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We introduce the study of potentially eventually exponentially positive (PEEP) sign patterns and establish several results using the connections between these sign patterns and the potentially eventually positive (PEP) sign patterns. It is shown that the problem of characterizing PEEP sign patterns is not equivalent to that of characterizing PEP sign patterns. A characterization of all 2 × 2 and 3 × 3 PEEP sign patterns is given.

We present the construction of a novel time-domain signature extraction methodology and the development of a supporting supervised pattern detection algorithm. We focus on the targeted identification of eclipsing binaries that demonstrate a feature known as the O'Connell effect. Our proposed methodology maps stellar variable observations to a new representation known as distribution fields (DFs). Given this novel representation, we develop a metric learning technique directly on the DF space that is capable of specif-1 arXiv:1911.03543v1 [astro-ph.IM] 8 Nov 2019 ically identifying our stars of interest. The metric is tuned on a set of labeled eclipsing binary data from the Kepler survey, targeting particular systems exhibiting the O'Connell effect. The result is a conservative selection of 124 potential targets of interest out of the Villanova Eclipsing Binary Catalog. Our framework demonstrates favorable performance on Kepler eclipsing binary data, taking a crucial step in preparing the way for large-scale data volumes from next-generation telescopes such as LSST and SKA.

Context. Comprehensive observations of variable stars can include time domain photometry in a multitude of filters, spectroscopy, estimates of color (e.g. U-B), etc. When the objective is to classify variable stars, traditional machine learning techniques distill these various representations (or views) into a single feature vector and attempt to discriminate among desired categories. Aims. In this work, we propose an alternative approach that inherently leverages multiple views of the same variable star. Methods. Our multi-view metric learning framework enables robust characterization of star categories by directly learning to discriminate in a multi-faceted feature space, thus, eliminating the need to combine feature representations prior to fitting the machine learning model. We also demonstrate how to extend standard multi-view learning, which employs multiple vectorized views, to the matrix-variate case which allows very novel variable star signature representations.Results. The performance of our proposed methods is evaluated on the UCR Starlight and LINEAR datasets. Both the vector and matrix-variate versions of our multi-view learning framework perform favorably -demonstrating the ability to discriminate variable star categories..

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