The dualistic approach of FCA: a further insight into Ontario Lake sediments

The investigation of object-by-attribute matrices is very common in statistics and data analysis with the aim of uncovering every possible relationship among objects and/or attributes. Formal Concept Analysis (FCA) is a method, which stems directly from partial order and lattice theory, which provides an efficient tool to symmetrically uncover linkages among objects and attributes whenever a relation stands among the two sets. It provides efficacious graphical representation and computes association rules between attributes, thus helping in the detection of possible synergism or antagonism of attributes. In this paper, FCA potentialities are discussed and described by means of a case study already investigated by other partial order techniques: the case of Lake Ontario sediment samples. Data derive from a ‘test battery’ for a simultaneous analysis of degradation of Lake Ontario samples, which are basically of two typologies: hygienic and toxicity tests. A multi-valued approach is adopted to cope with the ordinal feature of data. Results highlight interesting interaction among hygienic compounds and a synergism between the two toxicity tests.