An improved incremental nonlinear dimensionality reduction for isometric data embedding

• An effective method to update the neighborhood graph and geodesic distances matrix.
• A simple method to judge the short circuits in the incremental neighborhood graph.
• A better solution of the incremental eigen-decomposition problem.

Manifold learning has become a hot issue in the field of machine learning and data mining. There are some algorithms proposed to extract the intrinsic characteristics of different type of high-dimensional data by performing nonlinear dimensionality reduction, such as ISOMAP, LLE and so on. Most of these algorithms operate in a batch mode and cannot be effectively applied when data are collected sequentially. In this paper, we proposed a new incremental version of ISOMAP which can use the previous computation results as much as possible and effectively update the low dimensional representation of data points as many new samples are accumulated. Experimental results on synthetic data as well as real world images demonstrate that our approaches can construct an accurate low-dimensional representation of the data in an efficient manner.