Quantifying similarities between time series in a meaningful way remains a challenge in time series analysis, despite many advances in the field. Most real-world solutions still rely on a few popular measures, such as Euclidean Distance (EuD), Longest Common Subsequence (LCSS), and Dynamic Time Warping (DTW). The strengths and weaknesses of these measures have been studied extensively, and incremental improvements have been proposed. In this study, however, we present a different similarity measure that fuses the notion of Dubuc’s variation from fractal analysis with the Intersection- over-Union (IoU) measure which is widely used in object recognition (also known as the Jaccard Index). In this proof-of-concept paper, we introduce the Multiscale Dubuc Distance (MDD) measure and prove that it is a metric, possessing desirable properties such as the triangle inequality. We use 95 datasets from the UCR Time Series Classification Archive to compare MDD’s performance with EuD, LCSS, and DTW. Our experiments show that MDD’s overall success, without any case-specific customization, is comparable to DTW with optimized window sizes per dataset. We also highlight several datasets where MDD’s performance improves significantly when its single parameter is customized. This customization serves as a powerful tool for gauging MDD’s sensitivity to noise. Lastly, we show that MDD’s running time is linear in the length of the time series, which is crucial for real-world applications involving very large datasets.

Forecasting the occurrence of solar flares is a typical 21st century rare-event classification task. Over the past two decades, many studies have implemented various techniques and approaches for classification of strong and weak solar flares. The release of the recent flare forecasting benchmark dataset, named SWAN-SF, has opened the door for taking advantage of multivariate time series (MVTS) of pre-flare magnetic fields’ activity in order to potentially achieve higher performance and increase the robustness of the new forecasting models. In this study, we take a new approach and explore the effectiveness of imaging algorithms on the time series. We convert MVTS data into multi-channel image data using Gramian Angular Fields (GAF) and Markov Transition Fields (MTF) to explore the proven strength of deep neural networks in the Image Processing domain, on flares’ MVTS data. Inspired by GAF, we propose another imaging matrix that our experiments show that it significantly improves the performance of the CNN, by 120% in terms of TSS and 440% in terms of HSS2. Finally, we juxtapose two approaches to tackle the flare forecasting problem: one, to utilize a time-series specific Support Vector Classifier for classification of flares, and the other, to train a Convolutional Neural Network (CNN) on the derived images using GAF, MTF, and our modified GAF.

Image super-resolution is a branch of image processing that is concerned with enhancing the spatial resolution and quality of images by learning the intrinsic details and relations between the lower resolution input and the higher resolution output images. It is widely accepted as an ill-posed problem, which has seen tremendous advancements with deep learning-based models. In this work, we present two super resolution models, Sub-Pixel Convolutional Neural Network (CNN) and Enhanced Deep Residual Networks (ResNet), which can be used for improving the spatial resolution of solar magnetograms. While the ill-posed nature of problem is still a challenge, there are several application areas, including space weather prediction, which can greatly benefit from the improved spatial resolution of solar magnetograms. Along with classical raster inputs we try to improve the model objective by giving HMI Active Region Patches. We show that through our experimental evaluation our models perform better than baselines and CNN-based super resolution model provides viable results for magnetogram super resolution.

Image super-resolution is a branch of image processing that is concerned with enhancing the spatial resolution and quality of images by learning the intrinsic details and relations between the lower resolution input and the higher resolution output images. It is widely accepted as an ill-posed problem, which has seen tremendous advancements with deep learning based models. In this work, we present two magnetogram super resolution models, Sub-Pixel Convolutional Neural Network (CNN) and Enhanced Deep Residual Networks (ResNet), which can be used for improving the spatial resolution of solar magnetograms. While the ill-posed nature of problem is still a challenge, there are several application areas, including space weather prediction, which can greatly benefit from the improved spatial resolution of solar magnetograms. We show that through our experimental evaluation our models perform better than baselines and Sub-Pixel CNN super resolution model provides viable results for magnetogram super resolution.

In analyses of rare-events, regardless of the domain of application, class-imbalance issue is intrinsic. Although the challenges are known to data experts, their explicit impact on the analytic and the decisions made based on the findings are often overlooked. This is in particular prevalent in interdisciplinary research where the theoretical aspects are sometimes overshadowed by the challenges of the application. To show-case these undesirable impacts, we conduct a series of experiments on a recently created benchmark data, named Space Weather ANalytics for Solar Flares (SWAN-SF). This is a multivariate time series dataset of magnetic parameters of active regions. As a remedy for the imbalance issue, we study the impact of data manipulation (undersampling and oversampling) and model manipulation (using class weights). Furthermore, we bring to focus the auto-correlation of time series that is inherited from the use of sliding window for monitoring flares' history. Temporal coherence, as we call this phenomenon, invalidates the randomness assumption, thus impacting all sampling practices including different cross-validation techniques. We illustrate how failing to notice this concept could give an artificial boost in the forecast performance and result in misleading findings. Throughout this study we utilized Support Vector Machine as a classifier, and True Skill Statistics as a verification metric for comparison of experiments. We conclude our work by specifying the correct practice in each case, and we hope that this study could benefit researchers in other domains where time series of rare events are of interest.

