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For my parents, who believed in me even when I did not believe in myself
This thesis would not have been possible without the help and support of my research advisor, Professor Darby Dyar. Her willingness to engage in interdisciplinary research and push me outside my comfort zone has been the greatest gift of my undergraduate career.
I would like to thank Marco Carmosino for teaching me much of what I know about programming and for being a great sounding board.
I am grateful to Elly Breves, who introduced me to this dataset and who has patiently answered my numerous LIBS questions. She is the best lab manager for whom anyone could hope.
Special thanks go out to Dr. Sam Clegg and Dr. Roger Weins of Los Alamos National Laboratory who collected this data, and to NASA, who funded this research through the Mars Fundamental Research Program.
Table of Contents
List of Figures and Tables vi
Research Goals 6
Laser-Induced Breakdown Spectroscopy 8
Emission Lines 11
LIBS Challenges for Geological Samples 12
Quantitative Analysis of Emission Spectra 14
What Makes a Good Model 14
Univariate Analysis 14
Multivariate Analysis 15
Partial Least Squares 16
Generalizing the Ridge and Lasso 23
Fused Lasso 24
Elastic Net 25
Fused Lasso versus Elastic Net 27
Sparse Partial Least Squares 28
Model Selection 32
Feature Selection 39
Samples and Experimental Methods 41
Statistical Analysis 42
Model Selection Heuristics 45
Model Selection 48
Partial Least Squares 48
Elastic Net 49
Sparse Partial Least Squares 50
Future/Related Work 67
Data Preprocessing: Averaged versus Unaveraged Spectra 67
Additional Techniques 67
Benchmark Experiments 68
Automatic Line Assignment to Known Peaks 68
LIBS on Mars: Going the Distance 69
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