Related papers: A theory of stratification learning
In this paper, we aim to compute numerical approximation integral by using an adaptive Monte Carlo algorithm. We propose a stratified sampling algorithm based on an iterative method which splits the strata following some quantities called…
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…
In this paper, we investigate a sheaf-theoretic interpretation of stratification learning from geometric and topological perspectives. Our main result is the construction of stratification learning algorithms framed in terms of a sheaf on a…
Point cloud analysis (such as 3D segmentation and detection) is a challenging task, because of not only the irregular geometries of many millions of unordered points, but also the great variations caused by depth, viewpoint, occlusion, etc.…
We survey the application of a relatively new branch of statistical physics--"community detection"-- to data mining. In particular, we focus on the diagnosis of materials and automated image segmentation. Community detection describes the…
We present a discriminative clustering approach in which the feature representation can be learned from data and moreover leverage labeled data. Representation learning can give a similarity-based clustering method the ability to…
Topological learning is a wide research area aiming at uncovering the mutual spatial relationships between the elements of a set. Some of the most common and oldest approaches involve the use of unsupervised competitive neural networks.…
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 i.e. the gradient of the log density of a noise-corrupted…
We start by considering the problem of estimating intrinsic distances on a smooth submanifold. We show that minimax optimality can be obtained via a reconstruction of the surface, and discuss the use of a particular mesh construction -- the…
We address the problem of learning linear system models from observing multiple trajectories from different system dynamics. This framework encompasses a collaborative scenario where several systems seeking to estimate their dynamics are…
The problem of learning a manifold structure on a dataset is framed in terms of a generative model, to which we use ideas behind autoencoders (namely adversarial/Wasserstein autoencoders) to fit deep neural networks. From a machine learning…
We propose a framework for the joint inference of network topology, multi-type interaction kernels, and latent type assignments in heterogeneous interacting particle systems from multi-trajectory data. This learning task is a challenging…
Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…
The paper tackles the problem of clustering multiple networks, directed or not, that do not share the same set of vertices, into groups of networks with similar topology. A statistical model-based approach based on a finite mixture of…
Mixup is a data augmentation technique that relies on training using random convex combinations of data points and their labels. In recent years, Mixup has become a standard primitive used in the training of state-of-the-art image…
We present a new way to summarize and select mixture models via the hierarchical clustering tree (dendrogram) constructed from an overfitted latent mixing measure. Our proposed method bridges agglomerative hierarchical clustering and…
Matrix Factorization has emerged as a widely adopted framework for modeling data exhibiting low-rank structures. To address challenges in manifold learning, this paper presents a subspace-constrained quadratic matrix factorization model.…
In order to efficiently explore the chemical space of all possible small molecules, a common approach is to compress the dimension of the system to facilitate downstream machine learning tasks. Towards this end, we present a data driven…
Subspace clustering has been extensively studied from the hypothesis-and-test, algebraic, and spectral clustering based perspectives. Most assume that only a single type/class of subspace is present. Generalizations to multiple types are…
In this paper, we propose a point cloud classification method based on graph neural network and manifold learning. Different from the conventional point cloud analysis methods, this paper uses manifold learning algorithms to embed point…