Determination of the consensus partition and cluster analysis of subjects in a free sorting task experiment

• We advocate using Adjusted Rand index as a measure of similarity between partitions given by subjects in a free sorting task.
• A technique for determining a consensus partition is proposed.
• The problem of segmenting subjects is tackled and a strategy based on Adjusted Rand index is described.
• The clustering technique is applied to the free sorting of wine aromas by a panel of subjects.

The purpose of this study is to investigate the problem of clustering subjects in a free sorting task. We compare different measures of agreement between partitions. From a simulation study, we advocate using the Adjusted Rand index. On the basis of this index, we propose a technique for determining a consensus partition as a summary of the initial partitions given by the subjects after a categorization task. Thereafter, the problem of clustering the subjects is explored. For this purpose, a method combining hierarchical clustering and a partitioning algorithm is described. These techniques are applied to a case study of the perception of wine aromas by a panel of subjects.