Comparison of Shrunken Regression Methods for Major Elemental Analysis of Rocks Using Laser-Induced Breakdown Spectroscopy (libs)




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Comparison of Shrunken Regression Methods for Major Elemental Analysis of Rocks Using Laser-Induced Breakdown Spectroscopy (LIBS)







Marie Veronica Ozanne



Thesis Advisor:

Professor M. Darby Dyar


Submitted to the Department of Chemistry at Mount Holyoke College in partial fulfillment of the requirements for a Bachelor of Arts with departmental honor


May 2012





For my parents, who believed in me even when I did not believe in myself







ACKNOWLEDGEMENTS

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.


fl.research.team.jpg



Table of Contents


Acknowledgements iii

List of Figures and Tables vi

Introduction 1

Research Goals 6

Background 8

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

Ridge 19

Lasso 21

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

Cross-validation 36

Feature Selection 39

Methods 41

Samples and Experimental Methods 41

Statistical Analysis 42

Model Selection Heuristics 45

Results 48

Overview 48

Model Selection 48

Partial Least Squares 48

Lasso 49

Elastic Net 49

Sparse Partial Least Squares 50

Discussion 53

Overview 53

SiO2 54

Al2O3 55

MnO 56

MgO 57

CaO 58

Na2O 59

K2O 60

TiO2 61

P2O5 62

Fe2O3 63

Conclusions 65

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

References 70

Appendix I


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