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Interval-valued functional data, a new type of data in symbolic data analysis, depicts the characteristics of a variety of big data and has drawn the attention of many researchers. Mean regression is one of the important methods for analyzing interval-valued functional data. However, this method is sensitive to outliers and may lead to unreliable results. As an important complement to mean regression, this paper proposes an interval-valued scalar-on-function linear quantile regression model. Specifically, we constructed two linear quantile regression models for the interval-valued response and interval-valued functional regressors based on the bivariate center and radius method. The proposed model is more robust and efficient than mean regression methods when the data contain outliers as well as the error does not follow the normal distribution. Numerical simulations and real data analysis of a climate dataset demonstrate the effectiveness and superiority of the proposed method over the existing methods. [ABSTRACT FROM AUTHOR]

Most recommendation systems are implemented using numerical or categorical data, that is, traditional data. This type of data can be a limiting factor when used to model complex concepts where there is internal variability or internal structure in the data. To overcome these limitations, symbolic data is used, where data can be represented by different types of values, such as intervals, lists, or histograms. This work introduces a single approach to constructing recommendation systems based on content or based on collaborative filtering using modal variables for users and items. In the content-based system, user profiles and item profiles are created from modal representations of their features, and a list of items is matched against a user profile. For collaborative filtering, user profiles are built, and users are grouped to form a neighborhood, products rated by users of this neighborhood are recommended based on the similarity between the neighbor and the user who will receive the recommendation. Experiments are carried out, using a movie domain dataset, to evaluate the effectiveness of the proposed approach. The outcomes suggest our ability to generate ranked lists of superior quality compared to previous methods utilizing symbolic data. Specifically, the lists created through the proposed method exhibit higher normalized discounted cumulative gain and, in qualitative terms, showcase more diverse content. [ABSTRACT FROM AUTHOR]

Luxembourg, known for its immigration history, attracts immigrants to work. This study analyses different immigrant groups in the labour market from 2014 to 2022 by using Labor Force Survey (LFS) data, Symbolic Data Analysis (SDA), and the Monitoring the Evolution of Clusters (MEC) framework.Based on the birthplace and length of residence in Luxembourg, in each year, microdata were aggregated into 21 symbolic objects. They were primarily described by 16 modal variables which are multi-valued variables with a frequency attached to each category. Moreover, clustering using complete linkage and the Chernoff’s distance was applied. The Heuristic Identification of Noisy Variables (HINoV) suggested that with just six variables, objects may be grouped homogeneously. The MEC framework traced temporal relations and transitions between the clusters, revealing some movements across the different years.Results indicate that people from the European Union (EU) and Neighbouring countries have similar profiles while the Portuguese have opposite characteristics. The Luxembourgers are somewhere in between. Profiling people from non-EU countries was challenging.The data and methodology used make it easy to replicate the work in other nations, enabling comparison of results and monitoring to continue in the future. [ABSTRACT FROM AUTHOR]

Environmental attitudes (environmental knowledge, awareness, and concern) are important drivers of pro-environmental behaviour for key destination stakeholder groups, including tourists, tourism business staff and residents. However, limited attention has been given to how individual attitudes within each role collectively contribute to the environmental sustainability of tourism destinations.The goal of the study is to fill this gap by conceptually and empirically linking the micro- and macro-levels of analysis, respectively focused on individuals and the destination. First, the concept of Destination Environmental Orientation (DEO) is proposed to indicate the collective attitude of a touristic place or destination towards the environment having micro-foundations in individuals' cognition, evaluation and affect. Then, focusing on local hotels' staff as a key destination stakeholder category, the study shows the methodological potential of Symbolic Data Analysis (SDA) to measure DEO based on underlying individual-level data about environmental knowledge, awareness, and concern. Survey-based data are collected among employees in thirty-three hotels located in eleven tourism municipalities of Naples, a province in the Campania region (Italy). The research identifies three groups of tourism municipalities with significant differences in the level of environmental orientation. The findings suggest that these groups exhibit different patterns of functioning and three models are identified based on context-related factors, i.e., the level of tourism developement, the reliance of tourism areas on natural resources, and geograhical and functional proximity among tourism municipalities: the "Mature tourism destination" model, the "Island tourism destination" model, and the "Strategically positioned touristic place" model. The implications to sustainable tourism theory and practice are discussed. [ABSTRACT FROM AUTHOR]

