Fig. 8: Negative gradient fields of the real/theoretical LOO loss.
From: Assessing and improving reliability of neighbor embedding methods: a map-continuity perspective
a We draw the negative gradient fields (force fields) − ∇yL(y; xε) based on the LOO loss under the same setting as in Fig. 3b. b We draw a similar field plot based on the hyperbolic term \(\frac{{{{\bf{y}}}}_{\parallel }-{{{\bf{y}}}}_{\perp }}{\parallel {{\mathbf{\theta }}}{\parallel }^{2}}\) from Theorem 1, where we take θ = (c1 − c2)/2 and c1, c2 are the centers of two clusters in the embedding. In addition, we add loss contours to both plots, which show hyperbolic paraboloids around the origin. We observe a strong alignment between the negative gradient field of the LOO loss and that of the theoretical analysis. Both field plots show a pull force towards the x-axis and a push force away from the y-axis. Source data are provided as a Source Data file.
