Selection of the optimal parameter value for the ISOMAP algorithm

The ISOMAP algorithm has recently emerged as a promising dimensionality reduction technique to reconstruct nonlinear low-dimensional manifolds from the data embedded in high-dimensional spaces, by which the high-dimensional data can be visualized nicely. One of its advantages is that only one parameter is required, i.e. the neighborhood size or K in the K nearest neighbors method, on which the success of the ISOMAP algorithm depends. However, it's an open problem how to select a suitable neighborhood size. In this paper, we present an effective method to select a suitable neighborhood size, which is much less time-consuming than the straightforward method with the residual variance, while yielding the same results. In addition, based on the characteristics of the Euclidean distance metric, a faster Dijkstra-like shortest path algorithm is used in our method. Finally, our method can be verified by experimental results very well.