Regularisation for PCA- and SVD-type matrix factorisations

Singular Value Decomposition (SVD) and its close relative, Principal Component Analysis (PCA), are well-known linear matrix decomposition techniques that are widely used in applications such as dimension reduction and clustering. However, an important limitation of SVD/PCA is its sensitivity to noise in the input data. In this paper, we take another look at the problem of regularisation and show that different formulations of the minimisation problem lead to qualitatively different solutions.

SVD-based Visualisation and Approximation for Time Series Data in Smart Energy Systems

Many time series in smart energy systems exhibit two different timescales. On the one hand there are patterns linked to daily human activities. On the other hand, there are relatively slow trends linked to seasonal variations. In this paper we interpret these time series as matrices, to be visualized as images. This approach has two advantages: First of all, interpreting such time series as images enables one to visually integrate across the image and makes it therefore easier to spot subtle or faint features. Second, the matrix interpretation also grants elucidation of the underlying structure using well-established matrix decomposition methods. We will illustrate both these aspects for data obtained from the German day-ahead market.