Finding Faults in PV Systems: Supervised and Unsupervised Dictionary Learning With SSTDR
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Engineering↗
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Convolutional dictionary learning for blind deconvolution of optical coherence tomography images
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Information Science↗
Heterogeneous Mixtures of Dictionary Functions to Approximate Subspace Invariance in Koopman Operators: Why Deep Koopman Operators Work
Abstract Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of functions drawn from a dictionary . In a widely used algorithm, extended dynamic mode decomposition (EDMD), the dictionary functions are drawn from a fixed class of functions. Deep learning combined with EDMD has been used to learn novel dictionary functions in an algorithm called deep dynamic mode decomposition (deepDMD). The learned representation both (1) accurately models and (2) scales well with the dimension of the original nonlinear system. In this paper, we analyze the learned dictionaries from deepDMD and explore the theoretical basis for their strong performance. We explore State-Inclusive Logistic Lifting (SILL) dictionary functions to approximate Koopman observables. Error analysis of these dictionary functions show they satisfy a property of subspace approximation, which we define as uniform finite approximate closure. Typically, a Koopman dictionary’s nonlinear functions are homogeneous. In this paper, we discover that structured mixing of heterogeneous dictionary functions drawn from different classes of nonlinear functions achieve the same accuracy and dimensional scaling as the deep-learning-based deepDMD algorithm Yeung et al. ( In: 2019 American Control Conference (ACC), 2019). We specifically show this by building a heterogeneous dictionary comprised of SILL functions and conjunctive radial basis functions (RBFs). This mixed dictionary achieves similar accuracy and dimensional scaling to deepDMD with an order of magnitude reduction in parameters, while maintaining geometric interpretability. These results strengthen the viability of dictionary-based Koopman models to solving high-dimensional nonlinear learning problems.
Johnson, Charles A.↗
A Pattern Dictionary Method for Anomaly Detection
In this paper, we propose a compression-based anomaly detection method for time series and sequence data using a pattern dictionary. The proposed method is capable of learning complex patterns in a training data sequence, using these learned patterns to detect potentially anomalous patterns in a test data sequence. The proposed pattern dictionary method uses a measure of complexity of the test sequence as an anomaly score that can be used to perform stand-alone anomaly detection. We also show that when combined with a universal source coder, the proposed pattern dictionary yields a powerful atypicality detector that is equally applicable to anomaly detection. The pattern dictionary-based atypicality detector uses an anomaly score defined as the difference between the complexity of the test sequence data encoded by the trained pattern dictionary (typical) encoder and the universal (atypical) encoder, respectively. We consider two complexity measures: the number of parsed phrases in the sequence, and the length of the encoded sequence (codelength). Specializing to a particular type of universal encoder, the Tree-Structured Lempel–Ziv (LZ78), we obtain a novel non-asymptotic upper bound, in terms of the Lambert W function, on the number of distinct phrases resulting from the LZ78 parser. This non-asymptotic bound determines the range of anomaly score. As a concrete application, we illustrate the pattern dictionary framework for constructing a baseline of health against which anomalous deviations can be detected.
97 MATHEMATICS AND COMPUTING↗
A dictionary learning algorithm for compression and reconstruction of streaming data in preset order
There has been an emerging interest in developing and applying dictionary learning (DL) to process massive datasets in the last decade. Many of these efforts, however, focus on employing DL to compress and extract a set of important features from data, while considering restoring the original data from this set a secondary goal. On the other hand, although several methods are able to process streaming data by updating the dictionary incrementally as new snapshots pass by, most of those algorithms are designed for the setting where the snapshots are randomly drawn from a probability distribution. In this paper, we present a new DL approach to compress and denoise massive dataset in real time, in which the data are streamed through in a preset order (instances are videos and temporal experimental data), so at any time, we can only observe a biased sample set of the whole data. Here, our approach incrementally builds up the dictionary in a relatively simple manner: if the new snapshot is adequately explained by the current dictionary, we perform a sparse coding to find its sparse representation; otherwise, we add the new snapshot to the dictionary, with a Gram-Schmidt process to maintain the orthogonality. To compress and denoise noisy datasets, we apply the denoising to the snapshot directly before sparse coding, which deviates from traditional dictionary learning approach that achieves denoising via sparse coding. Compared to full-batch matrix decomposition methods, where the whole data is kept in memory, and other mini-batch approaches, where unbiased sampling is often assumed, our approach has minimal requirement in data sampling and storage: i) each snapshot is only seen once then discarded, and ii) the snapshots are drawn in a preset order, so can be highly biased. Through experiments on climate simulations and scanning transmission electron microscopy (STEM) data, we demonstrate that the proposed approach performs competitively to those methods in data reconstruction and denoising.
