Ordinal Ones Research Articles

Graph-Based Dissimilarity Measurement for Cluster Analysis of Any-Type-Attributed Data.

Heterogeneous attribute data composed of attributes with different types of values are quite common in a variety of real-world applications. As data annotation is usually expensive, clustering has provided a promising way for processing unlabeled data, where the adopted similarity measure plays a key role in determining the clustering accuracy. However, it is a very challenging task to appropriately define the similarity between data objects with heterogeneous attributes because the values from heterogeneous attributes are generally with very different characteristics. Specifically, numerical attributes are with quantitative values, while categorical attributes are with qualitative values. Furthermore, categorical attributes can be categorized into nominal and ordinal ones according to the order information of their values. To circumvent the awkward gap among the heterogeneous attributes, this article will propose a new dissimilarity metric for cluster analysis of such data. We first study the connections among the heterogeneous attributes and build graph representations for them. Then, a metric is proposed, which computes the dissimilarities between attribute values under the guidance of the graph structures. Finally, we develop a new k -means-type clustering algorithm associated with this proposed metric. It turns out that the proposed method is competent to perform cluster analysis of datasets composed of an arbitrary combination of numerical, nominal, and ordinal attributes. Experimental results show its efficacy in comparison with its counterparts.

НАУЧНАЯ НЕСОСТОЯТЕЛЬНОСТЬ БАЛЬНО-РЕЙТИНГОВОЙ СИСТЕМЫ ОЦЕНКИ ЗНАНИЙ

The article constates nontriviality of the task provided with assessing knowledge. Here we analyze the scales for measuring knowledge that have found practical application in various countries and reveal the evolution of measuring knowledge in our country. Finally, we prove the inconsistency of the methodology for assessing knowledge in a 100point scale, which has become widespread in the national higher school. Nontriviality of the task provided with knowledge assessment is explained by double subjectivity (the subjectivity of the student's mastering knowledge and the subjectivity of the assessment of this knowledge by the teacher), as well as a scanty selection of control questions in comparison with the total volume of a discipline’s educational material which is an object of control. Despite this, the established grade is required to reflect objectively (!) the degree of a student’s mastering in the entire knowledge arsenal of a controlled discipline. Here we analyzed some of scales for measuring knowledge. These are the 4point scale, used for a long time in our country: the 10point scale, used in the Netherlands, Italy, Spain and Romania; the 20point scale used in Greece, Peru, Belgium and France, and the most widely used 100point scale, which measures knowledge in the United States, Turkey, India, Egypt and modern Russia. All marked scales belong to the class of relative or ordinal ones, and their application consists in assigning to each student a fixed reference value, reflecting the level of his knowledge in the discipline being examined. Despite the fact that the reference values of the measuring scales are denoted by numbers, in fact they are not numbers and arithmetic operations cannot be performed on them. Unfortunately, this natural rule is often violated. Many participants in the educational process have wish to strengthen the ordinal scale and further objectify the grades. It has led to the synthesis of ornate methodological superstructures on ordinal scales, which often do not stand up to scrutiny. Domestic educational institutions were especially keen on this. From the standpoint of measurement theory, an analysis was made of the methodology for applying the 100point scale for measuring knowledge, which, with minor modifications, has been used by national universities since the very beginning of market reforms. The analysis showed that to assess the knowledge of students, the mentioned methodology uses three measuring scales: a 20point scale at intermediate certifications, a 60point scale during a test or exam, and a 100point scale when forming the final grade in the discipline. The article proves the theoretical inconsistency of the applied methodology and develops recommendations for overcoming it.

