Pattern Recognition Based On Nonlinear Dimensionality Reduction

Image data taken with various capturing devices are usually multidimensional and therefore they are not very suitable for accurate classification normally expecting to operate only on a small set of relevant features. Hence, the task of dimensionality reduction has emerged with an aim to reduce or eliminate information bearing secondary importance and retain or highlight meaningful one. Since the nature of real-world data are often nonlinear, the linear dimensionality reduction techniques, such as Principal Component Analysis (PCA), fail to preserve a structure and relationships in a high-dimensional space when data are mapped into a low dimensional one. It means that nonlinear dimensionality reduction methods are on demand in this case, such as Isometric Mapping (Isomap) and Locally Linear Embedding (LLE). Their main attractive characteristics are few free parameters to be set and a non-iterative solution avoiding the convergence to a local minimum. The original nonlinear dimensionality reduction algorithms are non-supervised, which can't directly be applied in pattern recognition. In this paper, we further explore and extend original methods, add sample classification information to implement dimensionality reduction, and then train a simple classifier. In this way, we get a simple pattern recognition prototype. We test this system on some real-world face images and obtain much better results than traditional linear methods.