=Paper=
{{Paper
|id=Vol-3360/p09
|storemode=property
|title=A Simple Approach to Weather Predictions by using Naive
Bayes Classifiers
|pdfUrl=https://ceur-ws.org/Vol-3360/p09.pdf
|volume=Vol-3360
|authors=Agnieszka Lutecka,Zuzanna Radosz
|dblpUrl=https://dblp.org/rec/conf/system/LuteckaR22
}}
==A Simple Approach to Weather Predictions by using Naive
Bayes Classifiers==
https://ceur-ws.org/Vol-3360/p09.pdf
A Simple Approach to Weather Predictions by using Naive
Bayes Classifiers
Agnieszka Lutecka1 , Zuzanna Radosz1
1
Silesian University Of Technology, Faculty of Applied Mathematics, Kaszubska 23, 44-100 Gliwice, Poland
Abstract
This article presents and explains how we have used Naive Bayes Classifier and date base to predict the weather. We compare
the dependence of accuracy on the probability of different distributions for various types of data.
Keywords
Naive Bayes Classifier, probability distribution, Python
1. Introduction β’ π (π΅|π΄) is the probability that we would observe
such data if the hypothesis were true
Many IT systems use the widely understood artificial β’ π (π΄) is the a priori probability that the hypothe-
intelligence [1, 2]. Artificial intelligence methods also sis is true
apply to the data processing [3, 4, 5]. The wide appli- β’ π (π΅) is the probability of the observed data
cation of artificial intelligence also applies to systems
installed in cars, which are used, for example, to detect Importantly, the naive Bayes classifier assumes that
the quality of the surface [6]. Many technical problems the influence of the attributes is independent of each
lead to the optimization tasks [7, 8, 9], where the com- other, therefore π (π΅|π΄) can be written as
plexity of the [10, 11, 12] functional is a big challenge. π (π΅1 |π΄) * π (π΅2 |π΄) * ... * π (π΅π |π΄). (2)
Optimization processes concern many different areas of The naivety of this classifier follows from the above as-
life require constant search for new, more effective op- sumption.
timization methods [13, 14] based on the observation
of nature [15, 16, 17]. A very important and important
branch of artificial intelligence are the applications of 3. Description of how the
broadly understood [18] neural networks. Interesting
applications concern health protection [19], adult care
program works
[20, 21]. Artificial intelligence methods are also used We started the project with an analysis of data from the
for weather forecasting [22, 23, 24], as well as for the database. Initially, we shuffled and normalized the data
detection of features [25, 26, 27]. to the 0 β 1 range to operate on smaller numbers, thus
increasing the performance of our program. After di-
2. Program description viding into validation and training sets, we move on to
the main part of our program, i.e. the use of the naive
The task of our program is to predict the weather using Bayesian classifier. Its task is to return the name of the
the naive Bayes classifier. It is especially suitable for most probable weather for a given sample.
problems with a lot of input data, so it is perfect for our This algorithm uses a probability distribution defined by
project. It uses a conditional probability formula that a density function that describes how the probability of
looks like this: a random variable (x) is distributed. We implemented 5
different probability distributions to compare the algo-
π (π΅|π΄) * π (π΄) rithmβs efficiency for different probability density formu-
π (π΄|π΅) = (1)
π (π΅) las. We use the following distributions: Gauss, Laplace,
log-normal, uniform, triangular.
β’ π΄ is our hypothesis
β’ π΅ is the observed data (attribute values)
3.1. Gaussian distribution
SYSYEM 2022: 8th Scholarβs Yearly Symposium of Technology, Engi- It is one of the most important probability distributions,
neering and Mathematics, Brunek, July 23, 2022 playing an important role in statistics. The formula for
" agnilut814@polsl.pl (A. Lutecka); zuzarad785@polsl.pl the probability density is as follows:
(Z. Radosz)
Β© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License
1 β(π₯ β π)2
CEUR
Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org) β exp( ) (3)
2π 2
http://ceur-ws.org
Workshop
π 2π
ISSN 1613-0073
Proceedings
64
Agnieszka Lutecka et al. CEUR Workshop Proceedings 64β75
The probability function plot of this distribution is a bell- Where π is the mean value and π is the standard devi-
shaped curve (the so-called bell curve). ation.