We use a well-known deep neural network framework, called Mask R-CNN, for identification of solar filaments in full-disk H-$\alpha$ images from Big Bear Solar Observatory (BBSO). The image data, collected from BBSO's archive, are integrated with the spatiotemporal metadata of filaments retrieved from the Heliophysics Events Knowledgebase (HEK) system. This integrated data is then treated as the ground-truth in the training process of the model. The available spatial metadata are the output of a currently running filament-detection module developed and maintained by the Feature Finding Team; an international consortium selected by NASA. Despite the known challenges in the identification and characterization of filaments by the existing module, which in turn are inherited into any other module that intends to learn from such outputs, Mask R-CNN shows promising results. Trained and validated on two years worth of BBSO data, this model is then tested on the three following years. Our case-by-case and overall analyses show that Mask R-CNN can clearly compete with the existing module and in some cases even perform better. Several cases of false positives and false negatives, that are correctly segmented by this model are also shown. The overall advantages of using the proposed model are two-fold: First, deep neural networks' performance generally improves as more annotated data, or better annotations are provided. Second, such a model can be scaled up to detect other solar events, as well as a single multi-purpose module. The results presented in this study introduce a proof of concept in benefits of employing deep neural networks for detection of solar events, and in particular, filaments.

Machine learning-based space weather analytics has attracted much attention due to the potential damages that can be caused by the extreme space weather events. Using a recently released data benchmark, named SWAN-SF, designed for solar flare forecasting based on the pre-flare time series of solar magnetic field parameters, we conduct a case study on the impacts of statistical features derived from the multivariate time series. We investigate the relationship between the number of needed statistical features extracted from the multi-variate time series and the performance of flare forecast models. To that end, we employ random forest and mean decrease impurity to determine a feature selection methodology along with an evaluation procedure. The proposed evaluation method delivers a balance between the two frequently used metrics in this domain, namely True Skill Statistic and Heidke Skill Score. Our approach allows to introduce a generic feature selection and evaluation procedure that is independent from the minor and often obscured decisions that must be made for having a binary forecast model, while presenting interpretable and actionable tools that can help non-data experts make more informed and realistic decisions.

Space weather encapsulates the impact of variable solar activity on the vicinity of Earth and elsewhere in the solar system. A major agent of space weather, with significant effort already devoted to its prediction, is solar flares. Most existing analysis in this direction focus on the instantaneous (point-in-time) magnitude of various pre-flare parameters in flare host locations, solar active regions. Nonetheless, a recent trend places data-intensive studies, focusing on the pre-flare time series of these parameters, to the forefront. We take on this task in this study, focusing on the shape of pre-flare active region parameter time series by introducing a data-driven class profiling and clustering of these time series. We rely on data provided by the Space Weather ANalytics for Solar Flares (SWAN-SF) benchmark dataset. Our results indicate some potentially interesting temporal patterns that are unrelated to parameter magnitudes and may be used, both in tandem and independently from magnitudes, for future flare forecasting efforts. Our analysis also provides flexibility to define custom flare classes relying on pre-flare time series behavior and relate them to the existing, conventional NOAA / GOES flare classes.

Since its introduction to the computer science community, the Dynamic Time Warping (DTW) algorithm has demonstrated good performance with time series data. While this elastic measure is known for its effectiveness with time series sequence comparisons, the possibility of pathological warping paths weakens the algorithms potential considerably. Techniques centering on pruning off impossible mappings or lowering data dimensions such as windowing, slope weighting, step pattern, and approximation have been proposed over the years to reduce the possibility of pathological warping paths with Dynamic Time Warping. However, because the current DTW improvement techniques are mostly global methods, they are either limited in effect or limit the warping path excessively. We believe segmenting time series at significant feature points will alleviate some of the pathological warpings, and at the same time allowing us to obtain more intuitive warpings. Our heuristic approaches the problem from the human perspective of sequence comparison: by identifying global similarity before local similarities. We use easily identifiable peaks as the significant feature. The final distance is the DTW distance sum of all segments of time series. In this paper, we explore the impact of different peak identification parameters on Dynamic Time Warping and demonstrate how segmentation can help to avoid pathological warpings.

Directionality as a textural parameter is a great tool in many image-based tasks including the automated analysis of medical, geographical, or astronomical images. Tamura directionality is a popular parameters that measures the degree of texture directionality of images. In this study, we review the original idea and also address some ambiguities present in the original definition that play an important role in the effectiveness of this parameter. Then, we propose different ideas to attack each of the addressed ambiguities and find an optimal setting that maximizes the effectiveness of this parameter. Lastly, we evaluate the effect of our modifications on a large collection of solar images captured by the Solar Dynamic Observatory mission. We show that such modifications significantly improve the effectiveness of this parameter. Although, different settings might be obtained for images with different sort of texture, the methodology for finding an optimal setting remains the same regardless. The goal of our study is to make sure that parameters that are being frequently used in several areas, especially in the interdisciplinary research between solar physicists and computer scientists, are calculated accurately and effectively.