Results 11 to 20 of about 955,306 (131)
The Johnson-Lindenstrauss lemma and the sphericity of some graphs [PDF]
Journal of Combinatorial Theory Series B, 1988 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
P Frankl, H Maehara
exaly +5 more sources
On Sparsity and Sub-Gaussianity in the Johnson-Lindenstrauss Lemma
Trans. Mach. Learn. Res.We provide a simple proof of the Johnson-Lindenstrauss lemma for sub-Gaussian variables. We extend the analysis to identify how sparse projections can be, and what the cost of sparsity is on the target dimension.The Johnson-Lindenstrauss lemma is the theoretical core of the dimensionality reduction methods based on random projections.
Garivier, Aurélien, Pilliat, Emmanuel
core +11 more sources
Oblivious dimension reduction for k -means: beyond subspaces and the Johnson-Lindenstrauss lemma [PDF]
Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, 2019 We show that for n points in d-dimensional Euclidean space, a data oblivious random projection of the columns onto \(m \in O(\frac{(\log k+\log \log n)\log 1/\varepsilon)}{\varepsilon^6}) \) dimensions is suffcient to approximate the cost of all k-means clusterings up to a multiplicative \((1\pm \varepsilon)\)factor. The previous-best upper bounds on m
Luca Becchetti +4 more
openaire +6 more sources
An Analysis of the Johnson-Lindenstrauss Lemma with the Bivariate Gamma Distribution
, 2023 20 pages, 5 figures.
Jason Bernstein +2 more
exaly +4 more sources
The Johnson-Lindenstrauss Lemma Is Optimal for Linear Dimensionality Reduction [PDF]
, 2015 For any n > 1, 0 n^C for some constant C > 0, we show the existence of an N-point subset X of l_2^n such that any linear map from X to l_2^m with distortion at most 1 + epsilon must have m = Omega(min{n, epsilon^{-2}*lg(N)).
Nelson, Jelani, Larsen, Kasper Green
core +8 more sources
Randomized Projection Learning Method for Dynamic Mode Decomposition
Mathematics, 2021 A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on a projected space. In the spirit of Johnson–Lindenstrauss lemma, we will use a random projection to estimate the DMD modes in a reduced ...
Sudam Surasinghe, Erik M. Bollt
doaj +1 more source
Generalizing the Johnson–Lindenstrauss lemma to k-dimensional affine subspaces [PDF]
Studia Mathematica, 2009 Yehoram Gordon
exaly +2 more sources
SoftwareX, 2020 The performance of the high dimensional multivariate data analysis is seriously affected by the curse of dimensionality. Feature extraction acts as an important pre-processing step in data analysis process to avoid the curse of dimensionality.
R. Siddharth, G. Aghila
doaj +1 more source
Random projection ensemble classification with high‐dimensional time series
Biometrics, Volume 79, Issue 2, Page 964-974, June 2023., 2023 Abstract Multivariate time‐series (MTS) data are prevalent in diverse domains and often high dimensional. We propose new random projection ensemble classifiers with high‐dimensional MTS. The method first applies dimension reduction in the time domain via randomly projecting the time‐series variables into some low‐dimensional space, followed by ...
Fuli Zhang, Kung‐Sik Chan
wiley +1 more source
Scientific Programming, Volume 2022, Issue 1, 2022., 2022 The high dimensionality of the modern remote sensing data of construction land makes it complicated to extract image data. This paper proposes a dimensionality reduction and extraction strategy for the remote sensing data of construction land, with the aid of building information modeling (BIM) and geographical information system (GIS).
Yonghua Wang +4 more
wiley +1 more source