Abstract
Information is the resolution of uncertainty and manifests itself as patterns. Although complex, most observable phenomena are not random and instead are associated with deterministic, chaotic systems. The underlying patterns and symmetries expressed from these phenomena determine their information content and compressibility. While some patterns, such as the existence of Fourier modes, are easy to extract, advances in machine learning have enabled more comprehensive methods in feature extraction, most notably in their ability to elicit non-linear relationships. Herein we review methods concerned with the encoding and reconstruction of natural signals and how they might inform the discovery of useful transform bases. Additionally, we illustrate the efficacy of data-driven bases over generic ones in encoding information whilst discussing these developments in the context of “fourth paradigm” metrology. Toward this end, we propose that existing metrological standards and norms may need to be redefined within the context of a data-rich world.
Highlights
Non-random, chaotic signals arise from natural and engineered processes [1]
Greater data availability means that most contemporary measurements are not likely to retain especially surprising information, reflected in the truism that the more we know about our world, the less there is to discover
As the structure of the modes becomes more “normal”, the number of modes needed to retain reconstruction fidelity increases. This is reflected in the compressed sensing (CS) theorem [24,30] wherein given the reformalization of Equation (4), if we want to use a generic basis to recover a measured signal
Summary
Non-random, chaotic signals arise from natural and engineered processes [1]. As such, information obtained from physical systems is routinely captured and stored in increasingly large datasets. In fields where the structures and properties of physical phenomena are well documented, there are more assumptions that can be made about the design of measurement hardware, as well as the classification structure of a domain-specific taxonomy. While there are numerous species of insects that have yet to be discovered, enough have been identified to reasonably conclude that any unknown species that remain will most likely exhibit similar traits (i.e., comprising a chitinous exoskeleton and similar physical morphology). When entomologists go into the field to search for novel species, they bring equipment to measure, document, and collect their observations that is optimized for classifying prior observations. The axiom that many new observations are likely to be unsurprising (i.e., derivative as opposed to truly novel) raises an interesting epistemological question that is, by extension, extremely relevant in metrology
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