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Found 20 papers, 3 papers with code
The Parametric Stability of Well-separated Spherical Gaussian Mixtures
We quantify the parameter stability of a spherical Gaussian Mixture Model (sGMM) under small perturbations in distribution space.
Dictionary-based Manifold Learning
We propose a paradigm for interpretable Manifold Learning for scientific data analysis, whereby we parametrize a manifold with $d$ smooth functions from a scientist-provided dictionary of meaningful, domain-related functions.
Double Diffusion Maps and their Latent Harmonics for Scientific Computations in Latent Space
A second round of Diffusion Maps on those latent coordinates allows the approximation of the reduced dynamical models.
Tangent Space Least Adaptive Clustering
The biasing of dynamical simulations along collective variables uncovered by unsupervised learning has become a standard approach in analysis of molecular systems.
A class of network models recoverable by spectral clustering
Finding communities in networks is a problem that remains difficult, in spite of the amount of attention it has recently received.
Guarantees for Hierarchical Clustering by the Sublevel Set method
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 any assumptions about the distribution that generated the data.
Measuring the Robustness of Graph Properties
In this paper, we propose a perturbation framework to measure the robustness of graph properties.
How to tell when a clustering is (approximately) correct using convex relaxations
We introduce the Sublevel Set (SS) method, a generic method to obtain sufficient guarantees of near-optimality and uniqueness (up to small perturbations) for a clustering.
Manifold Coordinates with Physical Meaning
Manifold embedding algorithms map high-dimensional data down to coordinates in a much lower-dimensional space.
Graph Clustering: Block-models and model free results
In this paper, we propose a framework, in which we obtain "correctness" guarantees without assuming the data comes from a model.
Nearly Isometric Embedding by Relaxation
Many manifold learning algorithms aim to create embeddings with low or no distortion (i. e. isometric).
megaman: Manifold Learning with Millions of points
Manifold Learning is a class of algorithms seeking a low-dimensional non-linear representation of high-dimensional data.
Recursive Inversion Models for Permutations
We develop a new exponential family probabilistic model for permutations that can capture hierarchical structure, and that has the well known Mallows and generalized Mallows models as subclasses.
Graph Sensitive Indices for Comparing Clusterings
The motivation for looking at new ways for comparing clusterings stems from the fact that the existing clustering indices are based on set cardinality alone and do not consider the positions of data points.
Improved graph Laplacian via geometric self-consistency
We address the problem of setting the kernel bandwidth used by Manifold Learning algorithms to construct the graph Laplacian.
Estimating Vector Fields on Manifolds and the Embedding of Directed Graphs
This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information.
An Algorithmic Theory of Dependent Regularizers, Part 1: Submodular Structure
In Part 2, we describe the full regularization path of a class of penalized regression problems with dependent variables that includes the graph-guided LASSO and total variation constrained models.
Non-linear dimensionality reduction: Riemannian metric estimation and the problem of geometric discovery
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction.
An Experimental Comparison of Several Clustering and Initialization Methods
In the first part of the paper, we perform an experimental comparison between three batch clustering algorithms: the Expectation-Maximization (EM) algorithm, a winner take all version of the EM algorithm reminiscent of the K-means algorithm, and model-based hierarchical agglomerative clustering.
Directed Graph Embedding: an Algorithm based on Continuous Limits of Laplacian-type Operators
This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information.
