Title: Exploratory Segmentation and Fitting of a 3D Surface *

John Mark Agosta
Intel Research

Abstract:

In this talk we walk through the stages of a largely empirical exploratory analysis of a spatial data set using a full catalog of statistical learning techniques.

The data set consists of a 3D surface, of 17k points, with 4 measurements of different "components" at each point. The surface is divided into 31 patches, and there are 34 predictor variables with a value for each patch. The presumption of the analysis is that variation of each surface patch can be explained by the predictors.

The surface appears smooth, with characteristic curvature in each patch obscured by a "dimple" process over the entire surface. Our approach is to segment the surface into separate the dimple process from the less curved surface, and then to explore relationships between the segmented surface shape and the predictors.

Segmentation took two approaches, first a one dimensional EM approach, and then a robust regression approach using an asymmetric huber-style cost function. Fitting surface shape was done with both parametric functional and "random forest" regression methods. Various means have been explored for feature selection in a composite segmentation-functional regression model.

To date the results of the analysis are frustratingly inconclusive; we will trace the path of our analysis to the extent that the audience's patience and interest in the range of techniques allows. The analysis has been framed in the form of a Bayes net model when possible.

Perhaps of more interest are some ideas about more sophisticated methods that could be pursued, and thoughts about if and when we should decide when the task is complete.   

* This work has been done with the collaboration of Marzia Polito.