Related papers: Elastic principal manifolds and their practical ap…

Given a designer created free-form surface in 3d space, our method computes a grid composed of elastic elements which are completely planar and straight. Only by fixing the ends of the planar elements to appropriate locations, the 2d grid…

We present a framework for efficiently approximating differential-geometric primitives on arbitrary manifolds via construction of an atlas graph representation, which leverages the canonical characterization of a manifold as a finite…

There has been an intense recent activity in embedding of very high dimensional and nonlinear data structures, much of it in the data science and machine learning literature. We survey this activity in four parts. In the first part we cover…

We propose a new approach to analyze data that naturally lie on manifolds. We focus on a special class of manifolds, called direct product manifolds, whose intrinsic dimension could be very high. Our method finds a low-dimensional…

Principal component analysis is a simple yet useful dimensionality reduction technique in modern machine learning pipelines. In consequential domains such as college admission, healthcare and credit approval, it is imperative to take into…

A regularized version of Mixture Models is proposed to learn a principal graph from a distribution of $D$-dimensional data points. In the particular case of manifold learning for ridge detection, we assume that the underlying manifold can…

We provide a probabilistic and infinitesimal view of how the principal component analysis procedure (PCA) can be generalized to analysis of nonlinear manifold valued data. Starting with the probabilistic PCA interpretation of the Euclidean…

Classical vector analysis is the predominant formalism used by engineers of computational electromagnetism, despite the fact that manifold as a theoretical concept has existed for a century. This paper discusses the benefits of manifolds…

Motivated by the analysis of high-dimensional neuroimaging signals located over the cortical surface, we introduce a novel Principal Component Analysis technique that can handle functional data located over a two-dimensional manifold. For…

We propose a novel type of planar-to-spatial deployable structures that we call elastic geodesic grids. Our approach aims at the approximation of freeform surfaces with spatial grids of bent lamellas which can be deployed from a planar…

Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…

A core challenge in the interpretation of deep neural networks is identifying commonalities between the underlying algorithms implemented by distinct networks trained for the same task. Motivated by this problem, we introduce DYNAMO, an…

We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good…

One develops a fast computational methodology for principal component analysis on manifolds. Instead of estimating intrinsic principal components on an object space with a Riemannian structure, one embeds the object space in a numerical…

Flexibility at hardware level is the main driving force behind adaptive systems whose aim is to realise microarhitecture deconfiguration 'online'. This feature allows the software/hardware stack to tolerate drastic changes of the workload…

The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of…

We consider the classification problem and focus on nonlinear methods for classification on manifolds. For multivariate datasets lying on an embedded nonlinear Riemannian manifold within the higher-dimensional ambient space, we aim to…

This paper considers the problem of finding a meaningful template function that represents the common pattern of a sample of curves. To address this issue, a novel algorithm based on a robust version of the isometric featuring mapping…

Edge-centric distributed computations have appeared as a recent technique to improve the shortcomings of think-like-a-vertex algorithms on large scale-free networks. In order to increase parallelism on this model, edge partitioning -…

We propose a novel method of finding principal components in multivariate data sets that lie on an embedded nonlinear Riemannian manifold within a higher-dimensional space. Our aim is to extend the geometric interpretation of PCA, while…