Related papers: Manifold Hypothesis in Data Analysis: Double Geome…

For many machine learning tasks, the input data lie on a low-dimensional manifold embedded in a high dimensional space and, because of this high-dimensional structure, most algorithms are inefficient. The typical solution is to reduce the…

We present a generative learning framework for probabilistic sampling based on an extension of the Probabilistic Learning on Manifolds (PLoM) approach, which is designed to generate statistically consistent realizations of a random vector…

High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…

Parametrizations of data manifolds in shape spaces can be computed using the rich toolbox of Riemannian geometry. This, however, often comes with high computational costs, which raises the question if one can learn an efficient neural…

Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…

In change-point analysis, one aims at finding the locations of abrupt distributional changes (if any) in a sequence of multivariate observations. In this article, we propose some nonparametric methods based on averages of pairwise distances…

A new dimension reduction (DR) method for data sets is proposed by autonomous deforming of data manifolds. The deformation is guided by the proposed deforming vector field, which is defined by two kinds of virtual interactions between data…

We give explicit theoretical and heuristical bounds for how big does a data set sampled from a reach-1 submanifold M of euclidian space need to be, to be able to estimate the dimension of M with 90% confidence.

Estimating copulas with discrete marginal distributions is challenging, especially in high dimensions, because computing the likelihood contribution of each observation requires evaluating $2^{J}$ terms, with $J$ the number of discrete…

We present Manifold Alignment Determination (MAD), an algorithm for learning alignments between data points from multiple views or modalities. The approach is capable of learning correspondences between views as well as correspondences…

Monocular 3D human pose and shape estimation is an inherently ill-posed problem due to depth ambiguities, occlusions, and truncations. Recent probabilistic approaches learn a distribution over plausible 3D human meshes by maximizing the…

Feature selection is a widely used dimension reduction technique to select feature subsets because of its interpretability. Many methods have been proposed and achieved good results, in which the relationships between adjacent data points…

Motivated by the problem of nonparametric inference in high level digital image analysis, we introduce a general extrinsic approach for data analysis on Hilbert manifolds with a focus on means of probability distributions on such sample…

Outlier or anomaly detection is an important task in data analysis. We discuss the problem from a geometrical perspective and provide a framework that exploits the metric structure of a data set. Our approach rests on the manifold…

Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…

We consider the problems of classification and intrinsic dimension estimation on image data. A new subspace based classifier is proposed for supervised classification or intrinsic dimension estimation. The distribution of the data in each…

We consider problems of dimensionality reduction and learning data representations for continuous spaces with two or more independent degrees of freedom. Such problems occur, for example, when observing shapes with several components that…

In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…

We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches…

This article proposes a biconvex modification to convex biclustering in order to improve its performance in high-dimensional settings. In contrast to heuristics that discard a subset of noisy features a priori, our method jointly learns and…