Symbolic Data: Basics
Lynne Billard, Edwin Diday · 2019
This chapter describes what symbolic data are, how they may arise, and their different formulations. Some data are naturally symbolic in format, while others arise as a result of aggregating much larger data sets according to some scientific question(s) that generated the data sets in the first place. The chapter describes non-modal multi-valued or lists of categorical data, with modal multi-valued data, and considers interval-valued data, with modal interval data more commonly known as histogram-valued data. It also describes basic descriptive statistics, such as sample means, sample variances and covariances, and histograms, for the differing types of symbolic data. For quantitative data, these definitions implicitly assume that within each interval, or sub-interval for histogram observations, observations are uniformly spread across that interval. For list multi-valued data, the sample mean and sample variance are simply the respective classical values for the probabilities associated with each of the corresponding categories in the variable domain.