A simple nonlinear dimension reduction technique for high dimension data visualization
Rongrong Wang, Department of Computational Mathematics, Science and Engineering, Department of Mathematics, Michigan State University, USA
Over the past two decades, many nonlinear dimension reduction techniques are developed to address some of the limitations of linear dimension reduction techniques. However, every nonlinear DR technique has their own limitation. For example, LLE is known as best in preserving local structures, but is very unstable to outliers and sensitive to the number of k nearest neighbors. tSNE is excellent in data clustering, but cannot preserve the geometry of the high dimensional data. Isomap is good at preserving the geodesic distances but suffers from topological instability. In this talk, we propose a simple algorithm that has the advantages of both LLE and tSNE, i.e., it preserves both the locally linear structure and the clusters in the dataset.