Modeling students’ performance using graph convolutional networks

Many models were recently proposed to classify students, relying on a large amount of pre-labeled data to verify their classification effectiveness. However, those models lack to accurately classify students into various behavioral patterns, employing nominal class labels, rather than ordinal ones. Meanwhile, such models cannot analyze high-dimensional learning behaviors among learners according to students’ interaction with course videos. Since online learning data are huge, the main challenges associated with data are insufficient labeling and classification using nominal class labels. In this study, we proposed a model based on Graph Convolutional Network, as a semi-supervised classification task to classify students’ engagement in various behavioral patterns. First, we proposed a label function to label datasets instead of manual labeling, in which input and output data are labeled for classification to provide a learning foundation for future data processing. Accordingly, we hypothesized four behavioral patterns, namely (“High-engagement”, “Normal-engagement”, “At-risk”, and “Potential-At-risk”) based on students' engagement with course videos and their performance on the assessments/quizzes conducted after. Then, we built a heterogeneous knowledge graph representing learners, course videos as entities, and capturing semantic relationships among students according to shared knowledge concepts in videos. Our model intrinsically works for heterogeneous knowledge graphs as a semi-supervised node classification task. It was evaluated on a real-world dataset across multiple settings to achieve a better predictive classification model. Experiment results showed that the proposed model can predict with an accuracy of 84% and an f1-score of 78% compared to baseline approaches.

Heterogeneity in purchasing behavior for eco-friendly labeled food between households with and without children

While most previous studies have mainly regarded data on consumers’ buying cycle as ordinal ones, we assumed that it captures the number of times that consumers making purchases within a given period of time. In this respect, we used count data models to investigate the differences in factors influencing purchase frequency for eco-friendly labeled food between households with and without children. Main findings of the study are as follows. First, we found that the households with young children purchase eco-friendly labeled food more frequently within a given period of time. Second, we found the differences in purchasing behavior between two groups in terms of three perspectives: (1) loyalty, (2) consumption tendency (cost effectiveness versus satisfaction inclination), and (3) major purchasing items. Based on the results, we presented marketing strategies tailored to each group to expand the demand for eco-friendly food.

Фразеологические единицы с количественными числительными в английском языке

Without the description of the quantitative definiteness of the reality neither knowledge, nor human practice, nor communication is possible. In English the means of expressing ideas of quantity penetrate all the levels of language structure, phraseology as well. The purpose of the article is to investigate phraseological units with cardinal numerals in the English language. The article is focused on semantic analysis of 65 phraseological units with cardinal numeral component in the English language collected from the English phraseological dictionaries by several authors. There is always a special interest in linguistics to numerical phraseological units. Phraseological studies possess great significance as it displays the interrelation between the language and the society. Numerals take active part in the formation of phraseological units thus creating a large phraseological layer. Fixed expressions with cardinal numerals are more numerous in number than those with ordinal ones and include expressions with a wide range of numerals such as two, four, five, six, eight, fifty, hundred, thousand. They are commonly used in phraseological units to form a ‘human’ concept. The results of the investigation showed that the numbers one and two are the most productive numbers in the English phraseological units. The numbers one, three, six, nine and ten are used in different senses in these set expressions. The numbers seven and eight are unproductive in the English language. The results of this work can be used for further studying the semantics of numerals in phraseological units and identifying of phraseological units with a numeral component.

SET EXPRESSIONS WITH CARDINAL NUMERALS IN THE LANGUAGE OF NEWS MEDIA

The article is focused on set expressions with cardinal numerals in Spanish newspaper language. These fixed expressions are part of linguistic expressive means, which realize one of mass media functions. The purpose of the article is to analyze set expressions with cardinal numerals, classify them according to some criteria and determine newspaper spheres in which they are most frequently used. Fixed expressions with cardinal numerals are more numerous in number than those with ordinal ones, or multiple, partible or fractional numbers, and include expressions with numbers from zero to eight and numbers with a hundred, a thousand, and a million.For the purposes of the research fixed expressions with cardinal numerals are divided into two groups: the invariable expressions with a fixed cardinal numeral, and the variable expressions with a changeable cardinal numeral. In the article there are provided classifications of set expressions with cardinal numerals based on grammatical and semantic criteria, and their components. There is analyzed the use of fixed expressions in the language of newspapers. Set expressions with cardinal numerals form part of the phraseological thesaurus of the Spanish language and the language of news media in particular.

