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Thinking by classes in data science: the symbolic data analysis paradigm

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Data Science, considered as a science by itself, is in general terms, the extraction of knowledge from data. Symbolic data analysis (SDA) gives a new way of thinking in Data Science by extending the standard input to a set of classes of individual entities. Hence, classes of a given population are considered to be units of a higher level population to be studied. Such classes often represent the real units of interest. In order to take variability between the members of each class into account, classes are described by intervals, distributions, set of categories or numbers sometimes weighted and the like. In that way, we obtain new kinds of data, called ‘symbolic’ as they cannot be reduced to numbers without losing much information. The first step in SDA is to build the symbolic data table where the rows are classes and the variables can take symbolic values. The second step is to study and extract new knowledge from these new kinds of data by at least an extension of Computer Statistics and Data Mining to symbolic data. SDA is a new paradigm which opens up a vast domain of research and applications by giving complementary results to classical methods applied to standard data. SDA also gives answers to big data and complex data challenges as big data can be reduced and summarized by classes and as complex data with multiple unstructured data tables and unpaired variables can be transformed into a structured data table with paired symbolic‐valued variables. WIREs Comput Stat 2016, 8:172–205. doi: 10.1002/wics.1384

From a standard data table (X, Y) describing a set of individuals X by a set of standard variables Y, to a symbolic data table (X′, Y′) describing a set of teams X′ by a set of symbolic variables Y′.
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An example of RSDA package output in case of a principal component analysis of interval‐valued variables.
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A NETSYR output of a PCA extended to symbolic data.
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A symbolic data table provided by the SYR software
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Some symbolic data analysis tools output.
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From relational data base to symbolic data.
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Building a symbolic data table from several ground populations described by different sets of variables and a unique class variable.
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The biplot of histogram‐valued variables needing copulas models.
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The ground data table where seven individuals are described by three binary variables.
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The first cell of this table means that if y1y2z1z2 and Y has a better explanatory power than Z, it has also a better discriminatory power than Z.
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The explanatory power of Y is much higher than the one of Z and the discriminatory power of Z′ is higher than the one of Y′.
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The tables X/U and U/X.
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Graphical representation of the variability inside symbolic data by four numeric and two symbolic variables.
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Individuals are uniformly distributed inside the circle. Therefore, there is no correlation between Y1 and Y2.
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