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1
Content available remote On the Correlation between Random Variables and their Principal Components
Gniazdowski Zenon
Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki
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2023
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nr 28
41--55
EN
The article attempts to find an algebraic formula describing the correlation coefficients between random variables and the principal components representing them. As a result of the analysis, starting from selected statistics relating to individual random variables, the equivalents of these statistics relating to a set of random variables were presented in the language of linear algebra, using the concepts of vector and matrix. This made it possible, in subsequent steps, to derive the expected formula. The formula found is identical to the formula used in Factor Analysis to calculate factor loadings. The discussion showed that it is possible to apply this formula to optimize the number of principal components in Principal Component Analysis, as well as to optimize the number of factors in Factor Analysis.
2
Content available On the analysis of correlation between nominal data and numerical data
Gniazdowski Zenon
Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki
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2022
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nr 27
57--82
EN
The article investigates the possibility of measuring the strength of a linear corre lation relationship between nominal data and numerical data. Correlation coeffi cients for variables coded with real numbers as well as for variables coded with complex numbers were studied. For variables coded with real numbers, unam biguous measures of real linear correlation were obtained. In the case of complex coding, it has been observed that the obtained complex correlation coefficients change with the permutation of the phases in the complex numbers used to code classes of elements with equal cardinalities. It was found that a necessary condi tion for linear correlation is the possibility of linear ordering of a set with data. Since linear order is not possible in the set of complex numbers, complex correla tion coefficients cannot be used as a measure of linear correlation. In the event of such a situation, a substitute action was suggested that would prevent equal cardi nality of classes of identical elements contained in the set with nominal data. This action would consist in the correction of data, analogous to the correction during preprocessing or cleaning of data containing missing or outlier values.
3
Content available Principal Component Analysis versus Factor Analysis
Gniazdowski Zenon
Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki
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2021
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nr 24
35--88
EN
The article discusses selected problems related to both principal component analysis (PCA) and factor analysis (FA). In particular, both types of analysis were compared. A vector interpretation for both PCA and FA has also been proposed. The problem of determining the number of principal components in PCA and factors in FA was discussed in detail. A new criterion for determining the number of factors and principal components is discussed, which will allow to present most of the variance of each of the analyzed primary variables. An efficient algorithm for determining the number of factors in FA, which complies with this criterion, was also proposed. This algorithm was adapted to find the number of principal components in PCA. It was also proposed to modify the PCA algorithm using a new method of determining the number of principal components. The obtained results were discussed.
4
Content available O niektórych aspektach zdalnego egzaminowania z matematyki dyskretnej
Gniazdowski Zenon
Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki
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2020
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nr 23
51--82
PL
W niniejszym artykule opisano przypadek wykorzystania platformy Moodle do zdalnego egzaminowania z matematyki dyskretnej na informatycznych studiach pierwszego stopnia (inżynierskich). Opisany przypadek był konsekwencją problemów wynikająacych z zaistniałej konieczności zdalnego egzaminowania, spowodowanej pandemią koronawirusa COVID-19. W odpowiedzi na te problemy, na platformie Moodle przygotowano odpowiedni zestaw zadań egzaminacyjnych, które były przeznaczone do rozwiązywania przez studentów. W tym celu wykorzystano kilka nadających się do tego celu szablonów pytań, które oferuje platforma Moodle. Po przygotowaniu zadań utworzono quiz, który został wykorzystany do egzaminowania. W pracy opisano zarówno proces tworzenia zadań egzaminacyjnych, jak i proces tworzenia quizu, a także przedstawiono wnioski wynikające z przeprowadzonego eksperymentu.
EN
This article describes the case of using the Moodle platform for remote examination of discrete mathematics in first-cycle (engineering) studies. The described case was a consequence of problems resulting from the necessity of remote examination, caused by the COVID-19 coronavirus pandemic. In response to these problems, an appropriate set of examination tasks was prepared on the Moodle platform, which were intended for students to solve. For this purpose, several suit-able question templates from the Moodle platform were used. After preparing the tasks, a quiz was created that was used for the examination. The paper describes both the process of creating examination tasks and the process of creating a quiz, as well as the conclusions resulting from the experiment.
5
Content available Extension of the one-dimensional Stoney algorithm to a two-dimensional case
Gniazdowski Zenon
Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki
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2019
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nr 20
41--66
EN
This article presents the extension of the one-dimensional Stoney algorithm to a two-dimensional case. The proposed extension consists in modifying the method of curvature estimation. The surface profile of the wafer before deposition of the thin film and after its deposition was locally approximated by the quadric. From this quadric, a quadratic form and the first degree surface were separated. An eigenproblem was solved for the matrix of this quadratic form. From eigenvectors a new coordinate system was created in which a new formula of the quadric was found. In this new coordinate system, the two-dimensional problem of estimating thecurvaturetensorhasbeensolvedbysolvingtwoindependentone-dimensional problems of curvature estimation. Returning to the primary coordinate system, in this primary system, a solution to the two-dimensional problem was obtained. The article proposes five versions of the two-dimensional Stoney algorithm, with diverse complexity and accuracy. The recommendation for the version of the algorithm that could be practically used was also presented.
6
Content available Detection of a Source Code Plagiarism in a Student Programming Competition
Gniazdowski Zenon, Boniecki Maciej
Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki
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2019
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nr 21
74--94
EN
The article presents a system for testing the independence of solutions to algorithmic problems sent by students as part of the student programming competition. First, the context was discussed, as well as the need to organize programming competitions resulting from this context. Then, an algorithm was proposed to study the mutual similarity of source codes of programs sent as part of a programming competition. Since, after implementation, the algorithm was used in practice, examples of its application for detecting the plagiarism of source codes of solutions in two programming competitions conducted as part ofmclasses on Algorithms and Numerical Methods were also presented. Finally, the effectiveness of the solutions used in the work was discussed.
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