Related papers: Projector operators in clustering

Clustering is an unsupervised technique of Data Mining. It means grouping similar objects together and separating the dissimilar ones. Each object in the data set is assigned a class label in the clustering process using a distance measure.…

Of crucial importance to the development of quantum computing and information has been the construction of a quantum operations formalism that admits a description of quantum noise while simultaneously revealing the behavior of an open…

The Quantum Query Model is a framework that allows us to express most known quantum algorithms. Algorithms represented by this model consist on a set of unitary operators acting over a finite Hilbert space, and a final measurement step…

The semantic frame induction tasks are defined as a clustering of words into the frames that they evoke, and a clustering of their arguments according to the frame element roles that they should fill. In this paper, we address the latter…

In a series of papers by Dai and colleagues [1,2], a feature map (or kernel) was introduced for semi- and unsupervised learning. This feature map is build from the output of an ensemble of classifiers trained without using the ground-truth…

Frames in a separable quaternionic Hilbert space were introduced and studied in [17] to have more applications. In this paper, we extend the study of frames in quaternionic Hilbert spaces and introduce different types of duals of a frame in…

The k-means algorithm is a partitional clustering method. Over 60 years old, it has been successfully used for a variety of problems. The popularity of k-means is in large part a consequence of its simplicity and efficiency. In this paper…

Mechanical resonators are gradually becoming available as new quantum systems. Quantum optics in combination with optomechanical interactions (quantum optomechanics) provides a particularly helpful toolbox for generating and controlling…

We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…

We address the problem of communicating domain knowledge from a user to the designer of a clustering algorithm. We propose a protocol in which the user provides a clustering of a relatively small random sample of a data set. The algorithm…

Classification neural networks fail to detect inputs that do not fall inside the classes they have been trained for. Runtime monitoring techniques on the neuron activation pattern can be used to detect such inputs. We present an approach…

In the last years, Distributed Visualization over Personal Computer (PC) clusters has become important for research and industrial communities. They have made large-scale visualizations practical and more accessible. In this work we survey…

An extension of Transformers is proposed that enables explicit relational reasoning through a novel module called the Abstractor. At the core of the Abstractor is a variant of attention called relational cross-attention. The approach is…

Following the B. Hiley belief that unresolved problems of conventional quantum mechanics could be the result of a wrong mathematical structure, an alternative basic structure is suggested. Critical part of the structure is modification of…

Motivated by the concept of network motifs we construct certain clustering methods (functors) which are parametrized by a given collection of motifs (or representers).

Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT…

Projective Norms are a class of tensor norms that map on the input and output spaces. These norms are useful for providing a measure of entanglement. Calculating the projective norms is an NP-hard problem, which creates challenges in…

Improving the explainability of the results from machine learning methods has become an important research goal. Here, we study the problem of making clusters more interpretable by extending a recent approach of [Davidson et al., NeurIPS…

We describe a framework for encoding cluster combinatorics using categorical methods. We give a definition of an abstract cluster structure, which captures the essence of cluster mutation at a tropical level and show that cluster algebras,…

This paper presents the definition and implementation of a quantum computer architecture to enable creating a new computational device - a quantum computer as an accelerator. In this paper, we present explicitly the idea of a quantum…