103 citations · 268 across the 27 of their papers we have counts for
15 papers · 1 filter
Manifold learning: what, how, and why
Marina Meilă, Hanyu Zhang
Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensi…
The Parametric Stability of Well-separated Spherical Gaussian Mixtures
Hanyu Zhang, Marina Meila
We quantify the parameter stability of a spherical Gaussian Mixture Model (sGMM) under small perturbations in distribution space. Namely, we derive the first explicit bound to show…
Double Diffusion Maps and their Latent Harmonics for Scientific Computations in Latent Space
Nikolaos Evangelou, Felix Dietrich, Eliodoro Chiavazzo +3
We introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning…
The decomposition of the higher-order homology embedding constructed from the -Laplacian
Yu-Chia Chen, Marina Meilă
The null space of the -th order Laplacian , known as the {\em -th homology vector space}, encodes the non-trivial topology of a manifold or a network.…
Distribution free optimality intervals for clustering
Marina Meilă, Hanyu Zhang
We address the problem of validating the ouput of clustering algorithms. Given data and a partition of these data into clusters, when can we say tha…
A class of network models recoverable by spectral clustering
Yali Wan, Marina Meila
Finding communities in networks is a problem that remains difficult, in spite of the amount of attention it has recently received. The Stochastic Block-Model (SBM) is a generative…
Helmholtzian Eigenmap: Topological feature discovery & edge flow learning from point cloud data
Yu-Chia Chen, Weicheng Wu, Marina Meilă +1
The manifold Helmholtzian (1-Laplacian) operator elegantly generalizes the Laplace-Beltrami operator to vector fields on a manifold . In this work, we propose the…
Guarantees for Hierarchical Clustering by the Sublevel Set method
Marina Meila
Meila (2018) introduces an optimization based method called the Sublevel Set method, to guarantee that a clustering is nearly optimal and "approximately correct" without relying on…
Selecting the independent coordinates of manifolds with large aspect ratios
Yu-Chia Chen, Marina Meilă
Many manifold embedding algorithms fail apparently when the data manifold has a large aspect ratio (such as a long, thin strip). Here, we formulate success and failure in terms of…
Manifold Coordinates with Physical Meaning
Samson Koelle, Hanyu Zhang, Marina Meila +1
Manifold embedding algorithms map high-dimensional data down to coordinates in a much lower-dimensional space. One of the aims of dimension reduction is to find intrinsic coordinat…
Improved graph Laplacian via geometric self-consistency
Dominique Perrault-Joncas, Marina Meila
We address the problem of setting the kernel bandwidth used by Manifold Learning algorithms to construct the graph Laplacian. Exploiting the connection between manifold geometry, r…
Estimating Vector Fields on Manifolds and the Embedding of Directed Graphs
Dominique Perrault-Joncas, Marina Meila
This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations…
An Algorithmic Theory of Dependent Regularizers, Part 1: Submodular Structure
Hoyt Koepke, Marina Meila
We present an exploration of the rich theoretical connections between several classes of regularized models, network flows, and recent results in submodular function theory. This w…
Non-linear dimensionality reduction: Riemannian metric estimation and the problem of geometric discovery
Dominique Perraul-Joncas, Marina Meila
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorit…
How the initialization affects the stability of the k-means algorithm
Sebastien Bubeck, Marina Meila, Ulrike von Luxburg
We investigate the role of the initialization for the stability of the k-means clustering algorithm. As opposed to other papers, we consider the actual k-means algorithm and do not…