Investigating paired differences for data sets with special structures after principal component analysis
Principal component analysis (PCA) is a popular technique for summarizing and exploring multivariate data sets. We propose how to conduct PCA of results from sensory studies that have a special structure, where only a subset of the product paired comparisons are of interest. We illustrate the proposed approach with two data sets, both from trained sensory panels. In the first example, assessors evaluated the intensities of multiple sensory attributes in a control smoothie and nine test smoothie formulations. In this example, the control-test paired comparisons are of primary interest, not the test-test pair comparisons. In the second example, assessors characterized several yogurt formulations continuously over time during consumption using a method for temporal sensory profiling. In this example, we considered the within-timepoint paired comparisons to be of primary interest. It is possible to conduct PCA conventionally based on each panel’s results. Doing so will extract variance from the matrix columns maximally, yielding the optimal space for investigating the variance in all paired comparisons. But this solution does not extract variance maximally from only a relevant subset of paired comparisons, indicating that the PCA conducted conventionally does not yield the optimal space for investigating the variance from only these relevant pairs. In this paper, building on recently published approaches, we find this optimal space by submitting to PCA a results matrix containing only the paired comparisons that are of primary interest. The PCA solution extracts a larger proportion of the sum of squares from the relevant paired comparisons and better separates the relevant pairs than PCA conducted conventionally. We show visually and numerically the advantages of the proposed approach. The methods proposed in this paper provide a deeper understanding of PCA and can be adapted to investigate data sets with other special structures and in other domains.
Castura, J.C., Varela, P. & Næs, T. (2023). Investigating paired differences for data sets with special structures after principal component analysis. 15th Pangborn Sensory Science Symposium. 20-25 August. Nantes, France. (Oral Presentation).