Spectral Learning And Clustering And Its Application

In this paper, we mainly study spectral learning and clustering methods and apply them to spectral color image segmentation, vector field visualization, data classification, motion analysis and synthesis and so on, including from unsuper-vised to supervised spectral learning, time-based spectral learning and vector field segmentation. In recent years, the related methods have been an active area. Each year, there are a huge amount of literatures appearing in the premier conferences and journals. The basic properties of spectrum have been deeply and completely studied. The famous spectral methods include principal components analysis (PCA), locally linear embedding (LLE]), normalized cut, local tangent space alignment (LTSA) and kernel algorithms such as Kernel PCA. In spite of their different research lines, their basic ideas are very similar.In this paper, we explore spectral learning and clustering techniques in the related fields. In particular, we have done the work in the following five aspects.1. We extend and apply spectral methods to time-dependent data, such as motion capture data.2. This paper proposed a method for spectral color image segmentation based on spectral learning and clustering techniques.3. Vector field segmentation is a key problem in vector field visualization. To solve this issue, we first convert vector fields to scalar fields and then apply popular spectral methods to obtain the segmentation of vector fields.4. Metric learning is used to improve the performance of classification of spectral methods while avoiding too much loss of information of data visualization. 5. Dynamic mapping is proposed in this work to generalize spectral methods to new test samples, furthermore, for the purpose of classification, we extend unsupervised spectral methods to their supervised version in terms of class membership.