Statistics Seminars: Principal curves and surfaces: The step beyond data visualization
16 January 2012 14:00 in CM221
Principal curves and surfaces have been proposed about two decades ago as a tool for nonlinear dimension reduction. Descriptively, they can be defined as smooth objects (of dimension 1 and 2, respectively) capturing the "middle" of a (potentially high-dimensional) data cloud.
Though a relatively large amount of literature has discussed methods and algorithms for the estimation of principal curves and surfaces, most of this research, rather surprisingly, stops here, and does not consider exploiting the fitted curve or surface once it is established. One reason for this reluctance may be that several rather cumbersome technicalities, such as the computation of distances or projection indexes, need to be solved before a fitted principal curve or surface can be used for further inferential purposes such as regression or classification.
In this talk, we give three examples, stemming from current collaborative work, which illustrate how "local" principal curves and surfaces can be efficiently used as a nonparametric dimension reduction tool, enabling further statistical analysis based on the fitted principal object. These examples include the tracing of elementary particles in liquid argon, the modelling of the shape of the corpus callosum, as well as the compression of the thermochemical state space of combustion systems.
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