The density function graph is as follows:
Figure 1: Graph of the probability density function
Source: Wikipedia.org
Figure 3: Graph of the probability density function
Where π is the expected or mean value and π stan- Source: Wikipedia.org
dard deviation. The red line corresponds to the standard
normal distribution.
3.2. Laplace Distribution 3.4. Triangular Distribution
Itβs a continuous probability distribution named after It is a continuous probability distribution of a random
Pierre Laplace. The probability density is given by the variable. The probability density of a triangular distribu-
formula: tion can also be expressed as:
1 β|π₯ β π|
exp( ) (4) β
0 dla π₯ < π β 6π
β§
2π π βͺ
βͺ β
Where π is the expected value, i.e. the mean, and b> 0 is + β16π dla π β 6π β€ π₯ β€ π
βͺ π₯βπ
β¨
6π 2 β
the scale parameter. The function graph looks like this: π (π₯) =
βͺβ π₯βπ 2 +
β1 dla π β€ π₯ β€ π + 6π
β© 6π 6π β
βͺ
βͺ
0 dla π₯ > π + 6π
(6)
Where π is the mean value and π is the standard devi-
ation.
The function graph looks like this:
Figure 2: Graph of the probability density function
Source: Wikipedia.org
3.3. Log Normal Distribution Figure 4: Graph of the probability density function
Source: Wikipedia.org
It is the continuous probability distribution of a positive
random variable whose logarithm is normally distributed.
Pattern:
1 β(πππ₯ β π)2 3.5. Uniform distribution
β exp( ) * 1(0, β) (5)
2πππ₯ 2π 2 It is a continuous probability distribution for which the
probability density in the range from a to b is constant
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Agnieszka Lutecka et al. CEUR Workshop Proceedings 64β75
and not equal to zero, and otherwise equal to zero. We column j, sr [j] - the mean value of the column j and
can see it in the formula below std [j] - standard deviation of the values from column j.
β These methods process the input data through the formu-
β¨0 dla π₯ < π ββ 3π
β§
βͺ
β las for the probability distribution and return the value
π (π₯) = 2β13π dla π β 3π β€ π₯ β€ π + 3π (7)of the probability density function at the point sample
β
0 dla π₯ > π + 3π [j], that is, the probability of sample [j] occurring under
βͺ
β©
the conditions sr [j] and st [j]. Finally, the algorithm
Where π is the mean value and π is the standard devia- returns the name of the weather most likely to occur at
tion. the sample input.
The function graph is as follows: Each probability distribution has a differently defined
density function. Therefore, the distributions may differ
in the results. Below we present the pseudocode of Naive-
Classifier class methods with an emphasis on processing
the input data by probability distributions.
