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Dimensionality Reduction with Image Data [PDF]
, 2004 A common objective in image analysis is dimensionality reduction. The most common often used data-exploratory technique with this objective is principal component analysis. We propose a new method based on the projection of the images as matrices after a Procrustes rotation and show that it leads to a better reconstruction of images.
Peña, Daniel, Benito, Mónica
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Dimensionality Reduction: Challenges and Solutions [PDF]
ITM Web of Conferences, 2022 The use of dimensionality reduction techniques is a keystone for analyzing and interpreting high dimensional data. These techniques gather several data features of interest, such as dynamical structure, input-output relationships, the correlation between
Ahmad Noor, Nassif Ali Bou
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Non-negative Matrix Factorization for Dimensionality Reduction [PDF]
ITM Web of Conferences, 2022 —What matrix factorization methods do is reduce the dimensionality of the data without losing any important information. In this work, we present the Non-negative Matrix Factorization (NMF) method, focusing on its advantages concerning other methods of ...
Olaya Jbari, Otman Chakkor
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Dimensional reduction of electromagnetism [PDF]
Journal of Mathematical Physics, 2022 We derive one- and two-dimensional models for classical electromagnetism by making use of Hadamard’s method of descent. Low-dimensional electromagnetism is conceived as a specialization of the higher-dimensional one, in which the fields are uniform along the additional spatial directions.
Rocco Maggi +5 more
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Modern Physics Letters A, 1999 Using an octonionic formalism, we introduce a new mechanism for reducing ten space–time dimensions to four without compactification. Applying this mechanism to the free, ten-dimensional, massless (momentum space) Dirac equation results in a particle spectrum consisting of exactly three generations.
Tevian Dray, Corinne A. Manogue
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Deformed dimensional reduction
Geometry & Topology, 2022 Since its first use by Behrend, Bryan, and Szendrői in the computation of motivic Donaldson-Thomas (DT) invariants of $\mathbb{A}_{\mathbb{C}}^3$, dimensional reduction has proved to be an important tool in motivic and cohomological DT theory. Inspired by a conjecture of Cazzaniga, Morrison, Pym, and Szendrői on motivic DT invariants, work of ...
Davison, Ben, Pădurariu, Tudor
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Shape-aware stochastic neighbor embedding for robust data visualisations
BMC Bioinformatics, 2022 Background The t-distributed Stochastic Neighbor Embedding (t-SNE) algorithm has emerged as one of the leading methods for visualising high-dimensional (HD) data in a wide variety of fields, especially for revealing cluster structure in HD single-cell ...
Tobias Wängberg +2 more
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DIMENSIONAL REDUCTION ON A SPHERE [PDF]
International Journal of Modern Physics B, 2006 The question of the dimensional reduction of two-dimensional (2d) quantum models on a sphere to one-dimensional (1d) models on a circle is addressed. A possible application is to look at a relation between the 2d anyon model and the 1d Calogero–Sutherland model, which would allow for a better understanding of the connection between 2d anyon exchange ...
Moller, Gunnar +2 more
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Dimensionality reduction using singular vectors
Scientific Reports, 2021 A common problem in machine learning and pattern recognition is the process of identifying the most relevant features, specifically in dealing with high-dimensional datasets in bioinformatics.
Majid Afshar, Hamid Usefi
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Dimensionality reduction in Bayesian estimation algorithms [PDF]
Atmospheric Measurement Techniques, 2013 An idealized synthetic database loosely resembling 3-channel passive microwave observations of precipitation against a variable background is employed to examine the performance of a conventional Bayesian retrieval algorithm.
G. W. Petty
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