An improved locally linear embedding for sparse data sets

Locally linear embedding is often invalid for sparse data sets because locally linear embedding simply takes the reconstruction weights obtained from the data space as the weights of the embedding space. This paper proposes an improved method for sparse data sets, a united locally linear embedding, to make the reconstruction more robust to sparse data sets. In the proposed method, the neighborhood correlation matrix presenting the position information of the points constructed from the embedding space is added to the correlation matrix in the original space, thus the reconstruction weights can be adjusted. As the reconstruction weights adjusted gradually, the position information of sparse points can also be changed continually and the local geometry of the data manifolds in the embedding space can be well preserved. Experimental results on both synthetic and real-world data show that the proposed approach is very robust against sparse data sets.