Prototypical Peripheral Toponym Pairs Expressing the Concept \u2018All Over the Country\u2019 as a Part of the Mental Map

Expressing the concept ‘all over the country’ by mentioning one or more name pairs is a well-known phenomenon. A Dutch example is ‘Van Delfzijl tot Maastricht’, Delfzijl being situated in the extreme north of the country, Maastricht in the south. Such expressions are not only used on the national level, but also on subnational (for example, provinces) and supranational levels. Obviously, they arise spontaneously, many of them being preceded (or followed) by phrases like “overal in Nederland” [all over the Netherlands]; it is improbable indeed that anyone would first turn to an atlas or map before creating them. This paper departs from the idea that, if a country (etc.) has oblong contours, toponym pairs may preferably be chosen which are most distant from each other; this would illustrate ‘ubiquity’ better than choosing shorter ones. It focuses on the Netherlands and will deal, among others, with the following questions: (1) Which toponyms are most ‘popular’, and why? (2) If toponyms refer to cities and towns, does their ‘popularity’ correlate with a high population, with news coverage, or both? (3) Is there a preference for any combination of compass directions, for example, for cardinal points (contrary to ordinal ones)? And if so, is the combination of compass directions concerned associated with the longitudinal direction (if the country concerned has oblong contours)? (4) Is there a fixed pattern in the direction expressed by the name order within name pairs? It is, for example, conceivable that there is a tendency to prefer N–S to S–N, considering the prominent position of the northern compass point.

An Analysis to the Structure and Semantic Function of “<i>Shang</i>(up)/<i>Xia</i>(down) + Quantity (+X)” That Indicates Quantity of Range

Structure “Shang(up)/Xia(down) + quantity (+X)” is not a simple combination of locality and quantity, instead, it is formed to mark a subcategory of the category indicating quantity of range. In the structure, “Shang(up)/Xia(down)” is of fixed direction, quantity is often seen to be expressed by singular numeral “yi”, the majority of measure words are ordinal ones, and X is mainly nominal and could often be omitted. “Shang(up)/Xia(down) + quantity (+X)” is constructed in a unique way: the directionality and demarcation of “Shang(up)/Xia(down)” would clearly highlight quantitative words’ significance of referring to a complex, while the bounding function of quantitative words would, in the other hand, demarcate the boundaries of orientated “Shang(up)/Xia(down)”.

Optimization of Weighted Correlated Multiple Responses Using a probabilistic index

Dealing with more than one response in the process optimization is a great issue in these recent years, so multiple response optimization studies have been grown in the published works. In the common problems, there are some input variables which can affect output responses but optimization can be more complex and more real when the responses have correlation with each other. In such problems analyst should consider the correlation structure in addition to input variables effects. In some cases, responses variables may emerge from another distributions rather than normal in which can be analyzed by the proposed method. Moreover, in some problems, response variables may have different importance for the decision maker. In this study, we try to propose an efficient method to find the best treatment in an experimental design which its correlated responses have different weights, either cardinal or ordinal ones. Also a heuristic method was proposed to deal with problems that have considerable number of correlated responses or treatments. The results of some numerical examples confirm the validity of the proposed method. Moreover a real case about Tehran air pollution is studied to show theapplicability of the proposed method in the real problems.

Improving Construction of Conditional Probability Tables for Ranked Nodes in Bayesian Networks

This paper elaborates on the ranked nodes method (RNM) that is used for constructing conditional probability tables (CPTs) for Bayesian networks consisting of a class of nodes called ranked nodes. Such nodes typically represent continuous quantities that lack well-established interval scales and are hence expressed by ordinal scales. Based on expert elicitation, the CPT of a child node is generated in RNM by aggregating weighted states of parent nodes with a weight expression. RNM is also applied to nodes that are expressed by interval scales. However, the use of the method in this way may be ineffective due to challenges which are not addressed in the existing literature but are demonstrated through an illustrative example in this paper. To overcome the challenges, the paper introduces a novel approach that facilitates the use of RNM. It consists of guidelines concerning the discretization of the interval scales into ordinal ones and the determination of a weight expression and weights based on assessments of the expert about the mode of the child node. The determination is premised on interpretations and feasibility conditions of the weights derived in the paper. The utilization of the approach is demonstrated with the illustrative example throughout the paper.

