Publications

High throughput instruments and analysis techniques are required in order to make good use of the genomic sequences that have recently become available for many species, including humans. These instruments and methods must work with tens of thousands of genes simultaneously, and must be able to identify the small subsets of those genes that are implicated in the observed phenotypes, or, for instance, in responses to therapies. Microarrays represent one such high throughput method, which continue to find increasingly broad application. This project has improved microarray technology in several important areas. First, we developed the hyperspectral scanner, which has discovered and diagnosed numerous flaws in techniques broadly employed by microarray researchers. Second, we used a series of statistically designed experiments to identify and correct errors in our microarray data to dramatically improve the accuracy, precision, and repeatability of the microarray gene expression data. Third, our research developed new informatics techniques to identify genes with significantly different expression levels. Finally, natural language processing techniques were applied to improve our ability to make use of online literature annotating the important genes. In combination, this research has improved the reliability and precision of laboratory methods and instruments, while also enabling substantially faster analysis and discovery.

We propose a novel algorithm based on Principal Component Analysis (PCA). First, we present an interesting approximation of PCA using Gram-Schmidt orthonormalization. Next, we combine our approximation with the kernel functions from Support Vector Machines (SVMs) to provide a nonlinear generalization of PCA. After benchmarking our algorithm in the linear case, we explore its use in both the linear and nonlinear cases. We include applications to face data analysis, handwritten digit recognition, and fluid flow.