Symbolic data analysis deals with complex data with symbolic objects, such as lists, histograms, and intervals. Spatial analysis for symbolic data is relatively underexplored. To fill the gap, this paper proposes a statistical framework for spatial interval-valued data (SIVD) analysis. We provide geostatistical methods for spatial prediction, predictive performance measure for prediction assessment, and visualization for mapping SIVD. The proposed methods are illustrated with both simulated and real examples. [ABSTRACT FROM AUTHOR]

Background: Knowing the predictive factors of the variation in a center-level continuous outcome of interest is valuable in the design and analysis of parallel-arm cluster randomized trials. The symbolic two-step method for sample size planning that we present incorporates this knowledge while simultaneously accounting for patient-level characteristics. Our approach is illustrated through application to cluster randomized trials in cancer care delivery research. The required number of centers (clusters) depends on the between- and within-center variance; the within-center variance is a function of estimates obtained by regressing the log within-center variance on predictive factors. Obtaining accurate estimates of the components needed to characterize the within-center variation is challenging. Methods: Using our previously derived sample size formula, our objective in the current research is to directly account for the imprecision in these estimates, using a Bayesian approach, to safeguard against designing an underpowered study when using the symbolic two-step method. Using estimates of the required components, including the number of centers that contribute to those estimates, we make formal allowance for the imprecision in these estimates on which a sample size will be based. Results: The mean of the distribution for power is consistently smaller than the single point estimate that the sample size formula yields. The reduction in power is more pronounced in the presence of increased uncertainty about the estimates with the reduction becoming more attenuated with increased numbers of centers that contribute to the estimates. Conclusions: Accounting for imprecision in the estimates of the components required for sample size estimation using the symbolic two-step method in the design of a cluster randomized trial yields conservative estimates of power. [ABSTRACT FROM AUTHOR]

Exploratory analysis and visualization of multiple time series data are essential for discovering the underlying dynamics of a series before attempting modeling and forecasting. This study extends two dimension reduction methods - principal component analysis (PCA) and sliced inverse regression (SIR) - to multiple time series data. This is achieved through the innovative path point approach, a new addition to the symbolic data analysis framework. By transforming multiple time series data into time-dependent intervals marked by starting and ending values, each series is geometrically represented as successive directed segments with unique path points. These path points serve as the foundation of our novel representation approach. PCA and SIR are then applied to the data table formed by the coordinates of these path points, enabling visualization of temporal trajectories of objects within a reduced-dimensional subspace. Empirical studies encompassing simulations, microarray time series data from a yeast cell cycle, and financial data confirm the effectiveness of our path point approach in revealing the structure and behavior of objects within a 2D factorial plane. Comparative analyses with existing methods, such as the applied vector approach for PCA and SIR on time-dependent interval data, further underscore the strength and versatility of our path point representation in the realm of time series data. [ABSTRACT FROM AUTHOR]

Symbolic data analysis is a research area related to machine learning and statistics, which provides tools to describe geo-objects, and enables several types of variables to be dealt with, including interval type variables. Moreover, despite the recent progress in understanding symbolic data, there are no studies in the literature that address this type of data in the context of spatial data analysis. Thus, in this paper, we propose two different approaches of the spatial regression model for symbolic interval-valued data. The first fits a linear regression model on the minimum and maximum values of the interval values and the second fits a linear regression model on the center and range values of the interval. In order to evaluate the performance of these approaches, we have performed Monte Carlo simulations in which we calculated the mean value of the performance metric of the models analyzed. Furthermore, we also analyzed two applications involving real data. In the first, we examined the performance of the models in the Brazilian State of Pernambuco. In the second application, we analyzed the performance of the models for the Brazilian Northeastern region. Both applications were related to socioeconomic variables. We observed that in areas with less spatial variability, the interval spatial regression model performs better when compared with a usual method. When considering areas with a higher spatial variability, both ways presented similar results. [ABSTRACT FROM AUTHOR]

