Wyniki wyszukiwania - Biblioteka Nauki

1

Analysis of nominal data – multi-way contingency table

100%

Stanimir A.

Mathematical Economics

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2011

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nr 7 (14)

229-240

EN

Presented in this paper the method of graphical presentation of the relationship between nominal variables and their categories gives the opportunity for an extensive diagnosis of dependence variables. Correspondence analysis and mosaic plots are based on the same grounds, i.e. contingency table or multi-way contingency table. Correspondence analysis can be used in the study of relationships between two or more nominal variables without limiting the number of categories. In the case of many variables, the multidimensional contingency table is used very often. Only the difficulty of construction of such a table and the combined variables can affect the decision of a researcher about the validity of using this solution. For mosaic plots the situation is different. These graphs represent very well the relationships between two categories of nominal variables with few categories. The introduction of another variable to the study, which is described by two or three categories, is also not too problematic, and the graph is easy to interpret. However, if in a multi-way contingency table variables are a combination of several primary variables, described with many categories, the mosaic plot is no longer as clear as the projection made in correspondence analysis.

2

Numerical Coding of Nominal Data

100%

Gniazdowski Z. , Grabowski M.

Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki

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2015

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tom nr 12

53--61

EN

In this paper, a novel approach for coding nominal data is proposed. For the given nominal data, a rank in a form of complex number is assigned. The proposed method does not lose any information about the attribute and brings other properties previously unknown. The approach based on these knew properties can been used for classification. The analyzed example shows that classification with the use of coded nominal data or both numerical as well as coded nominal data is more effective than the classification, which uses only numerical data.

3

88%

Grabowski M. , Korpusik M.

Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki

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2013

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tom nr 10

25--37

EN

Classification theory analytical paradigm investigates continuous data only. When we deal with a mix of continuous and nominal attributes in data records, difficulties emerge. Usually, the analytical paradigm treats nominal attributes as continuous ones via numerical coding of nominal values (often a bit ad hoc). We propose a way of keeping nominal values within analytical paradigm with no pretending that nominal values are continuous. The core idea is that the information hidden in nominal values influences on metric (or on similarity function) between records of continuous and nominal data. Adaptation finds relevant parameters which influence metric between data records. Our approach works well for classifier induction algorithms where metric or similarity is generic, for instance k nearest neighbor algorithm or proposed here support of decision tree induction by similarity function between data. The k-nn algorithm working with continuous and nominal data behaves considerably better, when nominal values are processed by our approach. Algorithms of analytical paradigm using linear and probability machinery, like discriminant adaptive nearest-neighbor or Fisher’s linear discriminant analysis, cause some difficulties. We propose some possible ways to overcome these obstacles for adaptive nearest neighbor algorithm.

4

Visualisation of nominal data – practical and theoretical remarks

75%

Mącik R.

Econometrics. Ekonometria. Advances in Applied Data Analytics

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2016

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nr 2 (52)

22-34

EN

Nominal data, due to their nature, are often analysed statistically in a quite limited and traditional way. Usually they come from open-ended or simple/multiple choice questions. In typical research projects, such data are often presented in the form of more or less complex tables (including contingency tables) and standard charts. The author’s experience shows that such a visualisation is perceived as boring, especially by younger people, accustomed to the presentation of content in the form of infographics. The article presents examples of data analysis and a visualisation of the nominal data based on the results of the author’s research, including theoretical reflections on the techniques and tools used. The starting point is the raw text data from the responses to the open-ended questions subjected to analyses of the frequency of words and expressions, including its visualisation through word clouds. The next step is categorization and tabulation at the level of individual variables including the visualisation of categories, to assess the contingency between two nominal variables (or the nominal and the ordinal one), including visualising the relationships via chord diagrams and the correspondence analysis.

5

On the analysis of correlation between nominal data and numerical data

75%

Gniazdowski Z.

Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki

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2022

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tom 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.