Supervised Aggregative Feature Extraction for Big Data Time Series Regression

In many applications, and especially those where batch processes are involved, a target scalar output of interest is often dependent on one or more time series of data. With the exponential growth in data logging in modern industries such time series are increasingly available for statistical modeling in soft sensing applications. In order to exploit time series data for predictive modelling, it is necessary to summarise the information they contain as a set of features to use as model regressors. Typically this is done in an unsupervised fashion using simple techniques such as computing statistical moments, principal components or wavelet decompositions, often leading to significant information loss and hence suboptimal predictive models. In this paper, a functional learning paradigm is exploited in a supervised fashion to derive continuous, smooth estimates of time series data (yielding aggregated local information), while simultaneously estimating a continuous shape function yielding optimal predictions. The proposed Supervised Aggregative Feature Extraction (SAFE) methodology can be extended to support nonlinear predictive models by embedding the functional learning framework in a Reproducing Kernel Hilbert Spaces setting. SAFE has a number of attractive features including closed form solution and the ability to explicitly incorporate first and second order derivative information. Using simulation studies and a practical semiconductor manufacturing case study we highlight the strengths of the new methodology with respect to standard unsupervised feature extraction approaches.

Time-dependent Suppression of Oscillatory Power in Evolving Solar Magnetic Fields

Oscillation amplitudes are generally smaller within magnetically active regions like sunspots and plage when compared to their surroundings. Such magnetic features, when viewed in spatially resolved power maps, appear as regions of suppressed power due to reductions in the oscillation amplitudes. Employing high spatial- and temporal-resolution observations from the Dunn Solar Telescope (DST) in New Mexico, we study the power suppression in a region of evolving magnetic fields adjacent to a pore. By utilizing wavelet analysis, we study for the first time how the oscillatory properties in this region change as the magnetic field evolves with time. Image sequences taken in the blue continuum, G-band, Ca ii K, and Hα filters were used in this study. It is observed that the suppression found in the chromosphere occupies a relatively larger area, confirming previous findings. Also, the suppression is extended to structures directly connected to the magnetic region, and is found to get enhanced as the magnetic field strength increased with time. The dependence of the suppression on the magnetic field strength is greater at longer periods and higher formation heights. Furthermore, the dominant periodicity in the chromosphere was found to be anti-correlated with increases in the magnetic field strength.