Data: Input πππ‘π, π πππππ, ππππ
Result: Weather Name
Extract weather records ;
Enter the weather record sets into the list πππππ ;
π := 0;
for π < πππ(πππππ ) do
Figure 5: Graph of the probability density function π‘π = [];
Source: Wikipedia.org π := 1;
for π < 7 do
Calculate the mean value of the column j ;
Calculate the column standard deviation j
3.6. Select Distributions ;
if ππππ == πππππππβ² π then
As we can see, the formulas differ significantly, which tr.append(NaiveClassifier.laplace
will definitely have a big impact on the effectiveness (sample[j],sr[j-1]));
of the program. We tried to choose such formulas for end
the probability density so that the values were not very if ππππ == πππ β ππππππππ¦ then
divergent, as we will present in the next paragraphs. tr.append(NaiveClassifier.logarytmiczny
(sample[j],std[j-1],sr[j-1]));
4. Algorithm end
if ππππ == ππππππ π‘ππππ¦ then
The naive Bayes classifier uses probability density func- tr.append(NaiveClassifier.jednostajny
tions to compute the probability of a given start con- (sample[j],std[j-1],sr[j-1]));
dition. The NaiveClassifier class has 6 static methods: end
βlaplaceβ, βlogarytmicznyβ, βjednastajnyβ, βtrojkatnyβ, if ππππ == π‘ππππππ‘ππ¦ then
βgaussβ, βbayesβ, where the first 5 are different proba- tr.append(NaiveClassifier.trojkatny
bility distributions . We use as many as 5 to compare (sample[j],std[j-1],sr[j-1]));
the algorithmβs effectiveness for different formulas on end
the probability density. The "bayes" method accepts the if ππππ == πππ’π π then
following input data: data β training set, sample β a set of tr.append(NaiveClassifier.gauss
values in the range 0-1 that represent successive database (sample[j],std[j-1],sr[j-1]));
columns, name β the name of the probability distribution end
(Gauss, Laplace, log-normal, uniform, triangular). At the end
beginning, the algorithm extracts the records with the Return the probability of the given weather;
given weather. Then, using the loops, the program goes end
through all the records of the training set, calculating Return the name of the most likely weather;
the mean values and standard deviation of each column Algorithm 1: Bayes algorithm
for each type of weather. Using the given "name", the
algorithm calls the appropriate method, where the input
data is: sample [j] - where j is the sample value for the
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Agnieszka Lutecka et al. CEUR Workshop Proceedings 64β75
Data: Input π₯, ππππ Data: Input π₯, π π‘π,π π
Result: The value of the density function at x Result: The value of the density function at x
π := 2; return (1/(dev*np.sqrt(2*np.pi)))*np.exp(-((x-
return mean)**2)/(2*dev**2));
((1/(2*b))*(math.exp(-(math.fabs(x-mean)/b))));
Algorithm 2: Laplaceβs algorithm Algorithm 6: Gauss algorithm
Data: Input π₯, π π‘π,π π
Result: The value of the density function at x 5. Databases
if π₯ > 0 then
return (1/((math.pi*2)**(1/2)*std*x))*math.exp(- 5.1. Database Analysis
((math.log(x)-sr)**2)/(2*std**2));
For our project, we use the Istanbul Weather Data
database, downloaded from the kaggle website. The
end database has 3896 records. It contains the following
else data columns: DateTime, Condition, Rain, MaxTemp,
return 0; MinTemp, SunRise, SunSet, MoonRise, MoonSet, Avg-
end Wind, AvgHumidity, AvgPressure.
Algorithm 3: Logarithmic algorithm
Data: Input π₯, π π‘π,π π
Result: The value of the density function at x
if π₯ < π π β 3 * *(1/2) * π π‘π then
return 0;
end
if π₯ >= π π β 3 * *(1/2) * π π‘π && π₯ <=
π π + 3 * *(1/2) * π π‘π then
return 1/(2*(3**(1/2))*std);
end
if π₯ > π π + 3 * *(1/2) * π π‘π then
return 0;
end
else
return 0; Figure 6: Data types in each column
end
Algorithm 4: Uniform algorithm
We analyzed the data using a matrix graph that shows
the relationships between weather variables.
Data: Input π₯, π π‘π,π π
The chart is dominated by warm colors, which means
Result: The value of the density function at x
that most of the records in our database are sunny and
if π₯ < π π β 6 * *(1/2) * π π‘π then
slightly cloudy.
return 0;
It can be seen that the data is presented in compact
end
groups. This means that the parameters for different
if π₯ >= π π β 6 * *(1/2) && π₯ <= π π then
weather conditions do not differ much from the others.
return (x-sr)/(6*std**2)+1/(6**(1/2)*std);
This can make our algorithm that determines the weather
end
based on these parameters not very accurate. There
if π₯ > π πππππ₯ <= π π‘π + 6 * *(1/2) * π π‘π then
may be situations where the algorithm will calculate the
return -(x-sr)/(6*std**2) + 1/(6**(1/2)*std);
weather "Sunny" because it was the most probable, but
end
the actual weather will be different. In the Experiments
if π₯ > π π + 6 * *(1/2) * π π‘π then
section, we will test and analyze the obtained results of
return 0;
the algorithmβs accuracy.
