Abstract
The paper describes the motivation of SOMs (Self Organising Maps) and how they are generally more accessible due to the wider available modern, more powerful, cost-effective computers. Their advantages compared to Principal Components Analysis and Partial Least Squares are discussed. These allow application to non-linear data, are not so dependent on least squares solutions, normality of errors and less influenced by outliers. In addition there are a wide variety of intuitive methods for visualisation that allow full use of the map space. Modern problems in analytical chemistry include applications to cultural heritage studies, environmental, metabolomic and biological problems result in complex datasets. Methods for visualising maps are described including best matching units, hit histograms, unified distance matrices and component planes. Supervised SOMs for classification including multifactor data and variable selection are discussed as is their use in Quality Control. The paper is illustrated using four case studies, namely the Near Infrared of food, the thermal analysis of polymers, metabolomic analysis of saliva using NMR, and on-line HPLC for pharmaceutical process monitoring.
Highlights
The analysis of multivariate data from laboratory instruments using computational methods has been a subject of academic pursuit since the 1970s, often loosely called chemometrics [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]
The early pioneers of the 1970s were primarily analytical chemists such as Bruce Kowalski and Luc Massart, Svante Wold was on the interface of analytical and organic chemistry. Methods such as PCA (Principal Components Analysis) [22,23,24,25,26,27] and PLS (Partial Least Squares) [28,29,30,31,32,33,34] were developed and widespread applications reported in the literature
Determining the number of significant variables we describe how to determine which variables are most significant, or are the most likely to be markers, for each class or grouping
Summary
These pioneering methods were first primarily developed as applied to traditional analytical chemistry. The desire of many laboratory based chemists to analyse data themselves still poses a problem: in areas such as biology and medicine it is usual for there to be separate data analysis groups, so novel computational approaches can be adopted much faster and do not need to wait for commercial package developers. As the number of iterations increase, the region of cells that is adjusted around the BMU is reduced, and the amount of adjustment (often called the learning rate) reduces This means that the maps start to stabilise. Most SOMs are developed using a random starting point, there are modifications that allow an initial map that reduces the number of iterations by basing it on the pattern of the samples, e.g, as obtained via PCA. Often the cells are represented as hexagons, as we will do in this paper, but can be represented by squares
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