Investigating only a subset of paired comparisons after principal component analysis

Principal component analysis (PCA) is often used to summarize and explore multivariate data sets, including sensory evaluation data sets. We propose how to conduct PCA of a results matrix in which only a subset of the paired comparisons is 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 test-control paired comparisons are of primary interest, not the test-test paired 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. However, this solution does not extract variance maximally from only the 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 manuscript, 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 a PCA conducted conventionally. We show visually and numerically the advantages of the proposed approach. The methods proposed in this paper can be adapted to investigate only a subset of paired comparisons in other data sets in sensory evaluation and in other domains.

Automated summary

Principal component analysis (PCA) is commonly used to summarize and explore multivariate data sets, including sensory evaluation data sets. This study proposes a method to conduct PCA on a results matrix where only a subset of paired comparisons is of interest. The proposed approach is illustrated with two data sets from trained sensory panels. The results show that the PCA conducted with the proposed method extracts more variance from the relevant paired comparisons and better separates the relevant pairs compared to conventional PCA.