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no code implementations • 16 Sep 2022 • Boris Landa, Xiuyuan Cheng

In this work, we investigate this normalization in a setting where points are sampled from an unknown density on a low-dimensional manifold embedded in high-dimensional space and corrupted by possibly strong, non-identically distributed, sub-Gaussian noise.

1 code implementation • 22 Jun 2022 • Xiuyuan Cheng, Boris Landa

This paper proves the convergence of the bi-stochastically normalized graph Laplacian to manifold (weighted-)Laplacian with rates when $n$ data points are i. i. d.

no code implementations • 11 Dec 2020 • Boris Landa

Specifically, letting $\widetilde{A}\in\mathbb{R}^{M\times N}$ be a positive and bounded random matrix whose entries assume a certain type of independence, we provide a concentration inequality for the scaling factors of $\widetilde{A}$ around those of $A = \mathbb{E}[\widetilde{A}]$.

Probability Numerical Analysis Numerical Analysis 60B20, 60F10, 65F35,

no code implementations • 31 May 2020 • Boris Landa, Ronald R. Coifman, Yuval Kluger

When the data points reside in Euclidean space, a widespread approach is to from an affinity matrix by the Gaussian kernel with pairwise distances, and to follow with a certain normalization (e. g. the row-stochastic normalization or its symmetric variant).

1 code implementation • 12 Dec 2019 • Amitay Eldar, Boris Landa, Yoel Shkolnisky

We present the KLT (Karhunen Loeve Transform) picker, which is fully automatic and requires as an input only the approximated particle size.

1 code implementation • 1 Jun 2019 • Boris Landa, Yoel Shkolnisky

Solving this problem allows to discover low-rank structures masked by the existence of translations (which act as nuisance parameters), with direct application to Principal Components Analysis (PCA).

Statistics Theory Data Structures and Algorithms Information Theory Information Theory Statistics Theory

no code implementations • 6 Feb 2018 • Boris Landa, Yoel Shkolnisky

Essentially, the steerable GL extends the standard GL by accounting for all (infinitely-many) planar rotations of all images.

no code implementations • 9 Aug 2016 • Boris Landa, Yoel Shkolnisky

This paper describes a fast and accurate method for obtaining steerable principal components from a large dataset of images, assuming the images are well localized in space and frequency.

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