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02/01/2023
Dictionary-based Manifold Learning
We propose a paradigm for interpretable Manifold Learning for scientific...
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02/01/2023
The Parametric Stability of Well-separated Spherical Gaussian Mixtures
We quantify the parameter stability of a spherical Gaussian Mixture Mode...
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04/26/2022
Double Diffusion Maps and their Latent Harmonics for Scientific Computations in Latent Space
We introduce a data-driven approach to building reduced dynamical models...
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03/31/2022
To ArXiv or not to ArXiv: A Study Quantifying Pros and Cons of Posting Preprints Online
Double-blind conferences have engaged in debates over whether to allow a...
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07/30/2021
Distribution free optimality intervals for clustering
We address the problem of validating the ouput of clustering algorithms....
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07/23/2021
The decomposition of the higher-order homology embedding constructed from the k-Laplacian
The null space of the k-th order Laplacian â„’_k, known as the k-th homolo...
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04/21/2021
A class of network models recoverable by spectral clustering
Finding communities in networks is a problem that remains difficult, in ...
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03/13/2021
Helmholtzian Eigenmap: Topological feature discovery edge flow learning from point cloud data
The manifold Helmholtzian (1-Laplacian) operator Δ_1 elegantly generaliz...
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06/18/2020
Guarantees for Hierarchical Clustering by the Sublevel Set method
Meila (2018) introduces an optimization based method called the Sublevel...
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07/02/2019
Selecting the independent coordinates of manifolds with large aspect ratios
Many manifold embedding algorithms fail apparently when the data manifol...
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12/03/2018
Measuring the Robustness of Graph Properties
In this paper, we propose a perturbation framework to measure the robust...
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11/29/2018
A regression approach for explaining manifold embedding coordinates
Manifold embedding algorithms map high dimensional data, down to coordin...
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07/21/2018
How to sample connected K-partitions of a graph
A connected undirected graph G=(V,E) is given. This paper presents an al...
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03/09/2016
megaman: Manifold Learning with Millions of points
Manifold Learning is a class of algorithms seeking a low-dimensional non...
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05/30/2014
Estimating Vector Fields on Manifolds and the Embedding of Directed Graphs
This paper considers the problem of embedding directed graphs in Euclide...
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12/06/2013
An Algorithmic Theory of Dependent Regularizers, Part 1: Submodular Structure
We present an exploration of the rich theoretical connections between se...
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05/30/2013
Non-linear dimensionality reduction: Riemannian metric estimation and the problem of geometric discovery
In recent years, manifold learning has become increasingly popular as a ...
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01/30/2013
An Experimental Comparison of Several Clustering and Initialization Methods
We examine methods for clustering in high dimensions. In the first part ...
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01/16/2013
Tractable Bayesian Learning of Tree Belief Networks
In this paper we present decomposable priors, a family of priors over st...
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07/04/2012
Unsupervised spectral learning
In spectral clustering and spectral image segmentation, the data is part...
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06/20/2012
Consensus ranking under the exponential model
We analyze the generalized Mallows model, a popular exponential model ov...
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03/15/2012