The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion of ranking of observations which is absent in more than one dimension. Motivated by the rapid development of technology, in particular the advent of ‘Big Data’, we extend here that concept to general metric spaces, propose a natural depth measure and explore its properties as a statistical depth function. Working in a general metric space allows the depth to be tailored to the data at hand and to the ultimate goal of the analysis, a very desirable property given the polymorphic nature of modern data sets. This flexibility is thoroughly illustrated by several real data analyses. [ABSTRACT FROM AUTHOR]

In this study, we develop comprehensive symbolic interval‐valued time‐series models, including interval‐valued moving average, auto‐interval‐regressive moving average, and heteroscedastic volatility models. These models can be flexibly combined to adapt more effectively to various situations. To make inferences regarding these models, likelihood functions were derived, and maximum likelihood estimators were obtained. To evaluate the performance of our methods empirically, Monte Carlo simulations and real data analyses were conducted using the S&P 500 index and PM2.5 levels of 15 stations in southern Taiwan. In the former case, it was found that the proposed model outperforms all other existing methods, whereas in the latter case, the residuals deduced from the proposed models provide more intuitively appealing results compared to the conventional vector autoregressive models. Overall, our findings strongly confirm the adequacy of the proposed model. [ABSTRACT FROM AUTHOR]

Interval-valued data have been commonly encountered in practice, and Symbolic Data Analysis provides a solution to the statistical treatment of these data. Regression analysis for interval-valued symbolic data is a topic that has been widely investigated in the literature of symbolic data analysis, and several models from different paradigms have been proposed. There are basic regression assumptions, and it is essential to validate them. This paper introduces an approach to check interval regression model adequacy based on residual analysis. Concepts of ordinary and standardized interval residual are presented, and graphical analysis of these residuals is also proposed. To show the usefulness of the proposed approach, an application for estimating school dropout in the scenario of Brazilian municipalities is performed. We observed some outliers from the interval residuals analysis, and interval robust regression models are more suitable for estimating school dropout. [ABSTRACT FROM AUTHOR]

Summary: Structural health monitoring field is growing in the use of more modern techniques and tools in order to identify damages in civil structures. The improvements in signal processing techniques and data mining have, recently, been employed due to their powerful computational ability to detect damage in bridges. Despite the majority of researchers have been studying laboratory‐scale implementations and theoretical developments, the limited data to identify structural faults in real bridges are still a problem. The current study presents a novel approach for damage identification by using two improved methods such as decomposition techniques and machine learning algorithms. Since the data obtained from the traffic vibration in real bridges are non‐linear and time varying, the Hilbert–Huang transform is used to process the vibration data. Additionally, a phenomenon of mode mixing is presented in the current decomposition methods, such as empirical mode decomposition (EMD). Therefore, a novel improved completed ensemble EMD with adaptive noise (ICEEMDAN) was adopted. After the signal decomposition and identification of the damage parameter, a symbolic data analysis and clustering‐based approach were developed. Additionally, an unsupervised machine learning algorithm was used to group substructures with similar behavior and then detect damages. This learning method was used for automatically classifying the damages using a moving windows process sequentially applied to the structural response of the bridge. The validity of the approach is demonstrated using real data collected from a truss bridge. The results show that the proposed mixed method was effective and can endow better results in bridge health monitoring. [ABSTRACT FROM AUTHOR]

