Symbolic Data Research Articles

Modeling the contribution of auditory scene analysis principles to perceptual effects of orchestration

Auditory Scene Analysis (ASA) research has provided knowledge about the principles underlying auditory organization processes and has been successfully applied in computational ASA. Based on these findings, we applied these principles within a musical context. The aim is to understand and computationally model the perception of effects, such as blend and segregation, created by the combining and contrasting of properties of traditional Western instruments which result from three auditory processes: concurrent, sequential, and segmental grouping. The initial aim was to evaluate the extent to which the symbolic data provided in a musical score provide sufficient data to model the perception of these orchestral effects. Preliminary implementations have achieved an average accuracy score of 81%, suggesting that perceptual effects of orchestration can be partially retrieved by calculations based on ASA principles using symbolic data. However, many cases indicate that including properties of the acoustic signal would enhance the predictive power. This approach also provides us with the means to investigate the relative weights of the different principles involved in these grouping processes in order to understand their relative importance in musical contexts. These findings contribute to the creation of a framework for studying and understanding the perceptual characteristics of orchestration practice.

The Measurement of Social Cohesion at Province Level in Poland Using Metric and Interval-Valued Data

The notion of social cohesion is increasingly used in the political, economic and academic debate. Due to its multidimensional, the assessment of social cohesion is not easy, especially if it is conducted at a lower than national level of aggregation. The aim of the study is to assess social cohesion in provinces of Poland in 2018 using the hybrid approach involving multidimensional scaling and linear ordering based on an aggregate measure. This type of study is usually conducted using classic metric data. However, the traditional approach does not account for the variation between lower level units (i.e., districts). The authors propose a methodology which makes this possible. Additionally the results of assessment of the multidimensional phenomenon can be presented in a two-dimensional space. Classic metric data and symbolic interval-valued data (three data types: min-max, 1st decile and 9th decile, 2nd decile and 8th decile) are jointly represented in a single diagram. The consistency of the research method ensures comparability of results of linear ordering. Two criteria were used in the comparative analysis of four rankings of social cohesion. The results of the study clearly showed that the current level of social cohesion at the provinces level is geographically and historically dependent.

Where does Haydn end and Mozart begin? Composer classification of string quartets

For centuries, the history and music of Joseph Franz Haydn and Wolfgang Amadeus Mozart have been compared by scholars. Recently, the growing field of music information retrieval (MIR) has offered quantitative analyses to complement traditional qualitative analyses of these composers. In this MIR study, we classify the composer of Haydn and Mozart string quartets based on the content of their scores. Our contribution is an interpretable statistical and machine learning approach that provides high classification accuracies and musical relevance. We develop novel global features that are automatically computed from symbolic data and informed by musicological Haydn–Mozart comparative studies, particularly relating to the sonata form. Several of these proposed features are found to be important for distinguishing between Haydn and Mozart string quartets. Our Bayesian logistic regression model attains leave-one-out classification accuracies over 84%, higher than prior works and providing interpretations that could aid in assessing musicological claims. Overall, our work can help expand the longstanding dialogue surrounding Haydn and Mozart and exemplify the benefit of interpretable machine learning in MIR, with potential applications to music generation and classification of other classical composers.

Psda: A tool for extracting knowledge from symbolic data with an application in Brazilian educational data

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.

Hierarchical conceptual clustering based on quantile method for identifying microscopic details in distributional data

Symbolic data is aggregated from bigger traditional datasets in order to hide entry specific details and to enable analysing large amounts of data, like big data, which would otherwise not be possible. Symbolic data may appear in many different but complex forms like intervals and histograms. Identifying patterns and finding similarities between objects is one of the most fundamental tasks of data mining. In order to accurately cluster these sophisticated data types, usual methods are not enough. Throughout the years different approaches have been proposed but they mainly concentrate on the “macroscopic” similarities between objects. Distributional data, for example symbolic data, has been aggregated from sets of large data and thus even the smallest microscopic differences and similarities become extremely important. In this paper a method is proposed for clustering distributional data based on these microscopic similarities by using quantile values. Having multiple points for comparison enables to identify similarities in small sections of distribution while producing more adequate hierarchical concepts. Proposed algorithm, called microscopic hierarchical conceptual clustering, has a monotone property and has been found to produce more adequate conceptual clusters during experimentation. Furthermore, thanks to the usage of quantiles, this algorithm allows us to compare different types of symbolic data easily without any additional complexity.