Fast and highly efficient pseudo-likelihood methodology for large and complex ordinal data.

In longitudinal studies, continuous, binary, categorical, and survival outcomes are often jointly collected, possibly with some observations missing. However, when it comes to modeling responses, the ordinal ones have received less attention in the literature. In a longitudinal or hierarchical context, the univariate proportional odds mixed model (POMM) can be regarded as an instance of the generalized linear mixed model (GLMM). When the response of the joint multivariate model encompass ordinal responses, the complexity further increases. An additional problem of model fitting is the size of the collected data. Pseudo-likelihood based methods for pairwise fitting, for partitioned samples and, as introduced in this paper, pairwise fitting within partitioned samples allow joint modeling of even larger numbers of responses. We show that that pseudo-likelihood methodology allows for highly efficient and fast inferences in high-dimensional large datasets.

Biological Monitoring and the Occupational Physician

This article aims to introduce biological monitoring, which has been carried out in Japan for 25 years. Biological monitoring in occupational health is an assessment of the overall exposure to chemicals that are present in the workplace through measurement of the appropriate determinants in biological specimens in workers. Lead in blood and urinary δ-aminolevulinic acid in the urine of workers who handle lead, and urinary metabolites of workers who handle 8 kinds of organic solvents, are mandatory measurements. In 2013, insium and compounds, etheylbenzene (only coating workers), and cobalt and inorganic compounds were added to biological monitoring subjects, alongside the ordinal ones of specified chemical substances. Occupational physicians are required to carry out biological monitoring according to standardized protocols in order to correctly utilize biological monitoring results for occupational health management.

One first? Acquisition of the cardinal and ordinal uses of numbers in preschoolers

We studied the acquisition of the ordinal meaning of number words and examined its development relative to the acquisition of the cardinal meaning. Three groups of 3-, 4-, and 5-year-old children were tested in two tasks requiring the use of number words in both cardinal and ordinal contexts. Understanding of the counting principles was also measured by asking the children to assess the correctness of a cartoon character’s counting in both contexts. In general, the children performed cardinal tasks significantly better than ordinal ones. Tasks requiring the production of the number for a given quantity or position were solved more accurately than those testing the ability to select a set of n objects or the object in the nth position. Different profiles were obtained for the principles; those principles shared by the two contexts were mastered earlier in the cardinal context. Regarding order (ir)relevance, older children adhered to rigid ways of counting, producing better results in the ordinal context and incorrect rejections in the cardinal trials. Altogether, our data indicate that the acquisitions of cardinal and ordinal meanings of numbers are related, and cardinality precedes the development of ordinality.

A Simulation Study to Compare Competing Estimators in Structural Equation Models with Ordinal Variables

Structural equation models have been around for now a long time. They are intensively used to analyze data from di.erent fields such as psychology, social sciences, economics, management, etc. Their estimation can be performed using standard statistical packages such as LISREL. However, these implementations su.er from an important drawback: they are not suited for cases in which the variables are far from the normal distribution. This happens in particular with ordinal data that have a non symmetric distribution, a situation often encountered in practice. An alternative approach would be to use generalized linear latent variable models (GLLVM) as defined for example in Bartholomew and Knott 1999 and Moustaki and Knott (2000). These models consider the data as they are, i.e. binary or ordinal but the loglikelihood function is intractable and needs numerical approximations to compute it. Several approaches exist such as Gauss-Hermite quadratures or simulation based methods, as well as the Laplace approximation, i.e. the Laplace approximated maximum likelihood estimator (LAMLE) proposed by Huber, Ronchetti, and Victoria-Feser (2004) for these models. The advantage of the later is that it is very fast and hence can cope with relatively complicated models. In this paper, we perform a simulation study to compare the parameters' estimators provided by LISREL which is taken as a benchmark, and the LAMLE when the data are generated from a confirmatory factor analysis model with normal variables which are then transformed into ordinal ones. We will show that while the LISREL estimators can provide seriously biased estimators, the LAMLE not only is unbiased, but one can also recover an unbiased estimator of the correlation matrix of the original normal variables.

