Related papers: Manifold Learning with Geodesic Minimal Spanning T…
Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…
This paper presents mathematical results in support of the methodology of the probabilistic learning on manifolds (PLoM) recently introduced by the authors, which has been used with success for analyzing complex engineering systems. The…
Neural networks notoriously suffer from the problem of catastrophic forgetting, the phenomenon of forgetting the past knowledge when acquiring new knowledge. Overcoming catastrophic forgetting is of significant importance to emulate the…
Understanding the macroscopic characteristics of biological complexes demands precision and specificity in statistical ensemble modeling. One of the primary challenges in this domain lies in sampling from particular subsets of the…
Multimodal deep learning methods capture synergistic features from multiple modalities and have the potential to improve accuracy for stress detection compared to unimodal methods. However, this accuracy gain typically comes from high…
We develop algorithms for sampling from a probability distribution on a submanifold embedded in Rn. Applications are given to the evaluation of algorithms in 'Topological Statistics'; to goodness of fit tests in exponential families and to…
A random dot product graph (RDPG) is a generative model for networks in which vertices correspond to positions in a latent Euclidean space and edge probabilities are determined by the dot products of the latent positions. We consider RDPGs…
We developed a source detection algorithm based on the Minimal Spanning Tree (MST), that is a graph-theoretical method useful for finding clusters in a given set of points. This algorithm is applied to gamma-ray bidimensional images where…
This paper proposes a geometric estimator of dependency between a pair of multivariate samples. The proposed estimator of dependency is based on a randomly permuted geometric graph (the minimal spanning tree) over the two multivariate…
Nonlinear manifolds are pervasive in deep visual features, where Euclidean distances can misrepresent true similarity. This mismatch is particularly detrimental to prototype-based interpretable fine-grained recognition, where even subtle…
The shape of an object is an important characteristic for many vision problems such as segmentation, detection and tracking. Being independent of appearance, it is possible to generalize to a large range of objects from only small amounts…
The geometry of weight spaces and functional manifolds of neural networks play an important role towards 'understanding' the intricacies of ML. In this paper, we attempt to solve certain open questions in ML, by viewing them through the…
Recent advances in geometric deep-learning introduce complex computational challenges for evaluating the distance between meshes. From a mesh model, point clouds are necessary along with a robust distance metric to assess surface quality or…
The minimum degree spanning tree (MDST) problem requires the construction of a spanning tree $T$ for graph $G=(V,E)$ with $n$ vertices, such that the maximum degree $d$ of $T$ is the smallest among all spanning trees of $G$. In this paper,…
Many machine learning problems encode their data as a matrix with a possibly very large number of rows and columns. In several applications like neuroscience, image compression or deep reinforcement learning, the principal subspace of such…
We introduce a pioneering approach to self-supervised learning for point clouds, employing a geometrically informed mask selection strategy called GeoMask3D (GM3D) to boost the efficiency of Masked Auto Encoders (MAE). Unlike the…
This paper introduces an active learning framework for manifold Gaussian Process (GP) regression, combining manifold learning with strategic data selection to improve accuracy in high-dimensional spaces. Our method jointly optimizes a…
Representation learning is a fundamental but challenging problem, especially when the distribution of data is unknown. We propose a new representation learning method, termed Structure Transfer Machine (STM), which enables feature learning…
Consider an i.i.d. sample from an unknown density function supported on an unknown manifold embedded in a high dimensional Euclidean space. We tackle the problem of learning a distance between points, able to capture both the geometry of…
Understanding the reasons for the success of deep neural networks trained using stochastic gradient-based methods is a key open problem for the nascent theory of deep learning. The types of data where these networks are most successful,…