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Symbolic Data Analysis: Definition and Examples

With the advent of computers, large, very large datasets have become routine. What 
is not so routine is how to analyse these data and/or how to glean useful information 
from within their massive conﬁnes. One approach is to summarize large data sets in such 
a way that the resulting summary dataset is of a manageable size. One consequence 
of this is that the data may no longer be formatted as single values such as is the 
case for classical data, but may be represented by lists, intervals, distributions and 
the like. These summarized data are examples of symbolic data. This paper looks 
at the concept of symbolic data in general, and then attempts to review the methods 
currently available to analyse such data. It quickly becomes clear that the range of 
methodologies available draws analogies with developments prior to 1900 which formed 
a foundation for the inferential statistics of the 1900’s, methods that are largely limited 
to small (by comparison) data sets and limited to classical data formats. The scarcity of 
available methodologies for symbolic data also becomes clear and so draws attention to 
an enormous need for the development of a vast catalogue (so to speak) of new symbolic 
methodologies along with rigorous mathematical foundational work for these methods.