Estimating manifold dimension by inversion error

Video and image datasets can often be described by a small number of parameters, even though each image usually consists of hundreds or thousands of pixels. This observation is often exploited in computer vision and pattern recognition by the application of dimensionality reduction techniques. In particular, there has been recent interest in the application of a class of nonlinear dimensionality reduction algorithms which assume that an image dataset has been sampled from a manifold. From this assumption, it follows that estimating the dimension of the manifold is the first step in analyzing an image dataset. Typically, this estimate is obtained either by using a priori knowledge, or by applying one of the various statistical and geometrical methods available. Once an estimate is obtained, it is used as a parameter for the nonlinear dimensionality reduction algorithm. In this paper, we consider reversing this approach. Instead of estimating the dimension of the manifold in order to o...

• Type: Conference
• Year: 2005
• Where: SAC
• Authors: Shawn Martin, Alex Bäcker
• Keywords: Applied Computing, Dimensionality Reduction, Image Datasets, Reduction Algorithm, SAC 2005