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Abstract: Traditional nonlinear manifold learning methods have achieved great success in dimensionality reduction and feature extraction, most of which are batch modes. However, if new samples are observed, the batch methods need to be calculated repeatedly, which is computationally intensive, especially when the number or dimension of the input samples are large. This paper presents incremental learning algorithms for Laplacian eigenmaps, which computes the low-dimensional representation of data set by optimally preserving local neighborhood information in a certain sense. Sub-manifold analysis algorithm together with an alternative formulation of linear incremental method is proposed to learn the new samples incrementally. The locally linear reconstruction mechanism is introduced to update the existing samples’ embedding results. The algorithms are easy to be implemented and the computation procedure is simple. Simulation results testify the efficiency and accuracy of the proposed algorithms. [Copyright &y& Elsevier]

Abstract: Manifold learning is an important dimensionality reduction tool that discovers the structure of high dimensional data and provides understanding of multidimensional patterns in data mining, pattern recognition, and machine learning. Several manifold learning algorithms are applied to extract the intrinsic features of different prototypes in high dimensional space by preserving the local geometric characteristics. However, due to the locality geometry preservation, these manifold learning methods, including locally linear embedding (LLE), are sensitive to noise. To solve the noisy manifold learning problem, this paper proposes a Neighbor Smoothing Embedding (NSE) for noisy points sampled from a nonlinear manifold. Based on LLE and local linear surface estimator, the NSE smoothes the neighbors of each manifold data and then computes the reconstruction matrix of the projections on the principal surface. Experiments on synthetic data as well as real world patterns demonstrate that the suggested algorithm can efficiently maintain an accurate low-dimensional representation of the noisy manifold data with less distortion, and give higher average classification rates compared to others. [Copyright &y& Elsevier]