Sample size planning in the design and analysis of cluster randomized trials using the symbolic two-step method

IntroductionEvidence 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. MethodsOur 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. ResultsOur 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. ConclusionsOur symbolic two-step method provides an alternate approach in the design and analysis of CRTs evaluating novel improvement processes within care delivery research.

Composite likelihood methods for histogram-valued random variables

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.

Unsupervised acquisition of idiomatic units of symbolic natural language: An n-gram frequency-based approach for the chunking of news articles and tweets.

Symbolic sequential data are produced in huge quantities in numerous contexts, such as text and speech data, biometrics, genomics, financial market indexes, music sheets, and online social media posts. In this paper, an unsupervised approach for the chunking of idiomatic units of sequential text data is presented. Text chunking refers to the task of splitting a string of textual information into non-overlapping groups of related units. This is a fundamental problem in numerous fields where understanding the relation between raw units of symbolic sequential data is relevant. Existing methods are based primarily on supervised and semi-supervised learning approaches; however, in this study, a novel unsupervised approach is proposed based on the existing concept of n-grams, which requires no labeled text as an input. The proposed methodology is applied to two natural language corpora: a Wall Street Journal corpus and a Twitter corpus. In both cases, the corpus length was increased gradually to measure the accuracy with a different number of unitary elements as inputs. Both corpora reveal improvements in accuracy proportional with increases in the number of tokens. For the Twitter corpus, the increase in accuracy follows a linear trend. The results show that the proposed methodology can achieve a higher accuracy with incremental usage. A future study will aim at designing an iterative system for the proposed methodology.

Symbolic interval-valued data analysis for time series based on auto-interval-regressive models

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.

When Perfect Is Not Good Enough: On the Search Behaviour of Symbolic Heuristic Search

Symbolic search has proven to be a competitive approach to cost-optimal planning, as it compactly represents sets of states by symbolic data structures. While heuristics for symbolic search exist, symbolic bidirectional blind search empirically outperforms its heuristic counterpart and is therefore the dominant search strategy. This prompts the question of why heuristics do not seem to pay off in symbolic search. As a first step in answering this question, we investigate the search behaviour of symbolic heuristic search by means of BDDA⋆. Previous work identified the partitioning of state sets according to their heuristic values as the main bottleneck. We theoretically and empirically evaluate the search behaviour of BDDA⋆ and reveal another fundamental problem: we prove that the use of a heuristic does not always improve the search performance of BDDA⋆. In general, even the perfect heuristic can exponentially deteriorate search performance.

Local linear regression analysis for interval-valued data

Interval-valued data, a type of symbolic data, is given as an interval in which the observation object is not a single value. It can also occur frequently in the process of aggregating large databases into a form that is easy to manage. Various regression methods for interval-valued data have been proposed relatively recently. In this paper, we introduce a nonparametric regression model using the kernel function and a nonlinear regression model for the interval-valued data. We also propose applying the local linear regression model, one of the nonparametric methods, to the interval-valued data. Simulations based on several distributions of the center point and the range are conducted using each of the methods presented in this paper. Various conditions confirm that the performance of the proposed local linear estimator is better than the others.

