Fig. 1
RGSA illustration using a linear function f(x) = f([x1 x2]T) = 3x1 – 2x2: (a) surface plot of the function (gray), twenty random observables xs(k) (circles), and relocation vectors xc(k) – xs(k) (line segments); (b) relocation matrix vectors rs(k)vs(k) (thin lines), the largest principal component e1 (thick solid line), and the normalized gradient g = [3–2]T/131/2 (thick dotted line). In this example, all function variability occurs along the gradient g (the function is constant in the direction orthogonal to g), which is well aligned with the vector e1, obtained using the proposed RGSA.
