Nonlinear dimensionality reduction for structural discovery in image processing

Nonlinear dimensionality reduction techniques are a thriving area of research in many fields, including pattern recognition, statistical learning, medical imaging, and statistics. This is largely driven by our need to collect, represent, manipulate, and understand high-dimensional data in practically all areas of science. Here we define “high-dimensional” to be where dimension d > 10, and in many applications d ≫ 10. In this paper we discuss several nonlinear dimensionality reduction techniques and compare their characteristics, with a focus on applications to improve tractability and provide low-dimensional structural discovery for image processing.