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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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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.
Manogue, Corinne A., Dray, Tevian
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Dimensionality reduction methods [PDF]
Advances in Methodology and Statistics, 2005 In case one or more sets of variables are available, the use of dimensional reduction methods could be necessary. In this contest, after a review on the link between the Shrinkage Regression Methods and Dimensional Reduction Methods, authors provide a different multivariate extension of the Garthwaite's PLS approach (1994) where a simple linear ...
D'AMBRA L, AMENTA P, GALLO, Michele
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Dimensionality reduction of complex dynamical systems
iScience, 2021 Summary: One of the outstanding problems in complexity science and engineering is the study of high-dimensional networked systems and of their susceptibility to transitions to undesired states as a result of changes in external drivers or in the ...
Chengyi Tu +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 mappings [PDF]
2011 IEEE Symposium on Computational Intelligence and Data Mining (CIDM), 2011 A wealth of powerful dimensionality reduction methods has been established which can be used for data visualization and preprocessing. These are accompanied by formal evaluation schemes, which allow a quantitative evaluation along general principles and which even lead to further visualization schemes based on these objectives.
Bunte, Kerstin +3 more
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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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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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2D Dimensionality Reduction Methods without Loss [PDF]
Journal of Artificial Intelligence and Data Mining, 2019 In this paper, several two-dimensional extensions of principal component analysis (PCA) and linear discriminant analysis (LDA) techniques has been applied in a lossless dimensionality reduction framework, for face recognition application.
S. Ahmadkhani, P. Adibi, A. ahmadkhani
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