Fig. 4

The figure shows two methods for linear and nonlinear multivariate analysis: (a) Principal Component Analysis (PCA) and (b) Minimum Curvilinearity Embedding (MCE). PCA is a method for linear dimensionality reduction and the points on the PCA plot (representing the various topological measures) are distributed according to a circular pattern, which suggests the presence of non-linear relationships among the data points. MCE is a non-linear method for dimensionality reduction, therefore the data points are distributed more linearly compared to PCA. The X and Y axes of (a) are the principal components (PC) 1 and 2 respectively. The X and Y axes of (b) are the dimensions 1 and 2 of the embedding. Since multivariate analysis considers the overall strength of relationships between each pair of variables (individual data points of each plot), the topological measures with curves of similar shape tend to be closer in the reduced space. For instance, LCP-correlation and Power Lawness, which have high correlation values and a similar shape with respect to Von Frey test, are also close to each other. Points corresponding to topological measures with medium-high correlation values are shown in the same color as in Fig. 3, whereas measures in the low correlation range are colored in black