P-ISOMAP: An efficient parametric update for ISOMAP for visual analytics

One of the most widely-used nonlinear data embedding methods is ISOMAP. Based on a manifold learning framework, ISOMAP has a parameter k or ε that controls how many edges a neighborhood graph has. However, a suitable parameter value is often difficult to determine because of a time-consuming optimization process based on certain criteria, which may not be clearly justified. When ISOMAP is used to visualize data, users might want to test different parameter values in order to gain various insights about data, but such interaction between humans and such visualizations requires reasonably efficient updating, even for large-scale data. To tackle these problems, we propose an efficient updating algorithm for ISOMAP with parameter changes, called p-ISOMAP. We present not only a complexity analysis but also an empirical running time comparison, which show the advantage of p-ISOMAP. We also show interesting visualization applications of p-ISOMAP and demonstrate how to discover various characteristics of data through visualizations using different parameter values.