299 citations · 924 across the 25 of their papers we have counts for
30 papers
Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learning
Ya-Wei Eileen Lin, Ronald R. Coifman, Gal Mishne +1
Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Ou…
Robust estimation of position-dependent anisotropic diffusivity tensors from stochastic trajectories
Tiago S. Domingues, Ronald Coifman, Amir Haji-Akbari
Materials under confinement can possess properties that deviate considerably from their bulk counterparts. Indeed, confinement makes all physical properties position-dependent and…
On Complex Analytic tools, and the Holomorphic Rotation methods
Ronald R. Coifman, Jacques Peyrière, Guido Weiss
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional r…
Questionnaires to PDEs: From Disorganized Data to Emergent Generative Dynamic Models
David W. Sroczynski, Felix P. Kemeth, Ronald R. Coifman +1
Starting with sets of disorganized observations of spatially varying and temporally evolving systems, obtained at different (also disorganized) sets of parameters, we demonstrate t…
A common variable minimax theorem for graphs
Ronald R. Coifman, Nicholas F. Marshall, Stefan Steinerberger
Let be a collection of graphs defined on a common set of vertices but with different edge sets .…
Diffusion Earth Mover's Distance and Distribution Embeddings
Alexander Tong, Guillaume Huguet, Amine Natik +5
We propose a new fast method of measuring distances between large numbers of related high dimensional datasets called the Diffusion Earth Mover's Distance (EMD). We model the datas…
Multiscale decompositions of Hardy spaces
Ronald R. Coifman, Jacques Peyrière
An inspiration at the origin of wavelet analysis (when Grossmann, Morlet, Meyer and collaborators were interacting and exploring versions of multiscale representations) was provide…
Doubly-Stochastic Normalization of the Gaussian Kernel is Robust to Heteroskedastic Noise
Boris Landa, Ronald R. Coifman, Yuval Kluger
A fundamental step in many data-analysis techniques is the construction of an affinity matrix describing similarities between data points. When the data points reside in Euclidean…
LOCA: LOcal Conformal Autoencoder for standardized data coordinates
Erez Peterfreund, Ofir Lindenbaum, Felix Dietrich +4
We propose a deep-learning based method for obtaining standardized data coordinates from scientific measurements.Data observations are modeled as samples from an unknown, non-linea…
Co-manifold learning with missing data
Gal Mishne, Eric C. Chi, Ronald R. Coifman
Representation learning is typically applied to only one mode of a data matrix, either its rows or columns. Yet in many applications, there is an underlying geometry to both the ro…
A Remark on the Arcsine Distribution and the Hilbert Transform
Ronald R. Coifman, Stefan Steinerberger
It is known that if is a sequence of orthogonal polynomials in , then the roots are distributed according to an arcsine distribution…
Manifold learning with bi-stochastic kernels
Nicholas F. Marshall, Ronald R. Coifman
In this paper we answer the following question: what is the infinitesimal generator of the diffusion process defined by a kernel that is normalized such that it is bi-stochastic wi…
Two-sample Statistics Based on Anisotropic Kernels
Xiuyuan Cheng, Alexander Cloninger, Ronald R. Coifman
The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When…
Data-Driven Tree Transforms and Metrics
Gal Mishne, Ronen Talmon, Israel Cohen +2
We consider the analysis of high dimensional data given in the form of a matrix with columns consisting of observations and rows consisting of features. Often the data is such that…
Phase unwinding, or invariant subspace decompositions of Hardy spaces
Ronald R. Coifman, Jacques Peyrière
We consider orthogonal decompositions of invariant subspaces of Hardy spaces, these relate to the Blaschke based phase unwinding decompositions. We prove convergence in Lp. In part…
iMapD: intrinsic Map Dynamics exploration for uncharted effective free energy landscapes
Eliodoro Chiavazzo, Ronald R. Coifman, Roberto Covino +4
We describe and implement iMapD, a computer-assisted approach for accelerating the exploration of uncharted effective Free Energy Surfaces (FES), and more generally for the extract…
No equations, no parameters, no variables: data, and the reconstruction of normal forms by learning informed observation geometries
Or Yair, Ronen Talmon, Ronald R. Coifman +1
The discovery of physical laws consistent with empirical observations lies at the heart of (applied) science and engineering. These laws typically take the form of nonlinear differ…
Carrier frequencies, holomorphy and unwinding
Ronald R. Coifman, Stefan Steinerberger, Hau-tieng Wu
We prove that functions of intrinsic-mode type (a classical models for signals) behave essentially like holomorphic functions: adding a pure carrier frequency ensures tha…
Hierarchical Coupled Geometry Analysis for Neuronal Structure and Activity Pattern Discovery
Gal Mishne, Ronen Talmon, Ron Meir +3
In the wake of recent advances in experimental methods in neuroscience, the ability to record in-vivo neuronal activity from awake animals has become feasible. The availability of…
Provable approximation properties for deep neural networks
Uri Shaham, Alexander Cloninger, Ronald R. Coifman
We discuss approximation of functions using deep neural nets. Given a function on a -dimensional manifold , we construct a sparsely-connected depth-4…
Nonlinear phase unwinding of functions
Ronald R. Coifman, Stefan Steinerberger
We study a natural nonlinear analogue of Fourier series. Iterative Blaschke factorization allows one to formally write any holomorphic function as a series which successively u…
Bigeometric Organization of Deep Nets
Alexander Cloninger, Ronald R. Coifman, Nicholas Downing +1
In this paper, we build an organization of high-dimensional datasets that cannot be cleanly embedded into a low-dimensional representation due to missing entries and a subset of th…
Parsimonious Representation of Nonlinear Dynamical Systems Through Manifold Learning: A Chemotaxis Case Study
Carmeline J. Dsilva, Ronen Talmon, Ronald R. Coifman +1
Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in recent years to the analysis of large and complex data sets. However, such algorithm…
Data-Driven Reduction for Multiscale Stochastic Dynamical Systems
Carmeline J. Dsilva, Ronen Talmon, C. William Gear +2
Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is ofte…