Meta learning of bounds on the Bayes classifier error

Meta learning uses information from base learners (e.g. classifiers or estimators) as well as information about the learning problem to improve upon the performance of a single base learner. For example, the Bayes error rate of a given feature space, if known, can be used to aid in choosing a classifier, as well as in feature selection and model selection for the base classifiers and the meta classifier. Recent work in the field of f-divergence functional estimation has led to the development of simple and rapidly converging estimators that can be used to estimate various bounds on the Bayes error. We estimate multiple bounds on the Bayes error using an estimator that applies meta learning to slowly converging plug-in estimators to obtain the parametric convergence rate. We compare the estimated bounds empirically on simulated data and then estimate the tighter bounds on features extracted from an image patch analysis of sunspot continuum and magnetogram images.Comment: 6 pages, 3 figures, to appear in proceedings of 2015 IEEE Signal Processing and SP Education Worksho

Image patch analysis and clustering of sunspots: a dimensionality reduction approach

Sunspots, as seen in white light or continuum images, are associated with regions of high magnetic activity on the Sun, visible on magnetogram images. Their complexity is correlated with explosive solar activity and so classifying these active regions is useful for predicting future solar activity. Current classification of sunspot groups is visually based and suffers from bias. Supervised learning methods can reduce human bias but fail to optimally capitalize on the information present in sunspot images. This paper uses two image modalities (continuum and magnetogram) to characterize the spatial and modal interactions of sunspot and magnetic active region images and presents a new approach to cluster the images. Specifically, in the framework of image patch analysis, we estimate the number of intrinsic parameters required to describe the spatial and modal dependencies, the correlation between the two modalities and the corresponding spatial patterns, and examine the phenomena at different scales within the images. To do this, we use linear and nonlinear intrinsic dimension estimators, canonical correlation analysis, and multiresolution analysis of intrinsic dimension.Comment: 5 pages, 7 figures, accepted to ICIP 201

Image patch analysis of sunspots and active regions. I. Intrinsic dimension and correlation analysis

The flare-productivity of an active region is observed to be related to its spatial complexity. Mount Wilson or McIntosh sunspot classifications measure such complexity but in a categorical way, and may therefore not use all the information present in the observations. Moreover, such categorical schemes hinder a systematic study of an active region's evolution for example. We propose fine-scale quantitative descriptors for an active region's complexity and relate them to the Mount Wilson classification. We analyze the local correlation structure within continuum and magnetogram data, as well as the cross-correlation between continuum and magnetogram data. We compute the intrinsic dimension, partial correlation, and canonical correlation analysis (CCA) of image patches of continuum and magnetogram active region images taken from the SOHO-MDI instrument. We use masks of sunspots derived from continuum as well as larger masks of magnetic active regions derived from the magnetogram to analyze separately the core part of an active region from its surrounding part. We find the relationship between complexity of an active region as measured by Mount Wilson and the intrinsic dimension of its image patches. Partial correlation patterns exhibit approximately a third-order Markov structure. CCA reveals different patterns of correlation between continuum and magnetogram within the sunspots and in the region surrounding the sunspots. These results also pave the way for patch-based dictionary learning with a view towards automatic clustering of active regions.Comment: Accepted for publication in the Journal of Space Weather and Space Climate (SWSC). 23 pages, 11 figure

Image patch analysis of sunspots and active regions. II. Clustering via matrix factorization

Separating active regions that are quiet from potentially eruptive ones is a key issue in Space Weather applications. Traditional classification schemes such as Mount Wilson and McIntosh have been effective in relating an active region large scale magnetic configuration to its ability to produce eruptive events. However, their qualitative nature prevents systematic studies of an active region's evolution for example. We introduce a new clustering of active regions that is based on the local geometry observed in Line of Sight magnetogram and continuum images. We use a reduced-dimension representation of an active region that is obtained by factoring the corresponding data matrix comprised of local image patches. Two factorizations can be compared via the definition of appropriate metrics on the resulting factors. The distances obtained from these metrics are then used to cluster the active regions. We find that these metrics result in natural clusterings of active regions. The clusterings are related to large scale descriptors of an active region such as its size, its local magnetic field distribution, and its complexity as measured by the Mount Wilson classification scheme. We also find that including data focused on the neutral line of an active region can result in an increased correspondence between our clustering results and other active region descriptors such as the Mount Wilson classifications and the $R$ value. We provide some recommendations for which metrics, matrix factorization techniques, and regions of interest to use to study active regions.Comment: Accepted for publication in the Journal of Space Weather and Space Climate (SWSC). 33 pages, 12 figure

