Far beyond the classical data models: symbolic data analysis

Noirhomme­-Fraiture, Monique; Brito, Paula

doi:10.1002/sam.10112

Cited by 106 publications

(49 citation statements)

References 76 publications

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“…In fact, a symbolic data type is different from numeric data such that it could present human knowledge, nominal, categorical and synthetic data. These symbolic data types had been widely studied (see [2,3,5,23,37,40]) that includes (symbolic) interval-valued data. In this section, we review symbolic data with their dissimilarity measure definitions.…”

Section: Symbolic Data With Its Dissimilarity Measuresmentioning

confidence: 99%

Self-organizing map for symbolic data

Yang

Hung

Chen

2012

Fuzzy Sets and Systems

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Section: Symbolic Data With Its Dissimilarity Measuresmentioning

confidence: 99%

Self-organizing map for symbolic data

Yang

Hung

Chen

2012

Fuzzy Sets and Systems

View full text Add to dashboard Cite

“…Given the i-th and the j-th generic unit, we rewrite the indices of ρ (·,·) in Eq. (20) such that ρ i1,j2 denotes the correlation of the qfs Φ −1 i1 (t) and Φ −1 j2 (t), while ρ ·1,·2 denotes the correlation of the qfs associated with M W (y 1 ) (i.e.,Φ −1 i1 (t)) and M W (y 2 ) (i.e., Φ −1 j2 (t)). Using the proposed notation and the product of two qfs defined in Eq.…”

Section: Measures Of Interdependencementioning

confidence: 99%

“…When the data domain is categorical, a noteworthy approach is the Compositional data one [1]. Among the methods listed above, Symbolic Data Analysis (SDA) [7,6,4,20] approach provides models and techniques for generalizing the statistical treatment of most of them. In fact, SDA is a relatively new statistical approach designed for processing data described by set-valued variables (or Symbolic variables) like interval, multi-valued discrete, multi-categorical, histogram and modal variables.…”

Section: Introductionmentioning

confidence: 99%

Basic statistics for distributional symbolic variables: a new metric-based approach

Irpino

Verde

2014

Adv Data Anal Classif

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In data mining it is usual to describe a group of measurements using summary statistics or through their empirical distribution functions. Each summary of a group of measurements is the representation of a typology of individuals (sub-populations) or of the evolution of the observed variable for each individual. Therefore, typologies or individuals are expressible through multi-valued descriptions (intervals, frequency distributions). Symbolic Data Analysis, a relatively new statistical approach, aims at the treatment of such kinds of data. In the conceptual framework of Symbolic Data Analysis, the paper aims at presenting new basic statistics for numeric multi-valued data. First of all, we propose how to consider all numerical multi-valued descriptions as special cases of distributional data, i.e. as data described by distributions. Secondly, we extend some classic univariate (mean, variance, standard deviation) and bivariate (covariance and correlation) basic statistics taking into account the nature, the source and the interpretation of the variability of such data. As opposed to those proposed in the literature, the novel statistics are based on a distance between distributions, the ℓ2 Wasserstein distance. Using a clinic dataset, we compare the proposed approach to the existing one showing the main differences in terms of interpretation of results.

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“…To address this issue, symbolic data analysis (Diday and Noirhomme-Fraiture, 2008) has been introduced as an extension of classical data analysis methods to take into account complete and complex information (Noirhomme-Fraiture and Brito, 2011), such as interval-valued data, histogramvalued data, multimodal data, and others. By incorporate information that cannot be represented by classical data analysis, symbolic data analysis enables effective summarization and visualization of huge databases.…”

Section: Introductionmentioning

confidence: 99%

Forecasting Symbolic Candle Chart-Valued Time Series

Park¹,

Sakaori²

2014

Communications for Statistical Applications and Methods

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This study introduces a new type of symbolic data, a candle chart-valued time series. We aggregate four stock indices (i.e., open, close, highest and lowest) as a one data point to summarize a huge amount of data. In other words, we consider a candle chart, which is constructed by open, close, highest and lowest stock indices, as a type of symbolic data for a long period. The proposed candle chart-valued time series effectively summarize and visualize a huge data set of stock indices to easily understand a change in stock indices. We also propose novel approaches for the candle chart-valued time series modeling based on a combination of two midpoints and two half ranges between the highest and the lowest indices, and between the open and the close indices. Furthermore, we propose three types of sum of square for estimation of the candle chart valued-time series model. The proposed methods take into account of information from not only ordinary data, but also from interval of object, and thus can effectively perform for time series modeling (e.g., forecasting future stock index). To evaluate the proposed methods, we describe real data analysis consisting of the stock market indices of five major Asian countries'. We can see thorough the results that the proposed approaches outperform for forecasting future stock indices compared with classical data analysis.

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Far beyond the classical data models: symbolic data analysis

Cited by 106 publications

References 76 publications

Self-organizing map for symbolic data

Self-organizing map for symbolic data

Basic statistics for distributional symbolic variables: a new metric-based approach

Forecasting Symbolic Candle Chart-Valued Time Series

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