end
else
return 0; We also analyzed the data using a violin graph for all
end weather conditions and maximum temperature as we can
Algorithm 5: The triangle algorithm see below:
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Agnieszka Lutecka et al. CEUR Workshop Proceedings 64β75
Figure 7: Matrix graph
In the attached photo we can see how the temperature To normalize the data to the range 0-1, we changed int64
value changes for a given weather, for example for "Mod- to float64.
erate rain", i.e. moderate rain, the maximum temperature
ranges from 5 to 20 degrees.
6. Implementation
5.2. Database modification 6.1. ProcessingData class
DateTime, SunRise, SunSet, MoonRise, MoonSet will not Our project consists of two files: a file containing the
be used in our project, so we can get rid of them. program code - "Pogoda.ipnb" and the database - "Istan-
d a t a . drop ( β DateTime β , a x i s = 1 , bul Weather Data.csv". After analyzing the data from
i n p l a c e = True ) the database, we went to the "ProcessingData" class, in
d a t a . drop ( β S u n R i s e β , a x i s = 1 , which we created 3 static methods: shuffle, splitSet and
i n p l a c e = True ) normalize.
d a t a . drop ( β SunSet β , a x i s = 1 ,
i n p l a c e = True )
d a t a . drop ( β MoonRise β , a x i s = 1 ,
6.2. Shuffle method
i n p l a c e = True )
d a t a . drop ( β MoonSet β , a x i s = 1 , It takes base as input, i.e. our database. We use for loop
i n p l a c e = True ) to go through it selecting records and swapping them.
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Agnieszka Lutecka et al. CEUR Workshop Proceedings 64β75
Figure 8: Violin graph
Data: Input πππ π Data: Input π₯, π
Result: Database with jumbled records Result: Training and validation set
for π in range(len(base)-1,-1,-1): do π = πππ‘(πππ(π₯) * π)
take two records from the database, the π₯π ππππ = π₯[: π]
second with a random index and swap them π₯π ππ = π₯[π :]
end return xTrain, xVal;
return base; Algorithm 8: SplitSet algorithm
Algorithm 7: The shuffle algorithm
def s p l i t S e t ( x , k ) :
Program code n= i n t ( l e n ( x ) β k )
x T r a i n =x [ : n ]
@staticmethod
x V a l =x [ n : ]
def s h u f f l e ( base ) :
r e t u r n xTrain , xVal
f o r i in range ( len ( base )
β1 , β1 , β1) :
base . i l o c [ i ] , base . i l o c [ rd
6.4. Normalize method
. r a n d i n t ( 0 , i ) ]= b a s e .
i l o c [ rd . r a n d i n t ( 0 , i ) ] , Takes x, which is a database that will have records scram-
base . i l o c [ i ] bled using the shuffle method. At the beginning, we enter
return base all data from the database into the variable values, except
for the string value, and the values of the column names
into the variable columnNames. We loop through all the
6.3. Splitset method columns in the column, and then take all the rows in
the column column and store them in the variable data.
It takes as input x - database and k - division of the set. In
Variables max1 and min1 are assigned maximum and
the variable n we write the length of the set x multiplied
minimum values from date. Using the next loop, we go
by k to know how to divide this set. Then, to two xTrain
through all the rows and assign to the variable val the
variables, we write the data from the database to the
formula for normalization min-max, that is, we subtract
value n, creating the training set, and to the variable xVal
the coordinate database record [row, column] from the
- all data following the value n, creating the validation
value min1, and then divide this difference by the differ-
set. Finally, we return both of these sets.
ence between max1 and min1. Finally, we write the value
after normalization to the database. The method returns
us a normalized database.
