103 citations · 268 across the 27 of their papers we have counts for
27 papers
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…
Dictionary-based Manifold Learning
Hanyu Zhang, Samson Koelle, Marina Meila
We propose a paradigm for interpretable Manifold Learning for scientific data analysis, whereby we parametrize a manifold with smooth functions from a scientist-provided dictio…
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…
To ArXiv or not to ArXiv: A Study Quantifying Pros and Cons of Posting Preprints Online
Charvi Rastogi, Ivan Stelmakh, Xinwei Shen +4
Double-blind conferences have engaged in debates over whether to allow authors to post their papers online on arXiv or elsewhere during the review process. Independently, some auth…
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…
Measuring the Robustness of Graph Properties
Yali Wan, Marina Meila
In this paper, we propose a perturbation framework to measure the robustness of graph properties. Although there are already perturbation methods proposed to tackle this problem, t…
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…
How to sample connected -partitions of a graph
Marina Meila
A connected undirected graph is given. This paper presents an algorithm that samples (non-uniformly) a partition of the graph nodes , such that th…
megaman: Manifold Learning with Millions of points
James McQueen, Marina Meila, Jacob VanderPlas +1
Manifold Learning is a class of algorithms seeking a low-dimensional non-linear representation of high-dimensional data. Thus manifold learning algorithms are, at least in theory,…
Graph Sensitive Indices for Comparing Clusterings
Zaeem Hussain, Marina Meila
This report discusses two new indices for comparing clusterings of a set of points. The motivation for looking at new ways for comparing clusterings stems from the fact that the ex…
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…
An Experimental Comparison of Several Clustering and Initialization Methods
Marina Meila, David Heckerman
We examine methods for clustering in high dimensions. In the first part of the paper, we perform an experimental comparison between three batch clustering algorithms: the Expectati…
Unsupervised spectral learning
Susan Shortreed, Marina Meila
In spectral clustering and spectral image segmentation, the data is partioned starting from a given matrix of pairwise similarities S. the matrix S is constructed by hand, or learn…
Consensus ranking under the exponential model
Marina Meila, Kapil Phadnis, Arthur Patterson +1
We analyze the generalized Mallows model, a popular exponential model over rankings. Estimating the central (or consensus) ranking from data is NP-hard. We obtain the following new…
Estimation and Clustering with Infinite Rankings
Marina Meila, Le Bao
This paper presents a natural extension of stagewise ranking to the the case of infinitely many items. We introduce the infinite generalized Mallows model (IGM), describe its prope…