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We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…

Deep hashing enables image retrieval by end-to-end learning of deep representations and hash codes from training data with pairwise similarity information. Subject to the distribution skewness underlying the similarity information, most…

This study uses stacked generalization, which is a two-step process of combining machine learning methods, called meta or super learners, for improving the performance of algorithms in step one (by minimizing the error rate of each…

We introduce harmonization, an ensembling method that combines several "noisy" decoders to generate highly accurate decoding predictions. Harmonized ensembles of MWPM-based decoders achieve lower logical error rates than their individual…

Multilayer bootstrap network builds a gradually narrowed multilayer nonlinear network from bottom up for unsupervised nonlinear dimensionality reduction. Each layer of the network is a nonparametric density estimator. It consists of a group…

Deep neural networks have been used in various machine learning applications and achieved tremendous empirical successes. However, training deep neural networks is a challenging task. Many alternatives have been proposed in place of…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

In this paper we try to find examples of integrable natural Hamiltonian systems on the sphere $S^2$ with the symmetries of each Platonic polyhedra. Although some of these systems are known, their expression is extremely complicated; we try…

Clustering is an unsupervised machine learning method grouping data samples into clusters of similar objects. In practice, clustering has been used in numerous applications such as banking customers profiling, document retrieval, image…

This paper studies the hierarchical clustering problem, where the goal is to produce a dendrogram that represents clusters at varying scales of a data set. We propose the ParChain framework for designing parallel hierarchical agglomerative…

Hashing techniques are in great demand for a wide range of real-world applications such as image retrieval and network compression. Nevertheless, existing approaches could hardly guarantee a satisfactory performance with the extremely…

Parametric linear programming is a central operation for polyhedral computations, as well as in certain control applications.Here we propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems.This type…

Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…

The classification of imbalanced data streams, which have unequal class distributions, is a key difficulty in machine learning, especially when dealing with multiple classes. While binary imbalanced data stream classification tasks have…

The accuracy of meshless methods like Smoothed Particle Hydrodynamics (SPH) is highly dependent on the quality of the particle distribution. Existing particle initialization techniques often struggle to simultaneously achieve adaptive…

The hierarchical structure inherent in many real-world datasets makes the modeling of such hierarchies a crucial objective in both unsupervised and supervised machine learning. While recent advancements have introduced deep architectures…

Topological data analysis is an emerging field that applies the study of topological invariants to data. Perhaps the simplest of these invariants is the number of connected components or clusters. In this work, we explore a topological…

We consider the problem of maintaining a hierarchical agglomerative clustering (HAC) in the dynamic setting, when the input is subject to point insertions and deletions. We introduce DynHAC - the first dynamic HAC algorithm for the popular…

Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…

The performance of gradient-based optimization strategies depends heavily on the initial weights of the parametric model. Recent works show that there exist weight initializations from which optimization procedures can find the…