
Or Minkowski distance:
𝑛
∑︁ 1
Figure 2: Iris dataset information 𝐿𝑚 (𝑥, 𝑦) = ( |𝑥𝑖 − 𝑦𝑖 |𝑚 ) 𝑚 (3)
𝑖=1
In our algorithm, we chose the Minkowski metric.
3.1.2. Algorithm
The kNN (k-Nearest Neighbors) classifier is one of
the most important non-parametric classification
methods. The kNN algorithm does not create an
internal representation of the training data, but looks
for a solution only when the testing pattern appears. It
consists in assigning an object to a given class by
checking to which representatives a given object has
the shortest distance. The algorithm works as follows.
First, a sample is taken from the validation set. Next
for a given sample, the distance to each object in the
test set is calculated. Then list is created containing the
given test file object and the distance to the sample
which then is sorted from shortest distance to longest.
After that from this list, the k objects in the shortest test set were calculated. On their basis, the middle values
distance from the sample are analyzed. At the end the of species range values were determined.
sample is assigned to the class with the most objects. The classifier considers samples from the validation
set together with the selected characteristic weight.
Algorithm 1 kNN algorithm In the first approach implementation for each sample,
Input: Test set, validate set, 𝑘, 𝑚 the distance from the center of the interval is calculated
Output: The class to which the sample may belong and the minimum value is chosen, which determines
sample classification.
while 𝑖 < 𝑙𝑒𝑛(𝑣𝑎𝑙𝑖𝑑𝑎𝑡𝑒 𝑠𝑒𝑡) do
while 𝑗 < 𝑙𝑒𝑛(𝑡𝑒𝑠𝑡 𝑠𝑒𝑡) do
Calculate the distance using Minkowski
distance of test object j to the sample 𝑖
and add the result to the list of distances.
𝑗++
Sort the list of distances in ascending order. Figure 3: First approach algorithm visualization
Take the k objects with the smallest distance
and return the class x with the most objects.
Return from dictionary variety with the highest prob- Algorithm 2 Soft set algorithm - first approach
ability
Input: Test set, validation set, weight
Output: The class to which the sample was classified
3.2. Soft sets 𝑐𝑒𝑛𝑡𝑒𝑟𝑠 ← 𝑐𝑒𝑛𝑡𝑟𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑖𝑟𝑖𝑠 𝑡𝑦𝑝𝑒
The soft set term as a mathematical model offers a tool
for 𝑖𝑛𝑑𝑒𝑥 < 𝑙𝑒𝑛(𝑣𝑎𝑙𝑖𝑑𝑎𝑡𝑖𝑜𝑛 𝑠𝑒𝑡) do
for analysing vaguely defined objects. Soft set theory is
a generalisation of fuzzy set theory that was introduced
Creates nested list with iris type name, minimal
in 1999 by Dmitri Molodtsov.
and maximal values for each iris type in test set.
3.2.1. Formulas Creates nested list with iris type name, centre
There are a few ways in which soft set may be im- value for each iris type based on minimal
plemented, for example: including weight or not. In and maximal values.
this case weight was included. Pearson correlation
coefficients were calculated to properly choose the most 𝑟𝑜𝑤 ← 𝑙𝑖𝑠𝑡 𝑜𝑓 𝑡𝑟𝑎𝑖𝑡𝑠 𝑣𝑎𝑙𝑢𝑒𝑠 𝑜𝑓 𝑜𝑛𝑒 𝑠𝑎𝑚𝑝𝑙𝑒
appropriate weight values for particular characteristics. 𝑠𝑎𝑚𝑝𝑙𝑒𝑇 𝑦𝑝𝑒 ← 𝑖𝑟𝑖𝑠𝑡𝑦𝑝𝑒𝑛𝑎𝑚𝑒
𝑠𝑎𝑚𝑝𝑙𝑒𝑉 𝑎𝑙𝑢𝑒 ← 0
∑︀ 𝑖←0
( 𝑖 (𝑥𝑖 − 𝑥
¯ )(𝑦𝑖 − 𝑦¯) for 𝑡 𝑖𝑛 𝑟𝑜𝑤 do ◁ Add all trait values for sample
𝑟 = √︀∑︀ (4)
𝑠𝑎𝑚𝑝𝑙𝑒𝑉 𝑎𝑙𝑢𝑒+ = 𝑡 * 𝑤𝑒𝑖𝑔ℎ𝑡[𝑖]
√︀∑︀
𝑖 (𝑥𝑖 − 𝑥
¯ )2 𝑖 (𝑦𝑖 − 𝑦
¯) 2
𝑖+ = 1
for 𝑣𝑎𝑙𝑢𝑒 𝑖𝑛 𝑐𝑒𝑛𝑡𝑒𝑟𝑠 do ◁ Calculate distances
𝑥𝑖 characteristic value for i = 0,1,...,n 𝑐𝑒𝑛𝑡𝑟𝑒 = 𝑣𝑎𝑙𝑢𝑒[0]
𝑥 mean value for particular characteristic 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = |𝑐𝑒𝑛𝑡𝑟𝑒 − 𝑠𝑎𝑚𝑝𝑙𝑒𝑉 𝑎𝑙𝑢𝑒|
𝑦𝑖 value of compared characteristic for i = 0,1,...,n
𝑦 mean value for compared characteristic Chooses minimal distance and corresponding iris type.
