Isomap

Isomap on the “Swiss roll” data set. (A) Two points on the Swiss roll and their geodesic curve. (B) The KNN graph (with K = 7 and N = 2000) allows a graph geodesic (red) that approximates the smooth geodesic. (C) The Swiss roll "unrolled", showing the graph geodesic (red) and the smooth geodesic (blue). Replication of Figure 3 of [1].

Isomap is a nonlinear dimensionality reduction method. It is one of several widely used low-dimensional embedding methods.[1] Isomap is used for computing a quasi-isometric, low-dimensional embedding of a set of high-dimensional data points. The algorithm provides a simple method for estimating the intrinsic geometry of a data manifold based on a rough estimate of each data point’s neighbors on the manifold. Isomap is highly efficient and generally applicable to a broad range of data sources and dimensionalities.

  1. ^ a b Tenenbaum, Joshua B.; Silva, Vin de; Langford, John C. (22 December 2000). "A Global Geometric Framework for Nonlinear Dimensionality Reduction". Science. 290 (5500): 2319–2323. doi:10.1126/science.290.5500.2319.