… of principal surfaces are available. Recently, we proposed the probabilistic principal surface
(PPS) to address a number of issues associated with current principal surface algorithms. …

… to the cumnt probabilistic formulations of the principal curve and principal surface is … step
of the original principal curve algorithm in current probabilistic principal surface fomulations. …

… the probabilis0 tic principal surface (PPS), a general framework for computing principal
surfaces of … Un0 like any of the existing principal surface approximation algorithms, the PPS is …

… Turning to 3-D surfaces, we review parametric surfaces and discuss the difficulty of
determining good parameterizations for complex objects. We propose a solution which involves …

… and surfaces[1] can be used to compute a manifold that generalizes the property of principal
… A discrete non-parametric approximation[2] of principal surfaces that is much simpler to …

… Here we propose Probabilistic Principal Surfaces (PPS) as an effective high-D data visualization
and clustering tool for data mining applications, emphasizing its flexibility and …

… on the surface of a sphere as shown in figure 2(a). The next section briefly describes the
probabilistic principal surface model which is used to construct the spherical manifold. …

… fit to the data, rather than as a probabilistic model. Inspired by probabilistic PCA, we present
a latent variable model for PGA that provides a probabilistic framework for factor analysis on …

… to converge to the global maximum comprising the principal eigenvectors. We may show,
however, that minor eigenvector solutions are saddlepoints on the likelihood surface. …

… The NLPCA computed by such a multilayer sigmoidal neural network is equivalentÐwith
certain exceptions2Ðto a principal surface under the more general definition [15], [16]. To …