Program code
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Agnieszka Lutecka et al. CEUR Workshop Proceedings 64β75
Data: Input π₯ described in general in the "Algorithm" section, so now
Result: Standardized database we will look at the details. First, the method extracts the
π£πππ’ππ = π₯.π πππππ‘π π‘π¦πππ (ππ₯πππ’ππ =, , ππππππ‘β²β² ) database records with the given weather name into sepa-
ππππ’πππ ππππ = π£πππ’ππ .ππππ’πππ .π‘ππππ π‘() rate lists. Then each of the lists created above is put into
for ππππ’ππππππππ’πππ ππππ ): do the "names" list. Additionally, we create a stringnames
take all the rows from the column column list with string weather names and a values list that will
πππ₯1 = πππ₯(πππ‘π) πππ1 = πππ(πππ‘π) store the calculated probabilities for each weather.
for row in range(0,len(x) do
we go through all the lines
π£ππ = (π₯.ππ‘[πππ€, ππππ’ππ] β
πππ1)/(πππ₯1 β πππ1)
π₯.ππ‘[πππ€, ππππ’ππ] = π£ππ
end
end
return x;
Algorithm 9: The normalize algorithm
Program code
def normalize ( x ) :
v a l u e s =x . s e l e c t _ d t y p e s (
exclude =" o b j e c t " ) # s e l e c t
a l l d a t a from t h e d a t a b a s e
except the object , i . e .
string
columnNames= v a l u e s . columns .
tolist ()
f o r column i n columnNames :
d a t a =x . l o c [ : , column ] #
summon a l l rows i n
column column
max1=max ( d a t a )
min1=min ( d a t a )
f o r row i n r a n g e ( 0 , l e n ( x )
) : #we go t h r o u g h a l l
the l i n e s
v a l = ( x . a t [ row , column
] β min1 ) / ( max1βmin1
)
x . a t [ row , column ]= v a l
return x
6.5. NaiveClassifier class and bayes
method
The NaiveClassifier class has 6 static methods: "laplace",
"logarithmic", "uniform", "triangle", "gauss", "bayes". The
first 5 are methods describing the functions of different
probability distributions. The "bayes" method has been
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Agnieszka Lutecka et al. CEUR Workshop Proceedings 64β75
Data: Input πππ‘π, π πππππ, ππππ
Result: Weather name
Extract weather records ;
Enter weather record sets into πππππ ;
Enter weather names in the list π π‘πππππ ππππ ;
π£πππ’ππ := [] π := 0;
for π < πππ(πππππ ) do
π‘π = [];
π π = [];
π π‘π = [];
π := 1;
for π < 7 do
Calculate the mean value of the column j ;
Calculate the column standard deviation j
;
if π π[π β 1] == 0 then
sr[j-1]=0.0000001;
end
if π π‘π[π β 1] == 0 then
std[j-1]=0.0000001;
end
if ππππ == πππππππβ² π then
tr.append(NaiveClassifier.laplace
(sample[j],sr[j-1]));
end
if ππππ == πππ β ππππππππ¦ then
tr.append(NaiveClassifier.logarytmiczny
(sample[j],std[j-1],sr[j-1]));
end
if ππππ == ππππππ π‘ππππ¦ then
tr.append(NaiveClassifier.jednostajny
(sample[j],std[j-1],sr[j-1]));
end
if ππππ == π‘ππππππ‘ππ¦ then
tr.append(NaiveClassifier.trojkatny
(sample[j],std[j-1],sr[j-1]));
end
if ππππ == πππ’π π then
tr.append(NaiveClassifier.gauss
(sample[j],std[j-1],sr[j-1]));
end
end
values.append
(np.prod(tr)*len(names[i])/len(names));
end
πΌππππ₯ = π£πππ’ππ .πππππ₯(πππ₯(π£πππ’ππ ));
return value from π π‘πππππππππ at index πΌππππ ;
Algorithm 10: Bayes algorithm
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Agnieszka Lutecka et al. CEUR Workshop Proceedings 64β75
The next step is to loop through all the values of the @staticmethod
names list in sequence. Then we create auxiliary lists: tr d e f a n a l i z e ( T r a i n , Val , name ) :
[] - to store 6 probability values that correspond to the c o r r e c t =0
next database column, sr [] - to store the mean values f o r i in range ( len ( Val ) ) :
from each column, std - to store the standard deviations if NaiveClassifier .