Data Reduction in the String Space for Efficient kNN Classification Through Space Partitioning

Within the Pattern Recognition field, two representations are generally considered for encoding the data: statistical codifications, which describe elements as feature vectors, and structural representations, which encode elements as high-level symbolic data structures such as strings, trees or graphs. While the vast majority of classifiers are capable of addressing statistical spaces, only some particular methods are suitable for structural representations. The kNN classifier constitutes one of the scarce examples of algorithms capable of tackling both statistical and structural spaces. This method is based on the computation of the dissimilarity between all the samples of the set, which is the main reason for its high versatility, but in turn, for its low efficiency as well. Prototype Generation is one of the possibilities for palliating this issue. These mechanisms generate a reduced version of the initial dataset by performing data transformation and aggregation processes on the initial collection. Nevertheless, these generation processes are quite dependent on the data representation considered, being not generally well defined for structural data. In this work we present the adaptation of the generation-based reduction algorithm Reduction through Homogeneous Clusters to the case of string data. This algorithm performs the reduction by partitioning the space into class-homogeneous clusters for then generating a representative prototype as the median value of each group. Thus, the main issue to tackle is the retrieval of the median element of a set of strings. Our comprehensive experimentation comparatively assesses the performance of this algorithm in both the statistical and the string-based spaces. Results prove the relevance of our approach by showing a competitive compromise between classification rate and data reduction.

"Nyekah" Ceremony in Hindu Community in Sesetan Village, Denpasar: Ethno-Linguistic Study

Culture and language are habitual things that are always done by the generation in a region. This research focused on the study of ethno-linguistic that discovered the grammatical meaning, cultural meaning and symbolic meaning of ‘Nyekah’ ceremony in Sesetan village, Denpasar. This research is an ethno-linguistic study in which the researcher will examine the procession of Nyekah in the perspective of linguistic that is related with culture. The method of data collection used is participatory observation, in-depth interviews, and documentation. There were 22 lingual elements that those data were categorized as elliptical sentences. Those data were analyzed to find the grammatical and cultural meaning. Furthermore, in ‘Nyekah’ ceremony there were 6 symbolic data which were used in the ritual. Every symbol had deep meaning that were related with religion, human life and nature.

Hyperbolic Interaction Model for Hierarchical Multi-Label Classification

Different from the traditional classification tasks which assume mutual exclusion of labels, hierarchical multi-label classification (HMLC) aims to assign multiple labels to every instance with the labels organized under hierarchical relations. Besides the labels, since linguistic ontologies are intrinsic hierarchies, the conceptual relations between words can also form hierarchical structures. Thus it can be a challenge to learn mappings from word hierarchies to label hierarchies. We propose to model the word and label hierarchies by embedding them jointly in the hyperbolic space. The main reason is that the tree-likeness of the hyperbolic space matches the complexity of symbolic data with hierarchical structures. A new Hyperbolic Interaction Model (HyperIM) is designed to learn the label-aware document representations and make predictions for HMLC. Extensive experiments are conducted on three benchmark datasets. The results have demonstrated that the new model can realistically capture the complex data structures and further improve the performance for HMLC comparing with the state-of-the-art methods. To facilitate future research, our code is publicly available.

Emergency decision-making model of environmental emergencies based on case-based reasoning method

Environmental emergencies are characterized by high uncertainty, complex evolution, and potential for serious damage, thus posing enormous pressure and difficulties to the emergency responses of enterprises and governments. Improving the efficiency and quality of emergency decision-making constitutes the primary focus of today's research in this field. This study systematically analyzes the scenario evolution mechanism of environmental emergencies with a multi-dimensional scenario space method, and key scenario factors are identified from disaster-inducing factors, disaster-bearing factors, disaster-pregnant environments, and emergency actions. Based on these, an emergency decision-making model for environmental emergencies (EEEDM) is constructed based on case-based reasoning (CBR). First, different matching algorithms are designed for accurate numerical data, fuzzy semantic data, and symbolic data. The similarity between the target scenario and the historical scenario is calculated, and the historical scenario similarity set is built according to the given threshold value. Finally, the emergency action plan of the scenario is modified with its utility value evaluated. A solution that applies to the target scenario is then obtained. Additionally, the decision-making model proposed in this paper is validated by an example of environmental emergencies. The results show that this model is scientific and reasonable, and it can better realize the multi-dimensional expression and fast matching of the scenarios and meet the decision requirements of “scenario-response”. In practice, the model is capable of providing support for relevant departments' emergency decision-making.

