Results 1 to 10 of about 955,306 (131)
On variants of the Johnson–Lindenstrauss lemma [PDF]
Random Structures and Algorithms, 2008 AbstractThe Johnson–Lindenstrauss lemma asserts that an n‐point set in any Euclidean space can be mapped to a Euclidean space of dimension k = O(ε‐2 log n) so that all distances are preserved up to a multiplicative factor between 1 − ε and 1 + ε. Known proofs obtain such a mapping as a linear map Rn → Rk with a suitable random matrix.
Yonina C. Eldar, Deanna Needell
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Optimality of the Johnson-Lindenstrauss Lemma [PDF]
2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), 2017 For any integers $d, n \geq 2$ and $1/({\min\{n,d\}})^{0.4999} < \varepsilon<1$, we show the existence of a set of $n$ vectors $X\subset \mathbb{R}^d$ such that any embedding $f:X\rightarrow \mathbb{R}^m$ satisfying $$ \forall x,y\in X,\ (1-\varepsilon)\|x-y\|_2^2\le \|f(x)-f(y)\|_2^2 \le (1+\varepsilon)\|x-y\|_2^2 $$ must have $$ m = Ω ...
Kasper Green Larsen
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Accelerating Feature Based Registration Using the Johnson-Lindenstrauss Lemma [PDF]
Lecture Notes in Computer Science, 2009 We introduce an efficient search strategy to substantially accelerate feature based registration. Previous feature based registration algorithms often use truncated search strategies in order to achieve small computation times. Our new accelerated search strategy is based on the realization that the search for corresponding features can be dramatically
Simon Warfield +2 more
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A Quantized Johnson–Lindenstrauss Lemma: The Finding of Buffon’s Needle [PDF]
IEEE Transactions on Information Theory, 2015 In 1733, Georges-Louis Leclerc, Comte de Buffon in France, set the ground of geometric probability theory by defining an enlightening problem: What is the probability that a needle thrown randomly on a ground made of equispaced parallel strips lies on two of them?
Laurent Jacques
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Adaptive Block-Based Compressed Video Sensing Based on Saliency Detection and Side Information [PDF]
Entropy, 2021 The setting of the measurement number for each block is very important for a block-based compressed sensing system. However, in practical applications, we only have the initial measurement results of the original signal on the sampling side instead of ...
Wei Wang, Jianming Wang, Jianhua Chen
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Uncovering High-dimensional Structures of Projections from Dimensionality Reduction Methods [PDF]
MethodsX, 2020 Projections are conventional methods of dimensionality reduction for information visualization used to transform high-dimensional data into low dimensional space.
Michael C. Thrun, PhD +1 more
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Johnson‐Lindenstrauss lemma for circulant matrices** [PDF]
Random Structures and Algorithms, 2011 AbstractWe prove a variant of a Johnson‐Lindenstrauss lemma for matrices with circulant structure. This approach allows to minimize the randomness used, is easy to implement and provides good running times. The price to be paid is the higher dimension of the target space k = O(ε−2 log3 n) instead of the classical bound k = O(ε−2 log n).
Jan Vybíral
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RanBALL: An Ensemble Machine Learning Framework for Accurate Subtype Identification of Pediatric B-Cell Acute Lymphoblastic Leukemia. [PDF]
Adv Intell SystHere, we present RanBALL, an ensemble random projection‐based model for accurate and cost‐effective identification of B‐cell acute lymphoblastic leukemia subtypes is presented. By preserving patient‐to‐patient distance after dimension reduction by random projection and ensemble learning, RanBALL can facilitate the discovery of B‐ALL subtype‐specific ...
Li L +6 more
europepmc +2 more sources
Accelerating Image Registration With the Johnson–Lindenstrauss Lemma: Application to Imaging 3-D Neural Ultrastructure With Electron Microscopy [PDF]
IEEE Transactions on Medical Imaging, 2011 We present a novel algorithm to accelerate feature based registration, and demonstrate the utility of the algorithm for the alignment of large transmission electron microscopy (TEM) images to create 3-D images of neural ultrastructure. In contrast to the most similar algorithms, which achieve small computation times by truncated search, our algorithm ...
Ayelet Akselrod-Ballin +3 more
openaire +4 more sources
The Johnson–Lindenstrauss Lemma Almost Characterizes Hilbert Space, But Not Quite [PDF]
Discrete and Computational Geometry, 2009 Let $X$ be a normed space that satisfies the Johnson-Lindenstrauss lemma (J-L lemma, in short) in the sense that for any integer $n$ and any $x_1,\ldots,x_n\in X$ there exists a linear mapping $L:X\to F$, where $F\subseteq X$ is a linear subspace of dimension $O(\log n)$, such that $\|x_i-x_j\|\le\|L(x_i)-L(x_j)\|\le O(1)\cdot\|x_i-x_j\|$ for all $i,j ...
Assaf Naor
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