𝑟 Pearson correlation coefficient value Returns classified type.
3.2.2. Algorithm
Prior to classification data was prepared through shuf-
fling, normalizing, and splitting the database into a test
set and validation set in the ratio of 70 to 30.
In the developed implementation of the soft set, the
minimum and maximum values for each species of the
In the second approach algorithm, overlapping intervals 3.3. Naive Bayes
are considered and mean value is calculated to create
Naive Bayes classifier is a probabilistic machine learning
new intervals. Based on new intervals each sample is
model that’s used for classification task. At the begin-
being classified accordingly to these measures.
ning it reduces database by splitting an Iris database
to three smaller databases according to their variety.
After that classifier assigns the initial probability of a
given species appearing in the database. Next, it takes a
sample and counts a probability for each reduced
database. It uses one of two considered distribution
formulas. Subsequently, it multiplies the initial
Figure 4: Second approach algorithm - calculating mean value probability with all partial probabilities (with all
for overlapping intervals attributes that a reduced database has). And at the end
it compares which probability of three possible is the
highest.
3.3.1. Formulas
Normal distribution:
1 (𝑠𝑎 − 𝜇)2
𝑃 (𝑎𝑖 |𝑉 ) = √ 𝑒𝑥𝑝(− 𝑖 2 ) (5)
2𝜋𝜎 2 2𝜎
Figure 5: Second approach algorithm - determined intervals Triangular distribution:
⎧ √
0, 𝑠𝑎𝑖 < 𝜇 − 6𝜎𝑉
Algorithm 3 Soft set algorithm - second approach
⎪
⎪
⎪ 𝑠𝑎 𝑖 −𝜇 √
⎨
6𝜎 2
+ √16𝜎 , 𝜇 − 6𝜎 ≤ 𝑠𝑎𝑖 ≤ 𝜇
Input: Test set, validation set, weight 𝑃 (𝑎𝑖 |𝑉 ) = 𝑠𝑎 𝑖 −𝜇 1
√
− 2 + 6𝜎 , 𝜇 ≤ 𝑠𝑎𝑖 ≤ 𝜇 + 6𝜎)
√
Output: The class to which the sample was classified
⎪
⎩ 6𝜎 √
⎪
⎪
0 𝑠𝑎𝑖 > 𝜇 + 6𝜎)
Create sorted list of all minimal and maximal values (6)
