Concept of (dis)similarity in data analysis

(Dis)similarity matrices (the Euclidean distance matrix included) can be used for unsupervised and supervised data analysis. In this review, we use four different data sets (real and simulated, with different dimensionalities and a different correlation structure) to demonstrate the performance of dissimilarity-based approaches [e.g., hierarchical clustering, dissimilarity-Partial Least Squares (dissimilarity-PLS) and Non-parametric Multiple Analysis of Variance (NP-MANOVA)].Dissimilarity-PLS performs well for linear and highly non-linear data, both in regression and discrimination settings. NP-MANOVA allows for a fast randomization test of the statistical significance of the factors studied in the designed experiments.Dissimilarity-based approaches can be applied to data sets with numerous variables. However, if the studied data set contains numerous objects, a full dissimilarity matrix should be replaced with a dissimilarity matrix containing the distances of all of the objects to preselected “prototypes”. Although we focus on the Euclidean distance, any dissimilarity measure can be used in the approaches discussed, thus enlarging the areas of their application to different types of variable (e.g., nominal variables, and sensory data).

► (Dis)similarity matrices can be used for unsupervised and supervised data analysis.
► D-PLS method can be used for modeling non-linear problems.
► When working with dissimilarity matrices, it is very easy to identify X-outliers.