Liane Xu,Amit Singer
Liane Xu
Laplacian-based methods are popular for dimensionality reduction of data lying in ℝ N . Several theoretical results for these algorithms depend on the fact that the Euclidean distance locally approximates the geodesic distance on t...
Joyce Chew,Matthew Hirn,Smita Krishnaswamy et al.
Joyce Chew et al.
The scattering transform is a multilayered, wavelet-based transform initially introduced as a mathematical model of convolutional neural networks (CNNs) that has played a foundational role in our understanding of these networks' stability a...
The [Formula: see text] -invariant graph Laplacian Part I: Convergence rate and eigendecomposition [0.03%]
带参数[公式]的图拉普拉斯矩阵及其特征值分解（一）收敛率估计
Eitan Rosen,Paulina Hoyos,Xiuyuan Cheng et al.
Eitan Rosen et al.
Graph Laplacian based algorithms for data lying on a manifold have been proven effective for tasks such as dimensionality reduction, clustering, and denoising. In this work, we consider data sets whose data points lie on a manifold that is ...
The [Formula: see text] -invariant graph Laplacian part II: Diffusion maps [0.03%]
带参数的图拉普拉斯矩阵及其特征值问题（II）：扩散地图
Eitan Rosen,Xiuyuan Cheng,Yoel Shkolnisky
Eitan Rosen
The diffusion maps embedding of data lying on a manifold has shown success in tasks such as dimensionality reduction, clustering, and data visualization. In this work, we consider embedding data sets that were sampled from a manifold which ...
A Representation Theory Perspective on Simultaneous Alignment and Classification [0.03%]
从表示理论的角度看同时对齐和分类问题
Roy R Lederman,Amit Singer
Roy R Lederman
Single particle cryo-electron microscopy (EM) is a method for determining the 3-D structure of macromolecules from many noisy 2-D projection images of individual macromolecules whose orientations and positions are random and unknown. The pr...
Albert Chua,Matthew Hirn,Anna Little
Albert Chua
In this paper, we generalize finite depth wavelet scattering transforms, which we formulate as Lq(ℝn) norms of a cascade of continuous wavelet transforms (or dyadic wavelet transforms) and contractive nonlinearities. We then provide n...
Zydrunas Gimbutas,Nicholas F Marshall,Vladimir Rokhlin
Zydrunas Gimbutas
We present a fast method for evaluating expressions of the form u j = ∑ i = 1 , i ≠ j n α i x i - x j , for j = 1 , … , n , where αi are real numbers, and xi are points in a compact interval of R . This exp...
Fourier phase retrieval with a single mask by Douglas-Rachford algorithms [0.03%]
基于Douglas-Rachford算法的单掩模傅里叶相位恢复方法研究
Pengwen Chen,Albert Fannjiang
Pengwen Chen
The Fourier-domain Douglas-Rachford (FDR) algorithm is analyzed for phase retrieval with a single random mask. Since the uniqueness of phase retrieval solution requires more than a single oversampled coded diffraction pattern, the extra inf...
Robust recovery of complex exponential signals from random Gaussian projections via low rank Hankel matrix reconstruction [0.03%]
基于低秩Hankel矩阵重建的复指数信号鲁棒恢复
Jian-Feng Cai,Xiaobo Qu,Weiyu Xu et al.
Jian-Feng Cai et al.
This paper explores robust recovery of a superposition of R distinct complex exponential functions with or without damping factors from a few random Gaussian projections. We assume that the signal of interest is of 2N - 1 dimensions and R <...
Maurice A de Gosson
Maurice A de Gosson
Gabor frames can advantageously be redefined using the Heisenberg-Weyl operators familiar from harmonic analysis and quantum mechanics. Not only does this redefinition allow us to recover in a very simple way known results of symplectic cov...