for each column. We pass the next loop through all the c l a s s i f y ( Train , Val .
columns one by one. Then we calculate the mean and i l o c [ i ] , name ) == V a l .
standard deviation for a given column. The next step is i l o c [ i ] . Condition :
the conditions that prevent sr [] and std [] from occurring. c o r r e c t +=1
The time has come for timetables. Depending on the in- accuracy = c o r r e c t / len ( Val ) β100
put data "name" to the list tr [] we add the result of the return accuracy
function of the given distribution. After going through
the inner loop, we compute the value from Bayesβ theo-
rem. Based on the formula for conditional probability, we 7. Tests
multiply the values in the tr list, then multiply that prod-
uct by the list of names [i]. We divide the whole thing by We started our tests by checking the algorithmβs opera-
the length of the "names" list. We add the obtained result tion using various samples.
to the "values" list. After going through both loops, we
determine the index from the values list with the highest
value. Finally, we return the name of the weather with
the given index from the stringnames list.
6.6. AnalizingData class
Another class in our project is AnalizingData with the
Figure 9: Sample tests
Analyze method. This method measures the accuracy
as a percentage of the Bayes classifier. The input data
is: Train - training set, Val - validation set and name The above code shows us that depending on the value in
- name of the probability distribution. The algorithm the sample, the algorithm returns different values, which
first sets the value of the corrtect variable to 0. Then it proves the correct operation of the algorithm.
goes through the iterator loop and goes through all the
records of the Val set. If the value returned by the bayes The next step was to determine the accuracy of our al-
classifier at the input: Train, Val [i], name is the same gorithm for various probability distributions. For this we
as the weather name for the Val [i] record, increase the used the AnalizingData class with the analysis method.
variable correct by 1. Finally, the algorithm returns the We called the method for each of the 5 types of probabil-
accuracy, which we calculate by dividing correct by the ity distributions for the training and validation division
product the length of the validation set and 100. in the ratio of 7: 3, and then, using the plt package, we
displayed the graph.
Data: Input π ππππ, π ππ, ππππ
Result: Accuracy of the bayes algorithm
πππππππ‘ := 0
π := 0 for π < πππ(π ππ)): do
if
π πππ£ππΆπππ π ππ πππ.ππππ π ππ π¦(π ππππ, π ππ.ππππ[π], ππππ) ==
π ππ.ππππ[π].πΆπππππ‘πππ then
correct+=1;
end
end
accuracy=correct/len(Val)*100;
return x;
Algorithm 11: Analyze algorithm Figure 10: The graph of the accuracy of the algorithm de-
pending on the probability distribution
Program code
As you can see in the attached picture, the algorithm
c l a s s AnalizingData :
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Agnieszka Lutecka et al. CEUR Workshop Proceedings 64β75
has different accuracies depending on the probability dis-
tribution. The Gaussian distribution definitely exceeds
other distributions with its accuracy, which is over 60%.
This means that more than 60% of the weather names
returned were valid. However, the Laplace and uniform
distributions do not lag far behind. Their values are in the
range 50-60%. Log normal and triangular distributions
are the least efficient because their accuracy is less than
20%. Additionally, we measured the execution time of
the algorithm. It was almost 4.512 minutes.
Figure 12: Bar chart 1. for the training set 0.1
8. Experiments
8.1. Analysis of algorithm results for
normalized and non-normalized data
We tested the operation of our program for both nor-
malized and non-normalized values and we determined
the algorithm execution time for both data sets. The
graphs below show the dependence of the accuracy on
the probability of individual distributions.