Ferroelectric Domain Branching in KDP

We observed periodic and fractal domain structures on inclined sides of thick KDP c plates by using SEM. It is found that the domains of lower ordinal pre-fractal domain structures run through the thickness, but the domains generating higher ordinal ones stick on and branch those of the lower ordinal ones near the c surfaces. The period 2 L of the domain structure shows the thickness d dependence, 2 L œ d 0.7 . These verify the ferroelectric domain branching due to a depolarization field in KDP.

Ferroelectric Domain Branching in KDP

We observed periodic and fractal domain structures on inclined sides of thick KDP c plates by using SEM. It is found that the domains of lower ordinal pre-fractal domain structures run through the thickness, but the domains generating higher ordinal ones stick on and branch those of the lower ordinal ones near the c surfaces. The period 2 L of the domain structure shows the thickness d dependence, 2 L d 0.7 . These verify the ferroelectric domain branching due to a depolarization field in KDP.

How bad may learning curves be?

In this paper, we motivate the need for estimating bounds on learning curves of average-case learning algorithms when they perform the worst on training samples. We then apply the method of reducing learning problems to hypothesis testing ones to investigate the learning curves of a so-called ill-disposed learning algorithm in terms of a system complexity, the Boolean interpolation dimension. Since the ill-disposed algorithm behaves worse than ordinal ones, and the Boolean interpolation dimension is generally bounded by the number of system weights, the results can apply to interpreting or to bounding the worst-case learning curve in real learning situations. This study leads to a new understanding of the worst-case generalization in real learning situations, which differs significantly from that in the uniform learnable setting via Vapnik-Chervonenkis (VC) dimension analysis. We illustrate the results with some numerical simulations.

Path analysis with partial association measures

This paper discusses the use of partial association measures for carrying out path analyses on categorical data. The measures considered are essentially PRE (proportion of reduction in error of prediction) measures for nominal variables and concordance-discordance indices for ordinal ones. These measures provide a natural way to evaluate the strength of the path linking a non-measurable response variable to one of several categorical explanatory factors. Concerning the decomposition of raw association into direct and indirect effects, it is shown, however, that they do not share the properties of conventional path coefficients for measurable variables. Especially purely nominal association measures need to be interpreted with care. The scope of the partial measures for path analysis is illustrated through a study of the relationships between the educational styles experienced by swiss adolescents and their selfesteem.

Sensitivity and accuracy of the visual analogue scale: a psycho-physical classroom experiment.

1 Twenty-seven intelligent volunteers took part in a classroom experiment on two occasions to assess subjectively, ordinally related volumes of sound (offered in random sequence), using the visual analogue scale. 2 It was simple to use and largely acceptable. Big differences were significant by parametric tests but small ones were sometimes significant only with ordinal ones. Within-subject comparisons were more accurate and more sensitive than those between-subjects. The t-test was very robust. 3 Five out of 49 results were erroneously significant; they remained so no matter how the data were handled. It was concluded that this was due to a shift in either perception, cognition or scoring between the two sessions. 4 Arcsine transformations made little difference. The mechanism of these is fully discussed. A conversion to proportional scores resulted in very much improved sensitivity. 5 It is recommended that authors using the visual analogue scale: have valid reason in their own setting for using a transformation; present the distribution, or at least the medians and ranges of their raw scores; also use a simple but different measure so as to demonstrate internal consistency between them.