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Free keywords:
singular value decomposition; autocorrelation; rank deficiency; data reduction; coarsening; approximate SVD; Gaussian Random Fields
Abstract:
The Singular Value Decomposition (SVD) is a mathematical procedure with multiple applications in the geosciences. For instance, it is used in dimensionality reduction and as a support operator for various analytical tasks applicable to spatio-temporal data. Performing SVD analyses on large datasets, however, can be computationally costly, time consuming, and sometimes practically infeasible. However, techniques exist to arrive at the same output, or at a close approximation, which requires far less effort. This article examines several such techniques in relation to the inherent scale of the structure within the data. When the values of a dataset vary slowly, e.g., in a spatial field of temperature over a country, there is autocorrelation and the field contains large scale structure. Datasets do not need a high resolution to describe such fields and their analysis can benefit from alternative SVD techniques based on rank deficiency, coarsening, or matrix factorization approaches. We use both simulated Gaussian Random Fields with various levels of autocorrelation and real-world geospatial datasets to illustrate our study while examining the accuracy of various SVD techniques. As the main result, this article provides researchers with a decision tree indicating which technique to use when and predicting the resulting level of accuracy based on the dataset’s structure scale.
