Search results for "Principal geodesic analysis"
showing 2 items of 2 documents
A more distinctive representation for 3D shape descriptors using principal component analysis
2015
Many researchers have used the Heat Kernel Signature (or HKS) for characterizing points on non-rigid three-dimensional shapes and Classical Multidimensional Scaling (Classical MDS) method in object classification which we quote, in particular, the example of Jian Sun et al. (2009) [1]. However, in this paper, the main focuses on classification that we propose a concise and provably factorial method by invoking Principal Component Analysis (PCA) as a classifier to improve the scheme of 3D shape classification. To avoid losing or disordering information after extracting features from the mesh, PCA is used instead of the Classical MDS to discriminate-as much as possible-feature points for each…
Nonlinear data description with Principal Polynomial Analysis
2012
Principal Component Analysis (PCA) has been widely used for manifold description and dimensionality reduction. Performance of PCA is however hampered when data exhibits nonlinear feature relations. In this work, we propose a new framework for manifold learning based on the use of a sequence of Principal Polynomials that capture the eventually nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) is shown to generalize PCA. Unlike recently proposed nonlinear methods (e.g. spectral/kernel methods and projection pursuit techniques, neural networks), PPA features are easily interpretable and the method leads to a fully invertible transform, which is a desirable property…