Figure 13: Bar chart 2. for the training set 0.3
Figure 11: Bar chart for unnormalized data
The first plot shows the Bayesian operation for unnor-
malized data in a ratio of 7: 3, while the second plot shows Figure 14: Bar chart 3. for the training set 0.5
the operation for unnormalized data with the same par-
tition. The program launch time for the first graph was
4.512 minutes, while for the second graph it was 4.433
minutes. As we can see, the only significant difference
was when using the Laplace distribution, the accuracy of
which decreased by almost 10%. The remaining results
are similar for both types of data. The time difference is
insignificant as it is only 5.023s.
8.2. Analysis of the algorithmβs results
for different data divisions
The following charts show the efficiency of the algorithm
Figure 15: Bar chart 4. for the training set 0.9
for normalized data for various divisions into training
and validation sets:
The algorithm execution time decreases with the re-
duction of the training set. For the last execution of the algorithm, where the division was in the ratio of 9: 1, the
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Agnieszka Lutecka et al. CEUR Workshop Proceedings 64β75
time was only 1.467 minutes. However, the first calcula- [5] R. Avanzato, F. Beritelli, M. Russo, S. Russo, M. Vac-
tions, where the division was in the ratio of 1: 9, took as caro, Yolov3-based mask and face recognition al-
long as 9,517 minutes. This is because by reducing the gorithm for individual protection applications, in:
training set, we increase the number of records in the CEUR Workshop Proceedings, volume 2768, CEUR-
validation set. As a result, the algorithm will be called WS, 2020, pp. 41β45.
more times and the most time-consuming elements such [6] M. WoΕΊniak, A. Zielonka, A. Sikora, Driving sup-
as extracting records with a given weather or loops will port by type-2 fuzzy logic control model, Expert
be performed many times. Systems with Applications 207 (2022) 117798.
Analyzing the above, we can see that the accuracy [7] G. Borowik, M. WoΕΊniak, A. Fornaia, R. Giunta,
of the Gaussian distribution is superior to all of them, C. Napoli, G. Pappalardo, E. Tramontana, A soft-
its value is practically unchanged. The Laplace distri- ware architecture assisting workflow executions
bution is in second place, almost tapping 60%. The on cloud resources, International Journal of Elec-
value of the uniform distribution ranges from 50-55 %. It tronics and Telecommunications 61 (2015) 17β23.
achieves the most on the last chart where the training doi:10.1515/eletel-2015-0002.
set is 0.9. Triangular and log normal distributions reach [8] T. Qiu, B. Li, X. Zhou, H. Song, I. Lee, J. Lloret,
much lower values than the previously mentioned dis- A novel shortcut addition algorithm with particle
tributions. The jump is quite big, around 30%. However, swarm for multisink internet of things, IEEE Trans-
the log-normalized distribution only slightly exceeds the actions on Industrial Informatics 16 (2019) 3566β
triangular distribution once, and it is in the third graph. 3577.
Nevertheless, the accuracy values of both distributions [9] G. Capizzi, G. Lo Sciuto, C. Napoli, R. Shikler,
never exceed 20%. M. Wozniak, Optimizing the organic solar cell man-
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and neural networks, Energies 11 (2018).
9. Conclusion [10] M. WoΕΊniak, A. Sikora, A. Zielonka, K. Kaur, M. S.
Hossain, M. Shorfuzzaman, Heuristic optimization
We can conclude from this that the Gauss distribution
of multipulse rectifier for reduced energy consump-
is the best probability distribution for our database. The
tion, IEEE Transactions on Industrial Informatics
algorithm with this distribution, with each modification,
18 (2021) 5515β5526.
correctly determines about 60% of weather names, which
[11] G. Capizzi, G. Lo Sciuto, C. Napoli, E. Tramontana,
is a good but unsatisfactory value. This is due to the
M. WoΕΊniak, A novel neural networks-based tex-
way the data is distributed in the database. In the case
ture image processing algorithm for orange defects
of more different values for different weather conditions,
classification, International Journal of Computer
this algorithm could become much more efficient.
Science and Applications 13 (2016) 45β60.
[12] N. Brandizzi, S. Russo, R. Brociek, A. Wajda, First
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