of each iris type form test set. 𝑎𝑖 a current attribute in reduced database
𝑠𝑎𝑖 a current attribute of a sample
Creates nested list of new ranges for each iris type 𝜎 a standard deviation of an attribute
where mean value was calculated for overlapping sets 𝜇 a mean of an attribute in reduced database
and taken as new edge value for set. 𝑉 current reduced variety database
𝑠𝑜𝑟𝑡𝑒𝑑𝑉 𝑎𝑙𝑢𝑒𝑠 ← 𝑙𝑖𝑠𝑡 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑖𝑟𝑖𝑠 𝑡𝑦𝑝𝑒 𝑟𝑎𝑛𝑔𝑒 Counting probability:
𝑛𝑒𝑤𝑅𝑎𝑛𝑔𝑒𝑠 ← 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑖𝑟𝑖𝑠 𝑡𝑦𝑝𝑒 𝑟𝑎𝑛𝑔𝑒𝑠
4
for 𝑖𝑛𝑑𝑒𝑥 < 𝑙𝑒𝑛(𝑣𝑎𝑙𝑖𝑑𝑎𝑡𝑖𝑜𝑛 𝑠𝑒𝑡) do ∏︁
𝑟𝑜𝑤 ← 𝑙𝑖𝑠𝑡 𝑜𝑓 𝑡𝑟𝑎𝑖𝑡𝑠 𝑣𝑎𝑙𝑢𝑒𝑠 𝑜𝑓 𝑜𝑛𝑒 𝑠𝑎𝑚𝑝𝑙𝑒 𝑃 (𝑉 𝑎𝑟𝑖𝑒𝑡𝑦) = 𝑃 (𝐼𝑛𝑖𝑡) * 𝑃 (𝑎𝑖 |𝑉 𝑎𝑟𝑖𝑒𝑡𝑦) (7)
𝑖=1
𝑠𝑎𝑚𝑝𝑙𝑒𝑇 𝑦𝑝𝑒 ← 𝑖𝑟𝑖𝑠𝑡𝑦𝑝𝑒𝑛𝑎𝑚𝑒
𝑠𝑎𝑚𝑝𝑙𝑒𝑉 𝑎𝑙𝑢𝑒 ← 0
3.3.2. Algorithm
𝑖←0
for 𝑡 𝑖𝑛 𝑟𝑜𝑤 do To simplify how Naive Bayes actually works I will explain
𝑠𝑎𝑚𝑝𝑙𝑒𝑉 𝑎𝑙𝑢𝑒+ = 𝑡 * 𝑤𝑒𝑖𝑔ℎ𝑡[𝑖] everything based on Iris database.
𝑖+ = 1 At the beginning, the Naive Bayes algorithm takes
if 𝑠𝑎𝑚𝑝𝑙𝑒𝑉 𝑎𝑙𝑢𝑒 ∈ 𝑛𝑒𝑤𝑅𝑎𝑛𝑔𝑒𝑠[0] then two parameters. First is a test set and the second is a
𝐶𝑙𝑎𝑠𝑠𝑖𝑓 𝑖𝑒𝑑 𝑎𝑠 𝑆𝑒𝑡𝑜𝑠𝑎 validation set.
else if 𝑠𝑎𝑚𝑝𝑙𝑒𝑉 𝑎𝑙𝑢𝑒 ∈ 𝑛𝑒𝑤𝑅𝑎𝑛𝑔𝑒𝑠[1] then Afterwards, it splits the test set to three reduced
𝐶𝑙𝑎𝑠𝑠𝑖𝑓 𝑖𝑒𝑑 𝑎𝑠 𝑉 𝑒𝑟𝑠𝑖𝑐𝑜𝑙𝑜𝑟 databases according to their varieties.
else if 𝑠𝑎𝑚𝑝𝑙𝑒𝑉 𝑎𝑙𝑢𝑒 ∈ 𝑛𝑒𝑤𝑅𝑎𝑛𝑔𝑒𝑠[2] then Subsequently, it calculates a initial probability by
𝐶𝑙𝑎𝑠𝑠𝑖𝑓 𝑖𝑒𝑑 𝑎𝑠 𝑉 𝑖𝑟𝑔𝑖𝑛𝑖𝑐𝑎 counting the number of elements in reduced database
Returns classified type. divided by the number of all elements in the main
database. Next, for a given sample it calculates a
partial probability for each attributes in each reduced
database.
To do so, it takes a list of elements in each attribute and 2. Sensitivity
then it calculates a mean and a standard deviation.
After that, it calls a distribution function which passes 𝑇𝑃
(9)
the given sample’s current calculated attribute, the stan- 𝑇𝑃 + 𝐹𝑁
dard deviation and the mean.
