Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
Howard Weatherspoon - Albany State University
Co-Author(s): William Harris, Reed College, OR; Kate Rodriguez, University of California-Irvine, CA; V. Ara Apkarian, PhD, University of California-Irvine, CA
The application of Surface Enhanced Raman Spectroscopy (SERS) in the detection and identification of single molecules reaches the ultimate limit in analytic sensitivity. The SERS spectrum of a molecule is highly sensitive to various environmental factors such as molecular orientation and local fields determined by the atomistic morphology of the plasmonic antenna junction. These factors can be further manipulated with the use of lasers, thereby inducing a greater variety of signals, which in turn leads to more complex spectra. Principle Component Analysis (PCA) is a method, which transforms a number of correlated variables into a smaller number of linearly uncorrelated variables, called principal components. The use of PCA in signal processing allows analysis of large data sets through the decomposition of spectral sets into their unique components.
Our principle aim is to demonstrate the potential use of PCA in resolving complex SER spectra of single molecules and devise a protocol for their automated processing and assignment. We hypothesized that the bimodal fluctuation experienced by the bipyridyl ethylene (BPE) molecule can be visualized through the application of PCA in SERS spectra characterization. To test our hypothesis, a time series of BPE spectra (excitation: 633nm) was recorded at the nanojunction of gold nanosphere dimers. The time series of spectra was decomposed into its principle components and were placed through a lowpass filter to reduce hash, then the covariance matrix, eigenvectors, eigenvalues were calculated to produce a 3-D scatter plot, an average spectra plot, and a connectivity plot in Mathematica. Preliminary results demonstrated that BPE experienced a bimodal fluctuation during the SERS application. Future research involves assignment of the observed fluctuations to specific structures through automated machine learning algorithms for pattern recognition.
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Harris, William. ‘Fluctuation in SERS: Research Summary.’ n.d.
Laserna, Dr. Javier. ‘An Introduction to Raman Spetroscopy.’ 2001. University of Malaga, Spain.
Shlens, Jon. A Tutorial on Principal Component Analysis. 2003.
Smith, Lindsay I. A Tutorial on Prinipal Component Analysis. 2002.
Van Duyne, Richard P. ‘Surfaced-Enhanced Raman Spectroscopy.’ Annual Review of Analytical Chemistry (2008).
Funder Acknowledgement(s): This work was sponsored by the NSF Award #1414466 awarded to V. Ara Apkarian PhD, Director of the Chemistry at the Space Time-Limit (CaSTL) Center, University of California-Irvine, Irvine, CA.
Faculty Advisor: V. Ara Apkarian, email@example.com
Role: I did literary reviews on Principal Component Analysis (PCA) and how they're structured. Then built a PCA algorithm in Mathematica that were based on my readings in order to calculate the principal components and create visual representations of the data set. From there, I worked with my principle investigator to characterize our results in terms of how the molecule was effected during the SERS application. Next, was learning the machine learning algorithms that were built-in to Mathematica and determine which would be necessary for our project. I had to troubleshoot the classifying algorithm to fully understand how to properly structure it and implement it for the use of classifying theoretical data for our molecule and testing it against the experimental data.