Multivariate Analysis for the Processing of Signals

Real-world experiments are becoming increasingly more complex, needing techniques capable of tracking this complexity. Signal based measurements are often used to capture this complexity, where a signal is a record of a sample’s response to a parameter (e.g. time, displacement, voltage, wavelength) that is varied over a range of values. In signals the responses at each value of the varied parameter are related to each other, depending on the composition or state sample being measured. Since signals contain multiple information points, they have rich information content but are generally complex to comprehend. Multivariate Analysis (MA) has profoundly transformed their analysis by allowing gross simplification of the tangled web of variation. In addition MA has also provided the advantage of being much more robust to the influence of noise than univariate methods of analysis. In recent years, there has been a growing awareness that the nature of the multivariate methods allows exploitation of its benefits for purposes other than data analysis, such as pre-processing of signals with the aim of eliminating irrelevant variations prior to analysis of the signal of interest. It has been shown that exploiting multivariate data reduction in an appropriate way can allow high fidelity denoising (removal of irreproducible non-signals), consistent and reproducible noise-insensitive correction of baseline distortions (removal of reproducible non-signals), accurate elimination of interfering signals (removal of reproducible but unwanted signals) and the standardisation of signal amplitude fluctuations. At present, the field is relatively small but the possibilities for much wider application are considerable. Where signal properties are suitable for MA (such as the signal being stationary along the x-axis), these signal based corrections have the potential to be highly reproducible, and highly adaptable and are applicable in situations where the data is noisy or where the variations in the signals can be complex. As science seeks to probe datasets in less and less tightly controlled situations the ability to provide high-fidelity corrections in a very flexible manner is becoming more critical and multivariate based signal processing has the potential to provide many solutions. L’analyse multivariée, dont l’analyse en composantes principales (ACP), a transformé, dans des contextes concrets, l’étude de mesures complexes, formées de signaux chargés d’informations. Si la ré