97 MATHEMATICS AND COMPUTING↗
Dictionary Learning with Accumulator Neurons
The Locally Competitive Algorithm (LCA) uses local competition between non-spiking leaky integrator neurons to infer sparse representations, allowing for potentially real-time execution on massively parallel neuromorphic architectures such as Intel's Loihi processor. Here, we focus on the problem of inferring sparse representations from streaming video using dictionaries of spatiotemporal features optimized in an unsupervised manner for sparse reconstruction. Non-spiking LCA has previously been used to achieve unsupervised learning of spatiotemporal dictionaries composed of convolutional kernels from raw, unlabeled video. We demonstrate how unsupervised dictionary learning with spiking LCA (\hbox{S-LCA}) can be efficiently implemented using accumulator neurons, which combine a conventional leaky-integrate-and-fire (\hbox{LIF}) spike generator with an additional state variable that is used to minimize the difference between the integrated input and the spiking output. We demonstrate dictionary learning across a wide range of dynamical regimes, from graded to intermittent spiking, for inferring sparse representations of both static images drawn from the CIFAR database as well as video frames captured from a DVS camera. On a classification task that requires identification of the suite from a deck of cards being rapidly flipped through as viewed by a DVS camera, we find essentially no degradation in performance as the LCA model used to infer sparse spatiotemporal representations migrates from graded to spiking. We conclude that accumulator neurons are likely to provide a powerful enabling component of future neuromorphic hardware for implementing online unsupervised learning of spatiotemporal dictionaries optimized for sparse reconstruction of streaming video from event based DVS cameras.
artificial intelligence↗
Path-Based Dictionary Augmentation: A Framework for Improving $k$ -Sparse Image Processing
In this study, we have previously shown that augmenting orthogonal matching pursuit (OMP) with an additional step in the identification stage of each pursuit iteration yields improved $k$ -sparse reconstruction and denoising performance relative to baseline OMP. At each iteration a “path” or geodesic, is generated between the two dictionary atoms that are most correlated with the residual and from this path a new atom that has a greater correlation to the residual than either of the two bracketing atoms is selected. Here, we provide new computational results illustrating improvements in sparse coding and denoising on canonical datasets using both learned and structured dictionaries. The two methods of constructing a path are investigated for each dictionary type: the Euclidean geodesic formed by a linear combination of the two atoms and the 2-Wasserstein geodesic corresponding to the optimal transport map between the atoms. We prove here the existence of a higher-correlation atom in the Euclidean case under assumptions on the two bracketing atoms and introduce algorithmic modifications to improve the likelihood that the bracketing atoms meet those conditions. Although, we demonstrate our augmentation on OMP alone, in general it may be applied to any reconstruction algorithm that relies on the selection and sorting of high-similarity atoms during an analysis or identification phase.
97 MATHEMATICS AND COMPUTING↗
Cyber Threat Dictionary Using MITRE ATT&CK Matrix and NIST Cybersecurity Framework Mapping
Cyber-attack and defense frameworks offer numerous ways to protect systems and networks from threats. However, only a few of these numerous attack and defense frameworks provide countermeasures by linking multiple frameworks. Due to the lack of attack-defense mapped frameworks, a number of cyber security practitioners are often puzzled how to cope with cyber-attacks when it occurs. The objective of this paper is to present a tool called the “Cyber Threat Dictionary” to solve the problem . Cyber Threat Dictionary offers approaches and practical solutions to the threats by mapping MITRE ATT&CK Matrix to the NIST Cybersecurity Framework. By providing immediate solutions to cyber security practitioners, Cyber Threat Dictionary enables effective responses against cyber-attacks.
MITRE ATT&CK MATRIX, NIST Cybersecurity Framework,↗
Enhancing Regional Seismic Velocity Models With Higher‐Resolution Local Results Using Sparse Dictionary Learning
Abstract We use sparse dictionary learning to develop transformations between seismic velocity models of different resolution and spatial extent. Starting with data in the common region of both models, the method can enhance a regional lower‐resolution model to match the style and resolution of local higher‐resolution results while preserving its regional coverage. The method is demonstrated by applying it to two‐dimensional V S and three‐dimensional V P and V S regional and local velocity models in southern California. The enhanced reconstructed regional results exhibit clear visual improvements, especially in the reconstructed V P / V S ratios, and better correlations with geological features. Moreover, the reconstructed regional V P , V S models outperform the original ones in comparison of simulated earthquake waveforms to observations. The improved fitting to observed waveforms extends beyond the domain of the overlapping region. The developed dictionary learning approach provides physically interpretable results and offers a powerful tool for additional applications of data enhancement in earth sciences.
