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Phase Transition in the One-bit Johnson-Lindenstrauss Lemma
, 2019 The Johnson-Lindenstrauss Lemma (J-L Lemma) is a cornerstone of dimension reduction techniques. We study it in the one-bit context, namely we consider the unit sphere $ \mathbb S ^{N-1}$, with normalized geodesic metric, and map a finite set $ \mathbf{X} \subset \mathbb{S}^{N-1}$ into the Hamming cube $\mathbb{H}_m = \{0,1\}^m$, with normalized Hamming
Bah, Amadou, Kagy, Bryson, Smith, Emily
openaire +2 more sources
Sharp Generalization Error Bounds for Randomlyprojected Classifiers [PDF]
, 2013 • Main result- Generalisation bound for a generic linear classifier trained on randomly-projected data • Main ingredient of the proof: Flipping ...
Kabán, Ata +3 more
core +1 more source
On Using Toeplitz and Circulant Matrices for Johnson-Lindenstrauss Transforms [PDF]
, 2017 The Johnson-Lindenstrauss lemma is one of the corner stone results in dimensionality reduction. It says that given N, for any set of N, vectors X \subset R^n, there exists a mapping f : X --> R^m such that f(X) preserves all pairwise distances between ...
Freksen, Casper Benjamin +1 more
core +1 more source
An elementary proof of the Johnson-Lindenstrauss Lemma
, 1999 The Johnson-Lindenstrauss lemma shows that a set of n points in high dimensional Euclidean space can be mapped down into an O(log n=ffl 2 ) dimensional Euclidean space such that the distance between any two points changes by only a factor of (1 \Sigma ...
Sanjoy Dasgupta, Anupam Gupta
core
On randomness reduction in the Johnson-Lindenstrauss lemma
, 2012 A refinement of so-called fast Johnson-Lindenstrauss transform, due to Ailon and Chazelle (2006), and Matoušek (2008), is proposed. While it preserves the time efficiency and simplicity of implementation of the original construction, it reduces randomness used to generate the random transformation.
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Johnson-Lindenstrauss projection of high dimensional data [PDF]
, 2015 Johnson and Lindenstrauss (1984) proved that any finite set of data in a high dimensional space can be projected into a low dimensional space with the Euclidean metric information of the set being preserved within any desired accuracy.
Knoll, Fiona, Mao, Yue, Gao, Shuhong
core +1 more source
Tighter Bounds on Johnson Lindenstrauss Transforms [PDF]
, 2015 Johnson and Lindenstrauss (1984) proved that any finite set of data in a high dimensional space can be projected into a low dimensional space with the Euclidean metric information of the set being preserved within any desired accuracy.
Knoll, Fiona
core +1 more source
Johnson-Lindenstrauss Lemma Guided Network for Efficient 3D Medical Segmentation
CoRR30 pages, 12 figures.
Jinpeng Lu +6 more
openaire +3 more sources
Random projections as regularizers: learning a linear discriminant ensemble from fewer observations than dimensions [PDF]
, 2013 We examine the performance of an ensemble of randomly-projected Fisher Linear Discriminant classifiers, focusing on the case when there are fewer training observations than data dimensions.
Kabán, Ata, Durrant, Robert J.
core +1 more source
Sparser Johnson-Lindenstrauss Transforms [PDF]
, 2013 We give two different Johnson-Lindenstrauss distributions, each with column sparsity \(s = \Theta(\epsilon^{−1} log(1/\delta))\) and embedding into optimal dimension \(k = O(\epsilon^{−2} log(1/\delta))\) to achieve distortion \(1\pm \epsilon\) with ...
Kane, Daniel M +4 more
core +1 more source