Spatial Mass Spectral Data Analysis Using Factor and Correlation Models

ToF-SIMS is a powerful and information rich tool with high resolution and sensitivity compared to conventional mass spectrometers. Recently, its application has been extended to metabolic profiling analysis. However, there are only a few algorithms currently available to handle such output data from metabolite samples. Therefore some novel and innovative algorithms are undoubtedly in need to provide new insights into the application of ToF-SIMS for metabolic profiling analysis. In this thesis, we develop novel multivariate analysis techniques that can be used in processing ToF-SIMS data extracted from metabolite samples. Firstly, several traditional multivariate analysis methodologies that have previously been suggested for ToF-SIMS data analysis are discussed, including Clustering, Principal Components Analysis (PCA), Maximum Autocorrelation Factor (MAF), and Multivariate Curve Resolution (MCR). In particular, PCA is selected as an example to show the performance of traditional multivariate analysis techniques in dealing with large ToF-SIMS data extracted from metabolite samples. In order to provide more realistic and meaningful interpretation of the results, Non-negative Matrix Factorisation (NMF) is presented. This algorithm is combined with the Bayesian Framework to improve the reliability of the results and the convergence of the algorithm. However, the iterative process involved leads to considerable computational complexity in the estimation procedure. Another novel algorithm is also proposed which is an optimised MCR algorithm within alternating non-negativity constrained least squares (ANLS) framework. It provides a more simple approximation procedure by implementing a dimensionality reduction based on a basis function decomposition approach. The novel and main feature of the proposed algorithm is that it incorporates a spatially continuous representation of ToF-SIMS data which decouples the computational complexity of the estimation procedure from the image resolution. The proposed algorithm can be used as an efficient tool in processing ToF-SIMS data obtained from metabolite samples.