Spherical Principal Curves

Principal Curves

Principal curves are smooth one-dimensional curves that pass through the middle of a p-dimensional data set, providing a nonlinear summary of the data. They are nonparametric, and their shape is suggested by the data. The algorithm for constructing principal curves starts with some prior summary, such as the usual principal-component li e. The curve in each successive iteration is a smooth or l...

Principal Curves : Learning

and submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Computer Science) complies with the regulations of this University and meets the accepted standards with respect to originality and quality. The subjects of this thesis are unsupervised learning in general, and principal curves in particular. Principal curves were originally defined by Hastie [Has84...

Principal Curves : Learning , Design

Estimations of Principal Curves

Principal curves are smooth curves that minimize the average squared orthogonal distance to each point in a data set. Fitting a principal curve is a maximum-likelihood technique for nonlinear regression in the presence of Gaussian noise on both x and y. We choose two definitions of principal curves in the literature and then present experimental results to discuss over them.

Sequential Principal Curves Analysis

This report includes all the technical details of the Sequential Principal Curves Analysis (SPCA) in a single document. SPCA is an unsupervised nonlinear and invertible feature extraction technique. The identified curvilinear features can be interpreted as a set of nonlinear sensors: the response of each sensor is the projection onto the corresponding feature. Moreover, it can be easily tuned f...