Coronal Hole Detection and Open Magnetic Flux

Many scientists use coronal hole (CH) detections to infer open magnetic flux. Detection techniques differ in the areas that they assign as open, and may obtain different values for the open magnetic flux. We characterize the uncertainties of these methods, by applying six different detection methods to deduce the area and open flux of a near-disk center CH observed on 2010 September 19, and applying a single method to five different EUV filtergrams for this CH. Open flux was calculated using five different magnetic maps. The standard deviation (interpreted as the uncertainty) in the open flux estimate for this CH ≈ 26%. However, including the variability of different magnetic data sources, this uncertainty almost doubles to 45%. We use two of the methods to characterize the area and open flux for all CHs in this time period. We find that the open flux is greatly underestimated compared to values inferred from in situ measurements (by 2.2–4 times). We also test our detection techniques on simulated emission images from a thermodynamic MHD model of the solar corona. We find that the methods overestimate the area and open flux in the simulated CH, but the average error in the flux is only about 7%. The full-Sun detections on the simulated corona underestimate the model open flux, but by factors well below what is needed to account for the missing flux in the observations. Under-detection of open flux in coronal holes likely contributes to the recognized deficit in solar open flux, but is unlikely to resolve it

Coronal Hole Detection and Open Magnetic Flux

Many scientists use coronal hole (CH) detections to infer open magnetic flux. Detection techniques differ in the areas that they assign as open, and may obtain different values for the open magnetic flux. We characterize the uncertainties of these methods, by applying six different detection methods to deduce the area and open flux of a near-disk center CH observed on 2010 September 19, and applying a single method to five different EUV filtergrams for this CH. Open flux was calculated using five different magnetic maps. The standard deviation (interpreted as the uncertainty) in the open flux estimate for this CH approximate to 26%. However, including the variability of different magnetic data sources, this uncertainty almost doubles to 45%. We use two of the methods to characterize the area and open flux for all CHs in this time period. We find that the open flux is greatly underestimated compared to values inferred from in situ measurements (by 2.2-4 times). We also test our detection techniques on simulated emission images from a thermodynamic MHD model of the solar corona. We find that the methods overestimate the area and open flux in the simulated CH, but the average error in the flux is only about 7%. The full-Sun detections on the simulated corona underestimate the model open flux, but by factors well below what is needed to account for the missing flux in the observations. Under-detection of open flux in coronal holes likely contributes to the recognized deficit in solar open flux, but is unlikely to resolve it.Peer reviewe

A Comparison of Flare Forecasting Methods. III. Systematic Behaviors of Operational Solar Flare Forecasting Systems

A workshop was recently held at Nagoya University (31 October – 02 November 2017), sponsored by the Center for International Collaborative Research, at the Institute for Space-Earth Environmental Research, Nagoya University, Japan, to quantitatively compare the performance of today’s operational solar flare forecasting facilities. Building upon Paper I of this series (Barnes et al. 2016), in Paper II (Leka et al. 2019) we described the participating methods for this latest comparison effort, the evaluation methodology, and presented quantitative comparisons. In this paper we focus on the behavior and performance of the methods when evaluated in the context of broad implementation differences. Acknowledging the short testing interval available and the small number of methods available, we do find that forecast performance: 1) appears to improve by including persistence or prior flare activity, region evolution, and a human “forecaster in the loop”; 2) is hurt by restricting data to disk-center observations; 3) may benefit from long-term statistics, but mostly when then combined with modern data sources and statistical approaches. These trends are arguably weak and must be viewed with numerous caveats, as discussed both here and in Paper II. Following this present work, we present in Paper IV a novel analysis method to evaluate temporal patterns of forecasting errors of both types (i.e., misses and false alarms; Park et al. 2019). Hence, most importantly, with this series of papers we demonstrate the techniques for facilitating comparisons in the interest of establishing performance-positive methodologies

Robust Distributed Estimation in Sensor Networks using the Embedded Polygons Algorithm

Conference PaperWe propose a new iterative distributed algorithm for linear minimum mean-squared-error (LMMSE) estimation in sensor networks whose measurements follow a Gaussian hidden Markov graphical model with cycles. The <i>embedded polygons algorithm</i> decomposes a loopy graphical model into a number of linked embedded polygons and then applies a parallel block Gauss-Seidel iteration comprising local LMMSE estimation on each polygon (involving inversion of a small matrix) followed by an information exchange between neighboring nodes and polygons. The algorithm is robust to temporary communication faults such as link failures and sleeping nodes and enjoys guaranteed convergence under mild conditions. A simulation study indicates that energy consumption for iterative estimation increases substantially as more links fail or nodes sleep. Thus, somewhat surprisingly, energy conservation strategies such as low-powered transmission and aggressive sleep schedules could actually be counterproductive