When dealing with datasets comprising high‐dimensional points, it is usually advantageous
to discover some data structure. A fundamental information needed to this aim is the …

Dealing with uncertainty in applications of machine learning to real-life data critically
depends on the knowledge of intrinsic dimensionality (ID). A number of methods have been …

In this study, we prove that an intrinsic low dimensionality of covariates is the main factor that
determines the performance of deep neural networks (DNNs). DNNs generally provide …

We propose an algorithm called Sparse Manifold Clustering and Embedding (SMCE) for
simultaneous clustering and dimensionality reduction of data lying in multiple nonlinear …

In this work, we propose a novel framework for estimating the dimension of the data manifold
using a trained diffusion model. A diffusion model approximates the score function ie the …

Abstract The “Big Data” era has arisen, driven by the increasing availability of data from
multiple sources such as social media, online transactions, network sensors or mobile …

We study semi-supervised learning when the data consists of multiple intersecting
manifolds. We give a finite sample analysis to quantify the potential gain of using unlabeled …

Spectral clustering (SC) is a large family of grouping methods that partition data using
eigenvectors of an affinity matrix derived from the data. Though SC methods have been …

Recovering hidden structure from complex and noisy non-linear data is one of the most
fundamental problems in machine learning and statistical inference. While such data is often …

Many natural image sets are samples of a low-dimensional manifold in the space of all
possible images. Understanding this manifold is a key first step in understanding many sets …