Next, it multiplies the initial probability with four par-
tial probabilities. 3. Precision
At the end, it returns the variety of the highest proba-
𝑇𝑃
bility. (10)
𝑇𝑃 + 𝐹𝑃
Algorithm 4 Naive Bayes algorithm
Input: Test set, sample 4. F1 Score
Output: The class to which the sample may belong
2𝑇 𝑃
(11)
Make three reduced databases according to theirs 2𝑇 𝑃 + 𝐹 𝑃 + 𝐹 𝑁
varieties;
Make a list of attributes names in reduced databases;
Make a empty dictionary; 5. Specificity
𝑖←0
while 𝑖 < 𝑙𝑒𝑛(𝑟𝑒𝑑𝑢𝑐𝑒𝑑𝐷𝑎𝑡𝑎𝑏𝑎𝑠𝑒𝑠) do 𝑇𝑁
(12)
𝑖𝑛𝑖𝑡𝑃 𝑟𝑜𝑏 ← 𝑙𝑒𝑛(𝑟𝑒𝑑𝑢𝑐𝑒𝑑𝐷𝑎𝑡𝑎𝑏𝑎𝑠𝑒𝑠[𝑖]) 𝑇𝑁 + 𝐹𝑃
𝑙𝑒𝑛(𝑑𝑎𝑡𝑎𝐵𝑎𝑠𝑒)
𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ← 𝑖𝑛𝑖𝑡𝑃 𝑟𝑜𝑏
𝑗←0
For this purpose we will make one confusion matrix
while 𝑗 < 𝑙𝑒𝑛(𝑎𝑡𝑡𝑟𝑖𝑏𝑢𝑡𝑒𝑠) do based on one of three abstract class called Setosa. Based
Get a list of all values in the column[j] on that class the all three classifiers will be identify how
Calculate mean and standard deviation from the list well they classified given samples.
𝑝𝑎𝑟𝑡𝑖𝑎𝑙𝑃 𝑟𝑜𝑏 ← DistributionFunction(
sample[j], Setosa Versicolor Virginica
standardDeviation, Setosa TP FP FP
mean;) Versicolor FN TN FN
𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 ← 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 * 𝑝𝑎𝑟𝑡𝑖𝑎𝑙𝑃 𝑟𝑜𝑏; Virginica FN FN TN
Add to dictionary a new record
Return from dictionary variety with the highest probability
4.1. kNN
After testing, we noticed that the results for any k are
very similar to each other. This may be due to the fact
4. Experiments that the Setos class is significantly distant from the other
two classes, which means that there is a very high prob-
In order to properly analyze individual classifiers, we ability that the objects closest to the sample will also be
will perform a series of tests that will allow us to select Stetosa. Below are the results for k equal to 1 2 3 and
the best classifier using the confusion matrix. Confu- 4, respectively.
sion matrix is used in assessing the quality of a binary
classification. It describes how well the classifier classi- Table 1
fied given samples. It also gives us information about Table for k = 1
several things about the classifier such as:
k TP FP TN FN
1. Accuracy 1 16 0 27 2
𝑇𝑃 + 𝑇𝑁 AC SEN PRE F1 SPE
(8) 0.96 0.89 1.00 0.94 1.00
𝑇𝑃 + 𝑇𝑁 + 𝐹𝑃 + 𝐹𝑁
Table 2 Table 7
Table for k = 2 Results for Virginica class
k TP FP TN FN
Accuracy Sensitivity Precision F1 Specificity
2 19 0 22 4
0.96 1.00 0.87 0.93 0.94
AC SEN PRE F1 SPE
0.91 0.83 1.00 0.90 1.00 TP FP TN FN
13 2 30 3
Table 3
Table for k = 3
k TP FP TN FN For the Triangular distribution function results are:
3 14 0 29 2
AC SEN PRE F1 SPE Table 8
0.96 0.88 1.00 0.93 1.00 Results for Setosa class
Accuracy Sensitivity Precision F1 Specificity
Table 4 0.91 0.78 1.00 0.88 1.00
Table for k = 4
TP FP TN FN
k TP FP TN FN
14 0 27 4
4 18 0 26 1
AC SEN PRE F1 SPE
0.98 0.95 1.00 0.97 1.00
Table 9
Results for Versicolor class
4.2. Naive Bayes Accuracy Sensitivity Precision F1 Specificity
We considered in our article two distribution formulas. 0.91 0.83 0.94 0.88 0.96
In this section we decide which of these two are the best
TP FP TN FN
for our database.
15 1 26 3
For the Normal distribution function results are:
Table 10
Table 5 Results for Virginica class
Results for Setosa class
Accuracy Sensitivity Precision F1 Specificity
Accuracy Sensitivity Precision F1 Specificity
0.91 0.92 0.80 0.86 0.91
0.96 0.88 1.00 0.93 1.00
TP FP TN FN
TP FP TN FN
12 3 29 1
14 0 29 2
After analyzing above tables we decided that Normal
distribution is the best distribution function and it will
Table 6 be considered in the final test.