Geochemistry & Geophysics↗
Holographic pseudoentanglement and the complexity of the AdS/CFT dictionary
The `quantum gravity in the lab' paradigm suggests that quantum computers might shed light on quantum gravity by simulating the CFT side of the AdS/CFT correspondence and mapping the results to the AdS side. This relies on the assumption that the duality map (the `dictionary') is efficient to compute. In this work, we show that the complexity of the AdS/CFT dictionary is surprisingly subtle: there might be cases in which one can efficiently apply operators to the CFT state (a task we call 'operator reconstruction') without being able to extract basic properties of the dual bulk state such as its geometry (which we call 'geometry reconstruction'). Geometry reconstruction corresponds to the setting where we want to extract properties of a completely unknown bulk dual from a simulated CFT boundary state. We demonstrate that geometry reconstruction may be generically hard due to the connection between geometry and entanglement in holography. In particular we construct ensembles of states whose entanglement approximately obey the Ryu-Takayanagi formula for arbitrary geometries, but which are nevertheless computationally indistinguishable. This suggests that even for states with the special entanglement structure of holographic CFT states, geometry reconstruction might be hard. This result should be compared with existing evidence that operator reconstruction is generically easy in AdS/CFT. A useful analogy for the difference between these two tasks is quantum fully homomorphic encryption (FHE): this encrypts quantum states in such a way that no efficient adversary can learn properties of the state, but operators can be applied efficiently to the encrypted state. We show that quantum FHE can separate the complexity of geometry reconstruction vs operator reconstruction, which raises the question whether FHE could be a useful lens through which to view AdS/CFT.
FOS: Physical sciences↗
Automated construction of clear-sky dictionary from all-sky imager data
All-sky imagers (ASIs) have significant promise as scalable sensors for short-term solar irradiance forecasting. Many of the current computational techniques that use ASIs for this purpose rely on collections of clear-sky images indexed by time of day, solar angle, or both, called clear-sky dictionaries (CSDs). These CSDs act as baselines against which images can be compared to locate and classify clouds within the image frame. CSDs are often compiled by hand, where individuals visually inspect collections of images one at a time to find clear-sky images. This process is not scalable, and it is prone to error. This paper proposes an automated, nonparametric alternative that uses the principles of digital image processing to find clear-sky images within a set of images taken over several days. We use ground-truth measurements of the clearness index to assess the performance of our method, and we show that the images it selects accurately correspond to clear-sky images. We also compare our proposal, which is nonparametric, with a state-of-the-art parametric method. The numerical results indicate that the performance of the method proposed here is superior.
14 SOLAR ENERGY↗
Parsimonious Potential Energy Surface Expansions Using Dictionary Learning with Multipass Greedy Selection
Potential energy surfaces fit with basis set expansions have been shown to provide accurate representations of electronic energies and have enabled a variety of high-accuracy dynamics, kinetics, and spectroscopy applications. The number of terms in these expansions scales poorly with system size, a drawback that challenges their use for systems with more than similar to 10 atoms. A solution is presented here using dictionary learning. Subsets of the full set of conventional basis functions are optimized using a newly developed multipass greedy regression method inspired by forward and backward selection methods from the statistics, signal processing, and machine learning literatures. Here, the optimized representations have accuracies comparable to the full set but are 1 or more orders of magnitude smaller, and notably, the number of terms in the optimized multipass greedy expansions scales approximately linearly with the number of atoms.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Lidar Buoy Data Dictionary: For the 2020 – 2021 California Deployments
Pacific Northwest National Laboratory (PNNL) manages two AXYS WindSentinel™ buoys (Buoys #120 and #130) on behalf of the U.S. Department of Energy (DOE) that collect a comprehensive set of meteorological and oceanographic (metocean) data to support resource characterization for wind energy offshore. The buoys have been deployed off the California coast in partnership with the Bureau of Ocean Energy Management (BOEM) from September 2020 through October 2021. One buoy was deployed within the Morro Bay Call Area offshore central California; the other buoy was deployed within the Humboldt Call Area off the coast of northern California. The measurements from the buoys are used to characterize the metocean conditions near potential locations for offshore wind lease areas and are uploaded to DOE’s Data Archive and Portal (DAP). Plots are updated on the DAP webpage to visualize the recent metocean measurements. This document serves as a data dictionary – or reference guide – for understanding and interpreting the data available from the buoys. This document includes: (1) specifications for the buoy instrumentation (Section 2.0) (2) description of each plot and definition of measured parameters (Section 3.0) (3) description of data files and naming convention (Appendix A) (4) reference guide of measurements and variables (Appendix B).
17 WIND ENERGY↗
PSF Estimation in Crowded Astronomical Imagery as a Convolutional Dictionary Learning Problem
In this paper, we present a new algorithm for estimating the Point Spread Function (PSF) in wide-field astronomical images with extreme source crowding. Robust and accurate PSF estimation in crowded astronomical images dramatically improves the fidelity of astrometric and photometric measurements extracted from wide-field sky monitoring imagery. Our radically new approach utilizes convolutional sparse representations to model the continuous functions involved in the image formation. This approach avoids the need to detect and precisely localize individual point sources that is shared by existing methods. In experiments involving simulated astronomical imagery, it significantly outperforms the recent alternative method with which it is compared.
79 ASTRONOMY AND ASTROPHYSICS↗