Related papers: Projector operators in clustering
The purpose of this article is to study operators whose kernel share some key features of Bergman kernels from complex analysis, and are approximate projectors. It turns out that they must be associated with a rich set of geometric data, on…
Clustering is one of the main tasks in exploratory data analysis and descriptive statistics where the main objective is partitioning observations in groups. Clustering has a broad range of application in varied domains like climate,…
We describe the representation of arbitrary density operators in terms of expectation values of simple projection operators. Two representations are presented which yield non--recursive schemes for experimentally determining the density…
Clustering by projection has been proposed as a way to preserve network structure in linear multi-agent systems. Here, we extend this approach to a class of nonlinear network systems. Additionally, we generalize our clustering method which…
A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e. g.…
Quantum kernels are reproducing kernel functions built using quantum-mechanical principles and are studied with the aim of outperforming their classical counterparts. The enthusiasm for quantum kernel machines has been tempered by recent…
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…
Quantum computation is the suitable orthogonal encoding of possibly holistic functional properties into state vectors, followed by a projective measurement.
A quantum computer is a hypothetical device in which the laws of quantum mechanics are used to introduce a degree of parallelism into computations and which could therefore significantly improve on the computational speed of a classical…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
Recently, we have used a projection operator to fix the number of particles in a second quantization approach in order to deal with the canonical ensemble. Having been applied earlier to handle various problems in nuclear physics that…
We review clustering as an analysis tool and the underlying concepts from an introductory perspective. What is clustering and how can clusterings be realised programmatically? How can data be represented and prepared for a clustering task?…
Quantum physical resources are directional quantities that can be formalized by unit vectors or the associated orthogonal projection operators. When compared to classical computational states which are elements of (power) sets vector…
Projection operators for the use within ab initio no-core shell model, are suggested.
Embeddings are ubiquitous in machine learning, appearing in recommender systems, NLP, and many other applications. Researchers and developers often need to explore the properties of a specific embedding, and one way to analyze embeddings is…
The problem of construction of projection operators on eigen-subspaces of symmetry operators is considered. This problem arises in many approximate methods for solving time-independent and time-dependent quantum problems, and its solution…
This is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory. After a brief introduction, we discuss quantum algorithms. We outline basic properties of quantum…
There is a growing interest in characterizing circular data found in biological systems. Such data are wide ranging and varied, from signal phase in neural recordings to nucleotide sequences in round genomes. Traditional clustering…
Despite the growing popularity of explainable and interpretable machine learning, there is still surprisingly limited work on inherently interpretable clustering methods. Recently, there has been a surge of interest in explaining the…
Projection operators are central to the algebraic formulation of quantum theory because both wavefunction and hermitian operators(observables) have spectral decomposition in terms of the spectral projections. Projection operators are…