New interval clustering technology for symbolic data analysis (SDA) on smart phones is shown to be beneficial for mobile computing devices for smart data analysis in this paper. A new interval clustering method that combined the rough set with interval possibilistic fuzzy C-means (IPFCM) algorithm under Euclidean distance is proposed and implemented on smart phones. Symbolic clustering algorithms (SCAs) have been widely used for pattern recognition, data mining, artificial intelligence, etc. In general, the SCA is unsupervised classification that is divided into groups according to symbolic data sets. However, the traditional interval fuzzy C-means (IFCM) clustering method still has noisy and data overlapping problems associated with these symbolic interval data. Hence, a new rough set with the interval possibilistic fuzzy C-means (RIPFCM) clustering algorithm with Euclidean distance was proposed to address the symbolic interval data (SID). That is, the proposed method can perform better than the traditional IFCM clustering algorithm for SID clustering in noisy environments and with data overlapping problems. The new RIPFCM algorithm under the Euclidean distance method was proposed to deal with SID on new applications in smart phones. Consequently, this method shows the expansion of the smart phone's computing power and its future application in new SDA. [ABSTRACT FROM AUTHOR]

A histogram-valued random variable represents its value by a list of pairs of bins and their corresponding probabilities or relative frequencies. This type of data is a part of the symbolic data. There are many cases such as colors in image learning where histogram-valued data are naturally found. This study focuses on classification of the histogram-valued data by extending two approaches of support vector machine (SVM), namely, the expected-based and quantile-based probabilistic SVM on histogram-valued data. In both approaches, the cases of linear and nonlinear problems as well as the least-square classification are discussed. In addition, the extension to multi-class classification is also discussed. To compare the performance of the proposed procedures a simulation study has been done based on some generated data sets. The data are generated from various distributions with various parameters to represent different cases of classification, including binary and multi-class classification. Further, the methods are applied on two different real data sets. From the results, it can be concluded that our proposed methods perform well on wide range of classification problems. [ABSTRACT FROM AUTHOR]

It is essential to measure within-country differences in housing costs in order to evaluate costs of living, assessing and comparing poverty levels, quantifying salaries and disposable income of families and finally for designing housing policies at local level. To the authors knowledge, no studies have yet been carried out on the computation of Space Price Indexes for Housing Rents (SPIHRs). In this article we computed preliminary estimates of sub-national SPIHRs by using hedonic regression model, which is an extension of the Country Product Dummy method, for all the Italian regions. The hedonic regression is generally used to obtain multilateral spatial indexes, thus allowing us to obtain multilateral SPIHRs for the Italian regions. The estimates have been done using 2017 data from the Real Estate Market Observatory which is a part of the Italian Agency of Revenue and Tax. This data source is the most comprehensive source of information on Italian houses price rents with a wide geographical coverage, including data for each Italian municipality. The obtained results show significant differences across the Italian regions, thus highlighting the importance of calculating SPIHR in Italy on a regular basis and the need to continue researches in this field. [ABSTRACT FROM AUTHOR]

In this article we propose an extension of singular spectrum analysis for interval‐valued time series. The proposed methods can be used to decompose and forecast the dynamics governing a set‐valued stochastic process. The resulting components on which the interval time series is decomposed can be understood as interval trendlines, cycles, or noise. Forecasting can be conducted through a linear recurrent method, and we devised generalizations of the decomposition method for the multivariate setting. The performance of the proposed methods is showcased in a simulation study. We apply the proposed methods so to track the dynamics governing the Argentina Stock Market (MERVAL) in real time, in a case study over a period of turbulence that led to discussions of the government of Argentina with the International Monetary Fund. [ABSTRACT FROM AUTHOR]

The decision to adopt one or another of the sustainable land management alternatives should not be based solely on their respective benefits in terms of climate change mitigation but also based on the performances of the productive systems used by farm holdings, assessing their environmental impacts through the cost of fertilizer resources used. This communication uses the symbolic clustering tools in order to analyze the conditional quantile estimates of the fertilizer costs of yearly crop productions in agriculture, as a replacement proxy for internal soil erosion costs. After recalling the conceptual framework of the estimation of agricultural production costs, we present the empirical data model, the quantile regression approach and the interval principal component analysis clustering tools used to obtain typologies of European countries on the basis of the conditional quantile distributions of fertilizer cost empirical estimates. The comparative analysis of econometric results for yearly crops between European countries illustrates the relevance of the typologies obtained for international comparisons to assess land management alternatives based on their impact on agricultural carbon sequestration in soils. [ABSTRACT FROM AUTHOR]