Results for Versicolor class At the end we performed 100 test and we obtained the
Accuracy Sensitivity Precision F1 Specificity following results:
0.96 0.89 1.00 0.94 1.00
Table 11
TP FP TN FN Results for Setosa class
16 0 27 2 Accuracy Sensitivity Precision F1 Specificity
0.95 0.87 1.00 0.93 1.00
Table 12 Table 15
Results for Versicolor class Statistical results for second approach
Accuracy Sensitivity Precision F1 Specificity Accuracy F1 Sensitivity Precision Specificity
0.95 0.93 0.94 0.93 0.97 0.96 0.93 0.92 0.95 0.97
Table 13
Results for Virginica class For the most efficient implementation, the following
results were obtained for individual types of iris flowers.
Accuracy Sensitivity Precision F1 Specificity After performing 100 tests, the following results were
0.95 0.93 0.92 0.93 0.96 obtained.
Table 16
Results for Setosa class
4.3. Soft sets
The determined values of Pearson correlation coefficients Accuracy Sensitivity Precision F1 Specificity
for each characteristic of iris flowers allowed choosing 0.98 0.95 1.00 0.97 1.00
the weight of the features for the optimal classifier ac-
TP FP TN FN
curacy. An association between individual features was
considered and their influence on the classifier efficiency. 18 0 26 1
Based on these factors different weights were applied to
select the most suitable solution.
Table 17
Results for Versicolor class
Accuracy Sensitivity Precision F1 Specificity
0.98 0.93 1.00 0.97 1.00
TP FP TN FN
14 0 30 1
Figure 6: Pearson correlation coefficients for iris characteris-
tics
Table 18
Considering obtained correlation values, it was Results for Virginica class
concluded that the most important characteristics
are the following in descending order: petal-length, Accuracy Sensitivity Precision F1 Specificity
petal-width, sepal-length, and sepal-width. According 0.98 1.00 0.92 0.96 0.97
to these observations, successively assigning different
weight values, the best results were observed with TP FP TN FN
weight 𝑤 = [0.1, 0, 0.5, 0.4]. 12 1 32 0
The analysis of the results for both the first and
the second algorithm showed that the first algorithm is a
more effective soft set implementation. After performing
100 tests, the following results were obtained.
Table 14
Statistical results for first approach
Accuracy F1 Sensitivity Precision Specificity
0.96 0.94 0.92 0.96 0.98
5. Conclusion Table 23
Results for Versicolor class
In order to establish the most efficient classifier, the pre-
Accuracy Sensitivity Precision F1 Specificity
pared implementations were compared on the same par-
tition of the Iris database. In comparison, the following 0.96 0.89 1.00 0.94 1.00
results were statistically calculated.
TP FP TN FN
Results for kNN:
17 0 26 2
Table 19
Results for Setosa class
Table 24
Accuracy Sensitivity Precision F1 Specificity Results for Virginica class
0.96 0.87 1.00 0.93 1.00 Accuracy Sensitivity Precision F1 Specificity
TP FP TN FN 0.96 1.00 0.87 0.93 0.94
13 0 30 2 TP FP TN FN
13 2 30 0
Table 20
Results for Versicolor class Results for Soft sets:
Accuracy Sensitivity Precision F1 Specificity
Table 25
0.96 0.89 1.00 0.94 1.00
Results for Setosa class
TP FP TN FN Accuracy Sensitivity Precision F1 Specificity
17 0 26 2 0.98 0.93 1.00 0.96 1.00
TP FP TN FN
13 0 31 1
Table 21
Results for Virginica class
Accuracy Sensitivity Precision F1 Specificity
Table 26
0.96 1.00 0.87 0.93 0.94 Results for Versicolor class
TP FP TN FN Accuracy Sensitivity Precision F1 Specificity
13 2 30 0 0.98 0.93 1.00 0.96 1.00
TP FP TN FN
Results for Naive Bayes:
17 0 27 1
Table 22
Results for Setosa class
Table 27
Accuracy Sensitivity Precision F1 Specificity Results for Virginica class
0.96 0.87 1.00 0.93 1.00
Accuracy Sensitivity Precision F1 Specificity
TP FP TN FN
0.98 1.00 0.93 0.97 0.97
13 0 30 2
TP FP TN FN
14 1 30 0
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