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At least 19 records

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.↗

Flight Software Dictionary Development for the Mars2020 Rover

The Mars2020 project, developed and operated by the Jet Propulsion Laboratory (JPL), successfully landed the Perseverance rover and its flying companion Ingenuity on the surface of Mars on February 18th 2021. Perseverance combines heritage and cutting-edge flight software and hardware to accomplish crucial mission requirements related to Martian surface sampling. The design, development, and operation of NASA’s large strategic science missions require the ability to communicate spacecraft capabilities to hundreds of engineers across multiple disciplines. The interaction between flight and ground software development, Verification and Validation (V&V), Assembly, Test, and Launch Operations (ATLO), and management each demand quick understanding of unique slices of information for each discipline. This information includes the current capabilities of the flight system as well as future capabilities and their status as they are developed and tested. Despite the fundamental and critical nature of this information, the flight software dictionaries used to track it are a stumbling block for many projects. These dictionaries provide the cornerstone for the interpretation of data sent from the spacecraft, allowing for quick comprehension by engineers on the ground. During both spacecraft development and operations, flight software dictionary management includes significant challenges due to the large number of interfacing systems and the subtle yet distinct needs of each.The engineering of flight software dictionaries for Mars2020 had numerous challenges, most-notably: parallel dictionary development to support simultaneous separate flight software build campaigns for each mission phase (cruise and surface), managing requests for operations-enabling information without perturbing the heritage interface with the rover, and the introduction of new tools by the dictionary stakeholders that forced the dictionary team to innovate and redesign the heritage tool chain. These challenges generated guiding principles for the dictionary development effort: emphasize coding best practices and unit testing in the dictionary code development tool chain, use institutionally provided COTS (commercial-off-the-shelf) tools whenever possible, and maintain the heritage flight-ground interface all while advancing operations-enabling information via a loosely coupled interface.Throughout development and operations, the Mars2020 dictionary toolchain included IBM DOORS Next Generation, GitHub, Microsoft Excel, Docker, Jenkins, and a significant custom-built Python codebase. Significant interfaces included JPL’s command and control software, heritage flight software team tools and processes, and the many cloud-based ground tools developed for the mission.This paper will discuss the requirements for the Mars2020 dictionary development, the development team’s response to those requirements, lessons learned throughout the process, steps taken towards automated deliveries and continuous integration of stakeholder inputs, potential toolchain improvements for Mars2020, and key takeaways that could be applied to future missions.

Pyrzak, Guy↗

The SMAP Dictionary Management System

The Soil Moisture Active Passive (SMAP) Dictionary Management System is a web-based tool to develop and store a mission dictionary. A mission dictionary defines the interface between a ground system and a spacecraft. In recent years, mission dictionaries have grown in size and scope, making it difficult for engineers across multiple disciplines to coordinate the dictionary development effort. The Dictionary Management Systemaddresses these issues by placing all dictionary information in one place, taking advantage of the efficiencies inherent in co-locating what were once disparate dictionary development efforts.

systems engineering↗

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↗

Data-Dictionary-Editing Program

Access to data-dictionary relations and attributes made more convenient. Data Dictionary Editor (DDE) application program provides more convenient read/write access to data-dictionary table ("descriptions table") via data screen using SMARTQUERY function keys. Provides three main advantages: (1) User works with table names and field names rather than with table numbers and field numbers, (2) Provides online access to definitions of data-dictionary keys, and (3) Provides displayed summary list that shows, for each datum, which data-dictionary entries currently exist for any specific relation or attribute. Computer program developed to give developers of data bases more convenient access to the OMNIBASE VAX/IDM data-dictionary relations and attributes.

Cumming, A. P.↗

Dictionary Approaches to Image Compression and Reconstruction

This paper proposes using a collection of parameterized waveforms, known as a dictionary, for the purpose of medical image compression. These waveforms, denoted as lambda, are discrete time signals, where y represents the dictionary index. A dictionary with a collection of these waveforms Is typically complete or over complete. Given such a dictionary, the goal is to obtain a representation Image based on the dictionary. We examine the effectiveness of applying Basis Pursuit (BP), Best Orthogonal Basis (BOB), Matching Pursuits (MP), and the Method of Frames (MOF) methods for the compression of digitized radiological images with a wavelet-packet dictionary. The performance of these algorithms is studied for medical images with and without additive noise.

Ziyad, Nigel A.↗

Dictionary Approaches to Image Compression and Reconstruction

This paper proposes using a collection of parameterized waveforms, known as a dictionary, for the purpose of medical image compression. These waveforms, denoted as phi(sub gamma), are discrete time signals, where gamma represents the dictionary index. A dictionary with a collection of these waveforms is typically complete or overcomplete. Given such a dictionary, the goal is to obtain a representation image based on the dictionary. We examine the effectiveness of applying Basis Pursuit (BP), Best Orthogonal Basis (BOB), Matching Pursuits (MP), and the Method of Frames (MOF) methods for the compression of digitized radiological images with a wavelet-packet dictionary. The performance of these algorithms is studied for medical images with and without additive noise.

Ziyad, Nigel A.↗

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↗

Specifications for a Federal Information Processing Standard Data Dictionary System

The development of a software specification that Federal agencies may use in evaluating and selecting data dictionary systems (DDS) is discussed. To supply the flexibility needed by widely different applications and environments in the Federal Government, the Federal Information Processing Standard (FIPS) specifies a core DDS together with an optimal set of modules. The focus and status of the development project are described. Functional specifications for the FIPS DDS are examined for the dictionary, the dictionary schema, and the dictionary processing system. The DDS user interfaces and DDS software interfaces are discussed as well as dictionary administration.

Goldfine, A.↗

Data dictionaries in information systems - Standards, usage , and application

An overview of data dictionary systems and the role of standardization in the interchange of data dictionaries is presented. The development of the data dictionary for the Planetary Data System is cited as an example. The data element dictionary (DED), which is the repository of the definitions of the vocabulary utilized in an information system, is an important part of this service. A DED provides the definitions of the fields of the data set as well as the data elements of the catalog system. Finally, international efforts such as the Consultative Committee on Space Data Systems and other committees set up to provide standard recommendations on the usage and structure of data dictionaries in the international space science community are discussed.

Johnson, Margaret↗

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↗

Intertwining thesauri and dictionaries

The use of dictionaries and thesauri in information retrieval is discussed. The structure and functions of thesauri and dictionaries are described. Particular attention is given to the format of the NASA Thesaurus. The relationship between thesauri and dictionaries, the need to regularize terminology, and the capitalization of words are examined.

Buchan, R. L.↗

Definition and maintenance of a telemetry database dictionary

A telemetry dictionary database includes a component for receiving spreadsheet workbooks of telemetry data over a web-based interface from other computer devices. Another component routes the spreadsheet workbooks to a specified directory on the host processing device. A process then checks the received spreadsheet workbooks for errors, and if no errors are detected the spreadsheet workbooks are routed to another directory to await initiation of a remote database loading process. The loading process first converts the spreadsheet workbooks to comma separated value (CSV) files. Next, a network connection with the computer system that hosts the telemetry dictionary database is established and the CSV files are ported to the computer system that hosts the telemetry dictionary database. This is followed by a remote initiation of a database loading program. Upon completion of loading a flatfile generation program is manually initiated to generate a flatfile to be used in a mission operations environment by the core ground system.

Knopf, William P.↗

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,↗