My site has moved to ddiez.com.

Dissertation work

Pre June, 2009

My dissertation work is in collaboration with my advisory Rick Schoenberg and focuses on point pattern prototypes. The first problem we addressed focuses on computing the spike time distance, which is essentially a measure of how close two point patterns match up. Our focus was extending the 1-D computations, which are well-studied, to multiple dimensions efficiently. In our first paper (submitted), we introduce an incremental matching algorithm that computes the spike time distance in any dimensions and can be easily extended to other distance measures. We also prove the method is accurate.

The second problem we aimed to address is in regards to point pattern prototypes. If there are several point patterns -- possibly the locations of forest fires in CA for each year -- then the prototype of this collection of patterns would be a typical point (the typical pattern of forest fires in a year). More specifically, the prototype is defined to be the pattern that minimizes the sum of distances between it and all the patterns in the collection (using the spike time distance). While the prototype can be efficiently computed in 1-D, it is more computationally intensive in higher dimensions when the number of points per pattern is not necessarily small; we would like to compute prototypes in higher dimensions when there might be many more than a dozen points per pattern. Again in the first paper, we introduced a kernel smoothing method to estimate locations of the prototype's points in higher dimensions, making the prototype in higher dimensions accessible.

As an application in our first paper, we worked with Dr. Charles Woody of the Brain Research Institute at UCLA. Using neuronal spike times (time neurons fire), we computed the prototypes of these spike patterns of cats under different behavioral states. Using the prototype, we were able to identify similar findings to previous research, which we believe shows our methods are ready to be used in higher dimensions and in further applications that may not have been subject to prior investigation.

Post June, 2009

The most applicable extension of the prior methods focus on using marginal kernels to find prototype points more efficiently in higher dimensions. While this does not entirely do away the increased computations in higher dimensions, it brings applications that require several dimensions within reach.

To make prototype methods accessible, I am presently working on an R package that implements the methods. This package should be released in Winter, 2010, and I will also be writing a paper on the package that I will submit to the Journal of Statistical Software.

Ongoing theoretical work focuses on quantifying errors for the prototype and also searching for an adequate distance measure that would work well for clustered processes.