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On Manifold Learning in Plato's Cave: Remarks on Manifold Learning and Physical Phenomena. [PDF]
Int Conf Sampl Theory Appl SampTA, 2023 Many techniques in machine learning attempt explicitly or implicitly to infer a low-dimensional manifold structure of an underlying physical phenomenon from measurements without an explicit model of the phenomenon or the measurement apparatus. This paper presents a cautionary tale regarding the discrepancy between the geometry of measurements and the ...
Lederman RR, Toader B.
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Contagion Dynamics for Manifold Learning [PDF]
Frontiers in Big Data, 2022 Contagion maps exploit activation times in threshold contagions to assign vectors in high-dimensional Euclidean space to the nodes of a network. A point cloud that is the image of a contagion map reflects both the structure underlying the network and the
Barbara I. Mahler
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Multi-Manifold Learning Fault Diagnosis Method Based on Adaptive Domain Selection and Maximum Manifold Edge [PDF]
SensorsThe vibration signal of rotating machinery is usually nonlinear and non-stationary, and the feature set has information redundancy. Therefore, a high-dimensional feature reduction method based on multi-manifold learning is proposed for rotating machinery
Ling Zhao, Jiawei Ding, Pan Li, Xin Chi
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Adaptive Manifold Learning [PDF]
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2012 Manifold learning algorithms seek to find a low-dimensional parameterization of high-dimensional data. They heavily rely on the notion of what can be considered as local, how accurately the manifold can be approximated locally, and, last but not least, how the local structures can be patched together to produce the global parameterization.
Jing Wang +2 more
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Comparison of manifold learning algorithms for identifying geochemical anomalies associated with copper mineralization [PDF]
Scientific ReportsThe Baiyin district, situated within the northern Qilian orogenic belt, hosts the largest concentration of copper mineral resources in Gansu Province, Northwestern China. Geochemical anomaly patterns are crucial indicators for mineral exploration in this
Yuwen Min +5 more
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Galaxy Evolution with Manifold Learning [PDF]
EntropyMatter in the early Universe was nearly uniform, and galaxies emerged through the gravitational growth of small primordial density fluctuations. Astrophysics has been trying to unveil the complex physical phenomena that have caused the formation and ...
Tsutomu T. Takeuchi +2 more
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Curvature-aware manifold learning [PDF]
Pattern Recognition, 2018 Traditional manifold learning algorithms assumed that the embedded manifold is globally or locally isometric to Euclidean space. Under this assumption, they divided manifold into a set of overlapping local patches which are locally isometric to linear subsets of Euclidean space. By analyzing the global or local isometry assumptions it can be shown that
Yangyang Li
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A Study on Dimensionality Reduction and Parameters for Hyperspectral Imagery Based on Manifold Learning [PDF]
SensorsWith the rapid advancement of remote-sensing technology, the spectral information obtained from hyperspectral remote-sensing imagery has become increasingly rich, facilitating detailed spectral analysis of Earth’s surface objects.
Wenhui Song +5 more
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Remote Sensing, 2019 In remote sensing, hyperspectral and polarimetric synthetic aperture radar (PolSAR) images are the two most versatile data sources for a wide range of applications such as land use land cover classification.
Jingliang Hu +3 more
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Unsupervised manifold learning of collective behavior. [PDF]
PLoS Computational Biology, 2021 Collective behavior is an emergent property of numerous complex systems, from financial markets to cancer cells to predator-prey ecological systems. Characterizing modes of collective behavior is often done through human observation, training generative ...
Mathew Titus +2 more
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