Logistic regression models are a popular and effective method to predict the probability of categorical response data. However, inference for these models can become computationally prohibitive for large datasets. Here we adapt ideas from symbolic data analysis to summarize the collection of predictor variables into histogram form, and perform inference on this summary dataset. We develop ideas based on composite likelihoods to derive an efficient one-versus-rest approximate composite likelihood model for histogram-based random variables, constructed from low-dimensional marginal histograms obtained from the full histogram. We demonstrate that this procedure can achieve comparable classification rates to the standard full data multinomial analysis and against state-of-the-art subsampling algorithms for logistic regression, but at a substantially lower computational cost. Performance is explored through simulated examples, and analyses of large supersymmetry and satellite crop classification datasets. for this article are available online. [ABSTRACT FROM AUTHOR]

Symbolic data analysis data has provided several advances in regression models concerning the type of symbolic variable. Due to the advantages of using symbolic polygonal data, this paper introduces a linear regression approach for polygonal data based on the generalize linear model theory that provides a unified method to broad range of modeling problems for different types of response as asymmetric continuous and discrete. Ordinary polygonal residuals and a way for finding model inadequacies are presented. Moreover, a quality measure of fit for polygons is also proposed in this paper. Experimental evaluation results illustrate the usefulness of the proposed approach regarding synthetic and real polygonal data. • An approach based on Generalized Linear Models for symbolic polygonal data is proposed. • Polygonal residuals are defined for evaluating the adequacy of the fitted model. • The prediction quality is measured by a metric based on Euclidean distance and polygon vertices. • Synthetic and real polygonal data sets are considered in the experimental evaluation. [ABSTRACT FROM AUTHOR]

The research background of the paper covers the development of a country, that can be measured in various ways. Simple indicators, like GDP and also complex indicators such as HDI (human development index), can be used to measure country development. However, usually countries are divided into groups via setting some arbitrary levels of final measure. What is more, the composite (complex) indices have some problems and errors.

New interval clustering technology for symbolic data analysis (SDA) on smart phones is shown to be beneficial for mobile computing devices for smart data analysis in this paper. A new interval clustering method that combined the rough set with interval possibilistic fuzzy C-means (IPFCM) algorithm under Euclidean distance is proposed and implemented on smart phones. Symbolic clustering algorithms (SCAs) have been widely used for pattern recognition, data mining, artificial intelligence, etc. In general, the SCA is unsupervised classification that is divided into groups according to symbolic data sets. However, the traditional interval fuzzy C-means (IFCM) clustering method still has noisy and data overlapping problems associated with these symbolic interval data. Hence, a new rough set with the interval possibilistic fuzzy C-means (RIPFCM) clustering algorithm with Euclidean distance was proposed to address the symbolic interval data (SID). That is, the proposed method can perform better than the traditional IFCM clustering algorithm for SID clustering in noisy environments and with data overlapping problems. The new RIPFCM algorithm under the Euclidean distance method was proposed to deal with SID on new applications in smart phones. Consequently, this method shows the expansion of the smart phone’s computing power and its future application in new SDA.

