Results 31 to 40 of about 955,306 (131)

High‐Dimensional Text Clustering by Dimensionality Reduction and Improved Density Peak

Wireless Communications and Mobile Computing, Volume 2020, Issue 1, 2020., 2020
This study focuses on high‐dimensional text data clustering, given the inability of K‐means to process high‐dimensional data and the need to specify the number of clusters and randomly select the initial centers. We propose a Stacked‐Random Projection dimensionality reduction framework and an enhanced K‐means algorithm DPC‐K‐means based on the improved
Yujia Sun, Jan Platoš, Chao-Yang Lee
wiley   +1 more source

An Adaptive Grid and Incentive Mechanism for Personalized Differentially Private Location Data in the Local Setting

Mobile Information Systems, Volume 2020, Issue 1, 2020., 2020
With the proliferation of wireless communication and mobile devices, various location‐based services are emerging. For the growth of the location‐based services, more accurate and various types of personal location data are required. However, concerns about privacy violations are a significant obstacle to obtain personal location data.
Kangsoo Jung, Seog Park, Peter Brida
wiley   +1 more source

Using the Johnson-Lindenstrauss lemma in linear and integer programming

CoRR, 2015
The Johnson-Lindenstrauss lemma allows dimension reduction on real vectors with low distortion on their pairwise Euclidean distances. This result is often used in algorithms such as $k$-means or $k$ nearest neighbours since they only use Euclidean distances, and has sometimes been used in optimization algorithms involving the minimization of Euclidean ...
Ky Khac Vu, Pierre-Louis Poirion, Leo Liberti   +2 more
openaire   +2 more sources

A Union of Euclidean Metric Spaces is Euclidean

Discrete Analysis, 2016
A Union of Euclidean Metric Spaces is Euclidean, Discrete Analysis 2016:14, 15pp. A major theme in metric geometry concerns conditions under which it is possible to embed one metric space into another with small distortion. More precisely, if $M_1$ and $
Konstantin Makarychev, Yury Makarychev
doaj   +1 more source

Improving the Johnson-Lindenstrauss Lemma

, 2010
The Johnson-Lindenstrauss Lemma allows for the projection of $n$ points in $p-$dimensional Euclidean space onto a $k-$dimensional Euclidean space, with $k \ge \frac{24\ln \emph{n}}{3ε^2-2ε^3}$, so that the pairwise distances are preserved within a factor of $1\pmε$.
Rojo, Javier, Nguyen, Tuan
openaire   +2 more sources

A remark on dimensionality reduction in discrete subgroups of ℝd

Miskolc Mathematical Notes
In this short note, we prove a version of the Johnson-Lindenstrauss flattening Lemma for point sets taking values in discrete subgroups. More precisely, given d,λ0,N0∈ℕ𝜖∈(0,12)k=k(d,𝜖)=O( 1𝜖2log⁡d)λ∈ℕ𝒟⊂λλ0ℤd∩B(0,λN0)dF:𝒟→1λ0ℤk (1+𝜖+𝜖λλ0)
Rodolfo Viera
doaj   +1 more source

Johnson-Lindenstrauss Lemma, Linear and Nonlinear Random Projections, Random Fourier Features, and Random Kitchen Sinks: Tutorial and Survey

CoRR, 2021
This is a tutorial and survey paper on the Johnson-Lindenstrauss (JL) lemma and linear and nonlinear random projections. We start with linear random projection and then justify its correctness by JL lemma and its proof. Then, sparse random projections with $\ell_1$ norm and interpolation norm are introduced.
Benyamin Ghojogh, Ali Ghodsi 0001, Fakhri Karray, Mark Crowley 0001   +3 more
openaire   +3 more sources

Private Query Release via the Johnson-Lindenstrauss Transform

The Journal of Privacy and Confidentiality
We introduce a new method for releasing answers to statistical queries with differential privacy, based on the Johnson-Lindenstrauss lemma. The key idea is to randomly project the query answers to a lower dimensional space so that the distance between ...
Aleksandar Nikolov
doaj   +1 more source

Sparse Projection Attention: A Computationally Efficient Framework for Long Sequence Modeling

Mathematics
The self-attention mechanism has revolutionized sequence modeling but suffers from quadratic computational complexity with respect to sequence length, limiting its applicability to long sequences.
Mehdi Chrifi Alaoui, Nour-Eddine Joudar, Mohamed Ettaouil   +2 more
doaj   +1 more source

On the Computation of Tensor Functions under Tensor‐Tensor Multiplications with Linear Maps

Numerical Linear Algebra with Applications, Volume 33, Issue 3, June 2026.
ABSTRACT In this paper, we study the computation of both algebraic and non‐algebraic tensor functions under the tensor‐tensor multiplication with linear maps. In the case of algebraic tensor functions, we prove that the asymptotic exponent of both the tensor‐tensor multiplication and the tensor polynomial evaluation problem under this multiplication is
Jeong‐Hoon Ju, Susana López‐Moreno
wiley   +1 more source