Interval Fuzzy c-Regression Models with Competitive Agglomeration for Symbolic Interval-Valued Data

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.

Efficient Estimation of Interval-Valued Symbolic Data Regression Model

In the last two decades, regression analysis with interval-valued type data has received more and more attention. For the interval-valued symbolic data regression, the Minmax method and the center and range (CR) method are two widely used popular estimating approaches. In this paper, to improve the estimating eciency of these two estimating methods, seemingly unrelated regression approach has been applied to take account of the dependence information of two regression models of the Minmax method or the CR method. Finally, real data sets are analysed to examine the performance of our proposed procedure.

Improving symbolic data visualization for pattern recognition and knowledge discovery

This paper examines the visualization of symbolic data and considers the challenges rising from its complex structure. Symbolic data is usually aggregated from large data sets and used to hide entry specific details and to transform huge amounts of data (like big data) into analyzable quantities. It is also used to offer an overview in places where general trends are more important than individual details. Symbolic data comes in many forms like intervals, histograms, categories and modal multi-valued objects. Symbolic data can also be considered as a distribution. Currently, the de facto visualization approach for symbolic data is zoomstars which has many limitations. The biggest limitation is that the default distributions (histograms) are not supported in 2D as additional dimension is required. This paper proposes several new improvements for zoomstars which would enable it to visualize histograms in 2D by using a quantile or an equivalent interval approach. In addition, several improvements for categorical and modal variables are proposed for a clearer indication of presented categories. Recommendations for different approaches to zoomstars are offered depending on the data type and the desired goal. Furthermore, an alternative approach that allows visualizing the whole data set in comprehensive table-like graph, called shape encoding, is proposed. These visualizations and their usefulness are verified with three symbolic data sets in exploratory data mining phase to identify trends, similar objects and important features, detecting outliers and discrepancies in the data.

Mahalanobis-Taguchi System for Symbolic Interval Data Based on Kernel Mahalanobis Distance

Mahalanobis-Taguchi System (MTS), as a pattern recognition method by constructing a continuous measurement scale, has a very good performance on classification and feature selection for real-valued data. However, the record of symbolic interval data has become a common practice with the recent advances in database technologies. Kernel methods not only are powerful statistical nonlinear learning methods, but also can be defined over objects as diverse as graphs, sets, strings, and text documents. In this paper, we derive kernel Mahalanobis distance (KMD) to extend MTS to symbolic interval data. To evaluate the proposed method, four experiments with synthetic symbolic interval data sets and seven experiments with real symbolic interval data sets are performed and we have compared our method with MTS based on interval Mahalanobis distance (IMD). The experimental results show our method has a better classification performance than MTS based on IMD on Accuracy, Specificity, Sensitivity, and G-means. However, MTS based on IMD has a stronger dimension reduction rate than our method.

Dynamic time series smoothing for symbolic interval data applied to neuroscience

This work aimed to appraise a multivariate time series, high-dimensionality data-set, presented as intervals using a Symbolic Data Analysis (SDA) approach. SDA reduces data dimensionality, considering the complexity of the model information through a set-valued (interval or multi-valued). Additionally, Dynamic Linear Models (DLM) are distinguished by modeling univariate or multivariate time series in the presence of non-stationarity, structural changes and irregular patterns. We considered neurophysiological (EEG) data associated with experimental manipulation of verticality perception in humans, using transcranial electrical stimulation. The innovation of the present work is centered on use of a dynamic linear model with SDA methodology, and SDA applications for analyzing EEG data.