This study considers interval-valued time series data. To characterize such data, we propose an auto-interval-regressive (AIR) model using the order statistics from normal distributions. Furthermore, to better capture the heteroscedasticity in volatility, we design a heteroscedastic volatility AIR (HVAIR) model. We derive the likelihood functions of the AIR and HVAIR models to obtain the maximum likelihood estimator. Monte Carlo simulations are then conducted to evaluate our methods of estimation and confirm their validity. A real data example from the S&P 500 Index is used to demonstrate our method. [ABSTRACT FROM AUTHOR]

Symbolic polygonal data analysis is a new type of framework to extract valuable knowledge from a new structure of data using regular polygon built from data in class, big data, and complex data. This paper introduces a toolbox for symbolic polygonal data, named psda, that contains the main descriptive measures for this type of variable, e.g., mean, variance, correlation, and a polygonal linear regression model (plr). It is applied at the Brazilian Basic Education Assessment System (SAEB), giving a new perspective to the managers of the counties to realize the public policy in the Brazilian educational system. The hypothesis test showed that the polygonal linear regression model presented the best performance compared to some symbolic interval regression models in the SAEB application. [ABSTRACT FROM AUTHOR]

Introduction: Evidence that can be used to improve clinical practice patterns and processes is frequently generated through standard, parallel-arms cluster randomized trial (CRT) designs that test interventions implemented at the center-level. Although the primary endpoint of these trials is often a center-level outcome, patient-level factors may vary between centers and, consequently, may influence the center-level outcome. Furthermore, there may be important factors that predict the variation in the center-level outcome and this knowledge can help contextualize the trial results and inform practice patterns. Methods: Our symbolic two-step method that applies symbolic data analysis to account for patient-level factors when estimating and testing a center-level effect on both the average center-level outcome and its variation was developed for such settings. Herein, we sought to extend the method to prospectively size a CRT so that the application of our method in data analysis is consistent with the design. Results: Our formulaic approach to sample size planning incorporated predictive factors of the within-center variation and accounted for patient-level characteristics. The sample size approximation performed well in many different pragmatic settings. Conclusions: Our symbolic two-step method provides an alternate approach in the design and analysis of CRTs evaluating novel improvement processes within care delivery research.

Abstract Background Dengue fever is a leading cause of severe illness and hospitalization in Taiwan. This study sought to elucidate the linkage between dengue fever incidence and climate factors. Results The result indicated that temperature, accumulated rainfall, and sunshine play an important role in the transmission cycles of dengue fever. A predictive model equation plots dengue fever incidence versus temperature, rainfall, and sunshine, and it suggests that temperature, rainfall, and sunshine are significantly correlated with dengue fever incidence. Conclusions The data suggests that climate factors are important determinants of dengue fever in southern Taiwan. Dengue fever viruses and the mosquito vectors are sensitive to their environment. Temperature, rainfall and sunshine have well-defined roles in the transmission cycle. This finding suggests that control of mosquito by climatic factor during high temperature seasons may be an important strategy for containing the burden of dengue fever.

Symbolic data analysis has been proposed as a technique for summarising large and complex datasets into a much smaller and tractable number of distributions—such as random rectangles or histograms—each describing a portion of the larger dataset. Recent work has developed likelihood-based methods that permit fitting models for the underlying data while only observing the distributional summaries. However, while powerful, when working with random histograms this approach rapidly becomes computationally intractable as the dimension of the underlying data increases. We introduce a composite-likelihood variation of this likelihood-based approach for the analysis of random histograms in K dimensions, through the construction of lower-dimensional marginal histograms. The performance of this approach is examined through simulated and real data analysis of max-stable models for spatial extremes using millions of observed datapoints in more than K = 100 dimensions. Large computational savings are available compared to existing model fitting approaches. [ABSTRACT FROM AUTHOR]

In this study, a novel approach, interval fuzzy c-regression models with competitive agglomeration (IFCRMCA), is proposed to deal with the symbolic interval-valued data. The proposed IFCRMCA approach can identify the partition of the interval-valued data using both the distances to the cluster centers and the errors of interval regression models for each cluster. Due to the concepts of competitive agglomeration is used in the proposed approach, the pre-determination of the cluster number in the proposed IFCRMCA is not necessary. Various real experiments are carried on and the experimentally results shows that the proposed approaches are superior to the existing approaches. [ABSTRACT FROM AUTHOR]

