Alternative robust local embedding

Dimensionality reduction is a significant problem in pattern recognition and thus arouses broad interest in the machine learning community. Different from the traditional linear dimensionality reduction methods, recently some nonlinear methods have been proposed in virtue of manifold learning. These methods can efficiently discover the low-dimensional nonlinear manifold in a high-dimensional data space and further preserve the manifold structure of the data points in the low-dimensional embedding space. Despite their attractive properties, these nonlinear methods are sensitive to the outliers in the data sets. Moreover, the existing locally nonlinear dimensionality reduction methods generally neglect the globally structural information. In this paper, we address these problems in the context of locally linear embedding (LLE). Through capturing the local and global geometry information simultaneously, we propose an alternative approach to make the local embedding relatively more robust, called as alternative robust local embedding (ARLE). It can not only suppress an unfavorable influence of the outliers on the embedding process automatically, but also outperform LLE in 2-D data visualization due to the introduction of the global geometry. Experimental results and comparisons on both synthetic and real data sets show the effectiveness of ARLE.