If you are a student of science in the twenty-first century, but are not using computers, then you are probably not doing science. A little harsh, perhaps, and tendentious, undoubtedly. But this bugle-call over-simplification gets to the very heart of the reason that we wrote this book. Over the years we noticed, with increasing alarm, very gifted students entering our graduate program in marine chemistry and geochemistry with very little understanding of the applied mathematics and numerical modeling they would be required to know over the course of their careers. So this book, like many before it, started as a course – in this case, a course in modeling, data analysis, and numerical techniques for geochemistry that we teach every other year in Woods Hole. As the course popularity and web pages grew, we realized our efforts should be set down in a more formal fashion.
We wrote this book first and foremost with the graduate and advanced undergraduate student in mind. In particular, we have aimed the material at the student still in the stages of formulating their Ph.D. or B.Sc. thesis. We feel that the student armed with the knowledge of what will be required of them when they synthesize their data and write their thesis will do a much better job at collecting the data in the first place. Nevertheless, we have found that many students beyond these first years find this book useful as a reference.
‘From a drop of water,’ said the writer, ‘a logician could infer the possibility of an Atlantic or a Niagara without having seen or heard of one or the other. So all life is a great chain, the nature of which is known whenever we are shown a single link of it.’
Suppose you're looking for patterns or relationships in your data. For example, you may be trying to quantify the presence and distribution of certain water masses in a hydrographic section, or you may be looking for evidence and patterns of nitrogen fixation or denitrification in some nutrient data. Perhaps you're trying to find the best way to account for interferences from other elements (“matrix effects”) in your ICPMS data. You've gathered your data, maybe obtained from a cleverly designed experiment, or extracted from a hydrographic atlas or a collection of cruise data. The information you require lies within the relationships or correlations between the different properties or variables in your data set. But where (and how) do you look? If instinct leads you to look at the data covariance matrix, then your instinct is right! In this chapter we'll show you some techniques for extracting and analyzing this structure. We will start with some underlying basics that you'll need to understand these techniques, and we'll mention a few relatively intuitive approaches for analyzing data structure.
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