There is a growing need for flexible methods to analyze interval‐valued data, which can provide efficient data representations for very large data sets. However, the existing descriptive frameworks to achieve this ignore the process by which interval‐valued data are typically constructed, namely, by the aggregation of real‐valued data generated from some underlying process. In this paper, we develop the foundations of likelihood‐based statistical inference for intervals that directly incorporates the underlying data generating procedure into the analysis. That is, it permits the direct fitting of models for the underlying real‐valued data given only the interval‐valued summaries. This generative approach overcomes several problems associated with existing methods, including the rarely satisfied assumption of within‐interval uniformity. The new methods are illustrated by simulated and real data analyses. [ABSTRACT FROM AUTHOR]

Dynamic clustering defines partitions within data and prototypes to each partition. Distance metrics are responsible for checking the closeness between instances and prototypes. Considering the literature about interval data, distances depend on interval bounds and the information inside the intervals is ignored. This paper proposes new distances, which explore the information inside of intervals. It also presents a mapping of intervals to points, which preserves their spatial location and internal variation. We formulate a new hybrid distance for interval data based on the well-known L q distance for point data. This new distance allows for a weighted formulation of the hybridism. Hence, we propose a Hybrid L q distance, a Weighted Hybrid L q distance, as well as the adaptive version of the Hybrid L q distance for interval data. Experiments with synthetic and real interval data sets illustrate the usefulness of the hybrid approach to improve dynamic clustering for interval data. [ABSTRACT FROM AUTHOR]

In the application of statistical methods and models, as well as other data analysis methods, we encounter a number of limitations that make it necessary to find new approaches. The purpose of this article is to highlight the rationale for seeking new approaches to the analysis of mortality data in European countries observed by sex, age, and cause of death, to briefly present some results of recent work, and to point to research being conducted in collaboration with other researchers on this information.

Background: As a directly exposed part of the human body, the eyes are susceptible to external stimulations of air pollution. The ill effects of air pollution on human eyes are mostly irritation and inflammation, with conjunctivitis being a significant problem. Method: This study investigates the impact of air pollution on nonspecific conjunctivitis based on the data from ophthalmologic outpatient visits. The research focuses on the significance of air pollution's impact on ocular health. Data for ophthalmology outpatient visits were obtained from the National Health Insurance Research Database of Taiwan. Ambient air monitoring data were obtained from the Taiwan Environmental Protection Administration air pollution monitoring stations. Six regulated air pollutants were included in the studies. This study used symbolic data analysis to investigate the association between daily air pollutant concentrations and the number of outpatient visits for nonspecific conjunctivitis as well as the relationship between climate factors and air pollutants. Results: O3 (t-value=2.292, p-value=0.025) is positively correlated with nonspecific conjunctivitis cases; this result is the same as plot (d) in Figure 3. The relationship between nonspecific conjunctivitis cases and CO (t-alue=-1.183, p-value=0.240) / NO2 (t-alue=0.653, p-value=0.516) / NO2 (t-value=0.653, p-value=0.516) / SO2 (t-value=-0.942, p-value=0.349) is not statistically significant. Conclusion: The result of this study shows that the air pollutant, O3 is significantly related to nonspecific conjunctivitis. The air pollutant, O3 can increase chances of outpatient visits, suggesting that is a possible cause for nonspecific conjunctivitis. [ABSTRACT FROM AUTHOR]

Reasonable selection of black-start schemes is significant to the fast restoration of power system. Previous studies mostly focus on complete evaluation information. In this article, a comprehensive evaluation model based on symbolic data is proposed, which can address the issue of assessing black-start schemes under the condition of incomplete evaluation information. First, evaluation grade is established, and original evaluation matrix is transformed into symbolic data matrix. Then the symbolic data matrix is packaged, evaluation frequency matrix is gained, and weights of indexes are computed. Finally, weighted evaluation matrix is established based on the symbolic data matrix and weight vector, and negative ideal point approach is used to sort the black-start schemes. Experiments are carried out on the data of black-start path of Tianjin power grid, the results show that the proposed approach is effective. [ABSTRACT FROM AUTHOR]