Visualising complex data: dendrograms help in interpreting possessive classifier membership.

Do the nominal categorisation systems found in Oceanic languages have an impact on cognition? Many Oceanic languages have a set of possessive classifiers that are used to categorise alienable possessions according to how the possessor intends to use these possessions. Data from a suite of experiments were collected from six Oceanic languages spoken in Vanuatu and New Caledonia (Merei, Lewo, Vatlongos, North Ambrym, Nêlêmwa and Iaai). The inventory of possessive classifiers for each language ranges from two to 24.

We discuss the results from one experiment, card sorting. Participants sorted pictures of possessed entities into groups in two ways: (i) a free sort, where participants put the pictures into as many piles as they wanted according to perceived similarity; (ii) a structured sort, where participants were asked to group the images according to which classifier they could occur with. If possessive classifiers have an impact on cognition we expect to find similar groupings of pictures across the two tasks.

We explore the resulting data visually using hierarchical agglomerative clustering. This type of cluster analysis produces trees called dendrograms, which are a heuristic aid to explore categorisation data (Borcard et al. 2011:63). We present dendrograms for our experimental data and discuss ways of exploring the clusters. Fig. 1 shows a dendrogram for the structured sort for the Lewo language: its three possessive classifiers – drink, food and general – are represented by three distinct clusters. We outline the different statistical methods that make use of heuristic data exploration to compare clusters across different dendrograms (Robinson & Foulds 1981; Fowlkes & Mallows 1983; Lapointe & Legendre 1995). The value of these methods is that they help us to answer our key question as to whether the groupings made in the free sort (i) are similar to those made in the structured sort (ii). We then discuss how our findings bear on the relationship between classifier categories and cognition.

References
Borcard, D., F. Gillet & P. Legendre. (2011). Numerical Ecology with R. NY: Springer.

Fowlkes, E. B., & C. L. Mallows (1983). A method for comparing two hierarchical clusterings. Journal of the American statistical association, 78(383), 553-569.

Lapointe, F-J. & P. Legendre. (1995). Comparison tests for dendrograms: A comparative evaluation. Journal of Classification, 12(2), 265-282.

Robinson, D. F. & L. R. Foulds. (1981). Comparison of phylogenetic trees. Mathematical Biosciences, 53(1-2), 131–147.