A New Manifold Learning Algorithm Based on Incremental Spectral Decomposition

Abstract

Manifold learning is to construct nonlinear low-dimensional manifolds from sample data points embedded in high-dimensional spaces. In streaming data applications, new data points come continually, which will change the existing data points’ neighborhoods and their local distributions. Such applications call for incremental algorithms not only to deal with the adding of new data points but also to update the local neighborhoods of the existing data points. In this paper, we introduce a new manifold learning algorithm by updating the structure of eigen-problem iteratively. Incremental spectral decomposition is used in the iterative process and the resulting eigenvectors correspond to the low dimensional embedded coordinates. Experimental results show that 1) as the number of data points increases, the mapping results of the proposed approach become closer and closer to that of batch-style approaches, including LTSA and LE, and 2) the proposed approach outperforms the incremental ISOMAP (IISOMAP, a typical incremental manifold learning algorithm) in mapping accuracy. We argue that the new algorithm is suitable for incremental learning of large-scale data streams.