Related papers: Using Self-Organising Mappings to Learn the Struct…

We discover that deep ReLU neural network classifiers can see a low-dimensional Riemannian manifold structure on data. Such structure comes via the local data matrix, a variation of the Fisher information matrix, where the role of the model…

Multivariate information decompositions hold promise to yield insight into complex systems, and stand out for their ability to identify synergistic phenomena. However, the adoption of these approaches has been hindered by there being…

Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurately capturing these features requires a high-dimensional…

Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…

Self-Organizing Maps (SOMs) provide topology-preserving projections of high-dimensional data, yet their use as generative models remains largely unexplored. We show that the activation pattern of a SOM -- the squared distances to its…

Machine-part cell formation is used in cellular manufacturing in order to process a large variety, quality, lower work in process levels, reducing manufacturing lead-time and customer response time while retaining flexibility for new…

Machine learning allows unfolding high-dimensional spaces without binning at the LHC. The new SPINUP method extracts the unfolded distribution based on a neural network encoding the forward mapping, making it independent of the prior from…

Manifold learning approaches seek the intrinsic, low-dimensional data structure within a high-dimensional space. Mainstream manifold learning algorithms, such as Isomap, UMAP, $t$-SNE, Diffusion Map, and Laplacian Eigenmaps do not use data…

Many machine learning tasks, such as principal component analysis and low-rank matrix completion, give rise to manifold optimization problems. Although there is a large body of work studying the design and analysis of algorithms for…

Despite high-dimensionality of images, the sets of images of 3D objects have long been hypothesized to form low-dimensional manifolds. What is the nature of such manifolds? How do they differ across objects and object classes? Answering…

We propose a deep self-learning algorithm to learn the manifold structure of free-breathing and ungated cardiac data and to recover the cardiac CINE MRI from highly undersampled measurements. Our method learns the manifold structure in the…

Self-organization creates new order and shifts sub-boundaries while reorganizing energy and entropy within a control volume. This article examines pathway selection and tests whether maximizing the entropy generation rate can forecast…

Data augmentation is a widely used technique and an essential ingredient in the recent advance in self-supervised representation learning. By preserving the similarity between augmented data, the resulting data representation can improve…

It is shown that applying manifold learning techniques to Poincar\'e sections of high-dimensional, chaotic dynamical systems can uncover their low-dimensional topological organization. Manifold learning provides a low-dimensional embedding…

Deep neural networks can approximate functions on different types of data, from images to graphs, with varied underlying structure. This underlying structure can be viewed as the geometry of the data manifold. By extending recent advances…

Dataset distillation aims to synthesize a compact subset of the original data, enabling models trained on it to achieve performance comparable to those trained on the original large dataset. Existing distribution-matching methods are…

Unsupervised learning enables modeling complex images without the need for annotations. The representation learned by such models can facilitate any subsequent analysis of large image datasets. However, some generative factors that cause…

A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The…

We propose a novel algorithm for supervised dimensionality reduction named Manifold Partition Discriminant Analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is…

Self-Organizing Map (SOM) is a neural network model which is used to obtain a topology-preserving mapping from the (usually high dimensional) input/feature space to an output/map space of fewer dimensions (usually two or three in order to…