相关论文: Optimal Riemannian quantization with an applicatio…

In this paper, we present a novel method for co-clustering, an unsupervised learning approach that aims at discovering homogeneous groups of data instances and features by grouping them simultaneously. The proposed method uses the entropy…

Online information has increased tremendously in today's age of Internet. As a result, the need has arose to extract relevant content from the plethora of available information. Researchers are widely using automatic text summarization…

Quantization summarizes continuous distributions by calculating a discrete approximation. Among the widely adopted methods for data quantization is Lloyd's algorithm, which partitions the space into Vorono\"i cells, that can be seen as…

Deploying transformer-based neural networks on resource-constrained edge devices presents a significant challenge. This challenge is often addressed through various techniques, such as low-rank approximation and mixed-precision…

This work presents a quantum mechanical framework for analyzing quantization-based optimization algorithms. The sampling process of the quantization-based search is modeled as a gradient-flow dissipative system, leading to a…

Quantum annealing algorithms belong to the class of meta-heuristic tools, applicable for solving binary optimization problems. Hardware implementations of quantum annealing, such as the quantum processing units (QPUs) produced by D-Wave…

Analog quantum computation offers a route to machine learning using controllable physical dynamics as a computational resource. However, many existing approaches rely on task-specific protocols or observables that are difficult to access…

Low-Rank Representation (LRR) highly suffers from discarding the locality information of data points in subspace clustering, as it may not incorporate the data structure nonlinearity and the non-uniform distribution of observations over the…

The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the {\it correct target clustering} of the samples…

Clustering is an important technique for identifying structural information in large-scale data analysis, where the underlying dataset may be too large to store. In many applications, recent data can provide more accurate information and…

Spectral clustering is a powerful unsupervised machine learning algorithm for clustering data with non convex or nested structures. With roots in graph theory, it uses the spectral properties of the Laplacian matrix to project the data in a…

We introduce a new regularization scheme for Quantum Cosmology in Loop Quantum Gravity (LQG) using the tools of Quantum Reduced Loop Gravity (QRLG). It is obtained considering density matrices for superposition of graphs based on…

We consider optimization problems on Riemannian manifolds with equality and inequality constraints, which we call Riemannian nonlinear optimization (RNLO) problems. Although they have numerous applications, the existing studies on them are…

Clustering, or grouping, dataset elements based on similarity can be used not only to classify a dataset into a few categories, but also to approximate it by a relatively large number of representative elements. In the latter scenario,…

Clustering is a critical component of decision-making in todays data-driven environments. It has been widely used in a variety of fields such as bioinformatics, social network analysis, and image processing. However, clustering accuracy…

Optimal Transport (OT) has fueled machine learning (ML) across many domains. When paired data measurements $(\boldsymbol{\mu}, \boldsymbol{\nu})$ are coupled to covariates, a challenging conditional distribution learning setting arises.…

Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the…

A hybrid quantum-classical algorithm is a computational scheme in which quantum circuits are used to extract information that is then processed by a classical routine to guide subsequent quantum operations. These algorithms are especially…

Quantum Reinforcement Learning (QRL) offers potential advantages over classical Reinforcement Learning, such as compact state space representation and faster convergence in certain scenarios. However, practical benefits require further…

The Sinkhorn algorithm is a numerical method for the solution of optimal transport problems. Here, I give a brief survey of this algorithm, with a strong emphasis on its geometric origin: it is natural to view it as a discretization, by…