Related papers: Dynamic quantum clustering: a method for visual ex…
The fundamental aim of clustering algorithms is to partition data points. We consider tasks where the discovered partition is allowed to vary with some covariate such as space or time. One approach would be to use fragmentation-coagulation…
Micro-panel data are collected and analysed in many research and industry areas. Cluster analysis of micro-panel data is an unsupervised learning exploratory method identifying subgroup clusters in a data set which include homogeneous…
The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum random walk (QRW) with the problem of data clustering, and develop two clustering algorithms based on the one…
Quantum computing is a promising paradigm based on quantum theory for performing fast computations. Quantum algorithms are expected to surpass their classical counterparts in terms of computational complexity for certain tasks, including…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…
In this work clustering schemes for uncertain and structured data are considered relying on the notion of Wasserstein barycenters, accompanied by appropriate clustering indices based on the intrinsic geometry of the Wasserstein space where…
A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates…
It is often of interest to perform clustering on longitudinal data, yet it is difficult to formulate an intuitive model for which estimation is computationally feasible. We propose a model-based clustering method for clustering objects that…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
To cluster data is to separate samples into distinctive groups that should ideally have some cohesive properties. Today, numerous clustering algorithms exist, and their differences lie essentially in what can be perceived as ``cohesive…
Clustering is a data analysis method for extracting knowledge by discovering groups of data called clusters. Among these methods, state-of-the-art density-based clustering methods have proven to be effective for arbitrary-shaped clusters.…
This article sets up a formalism to describe stochastic thermodynamics for driven out-of-equilibrium open quantum systems. A stochastic Schr\"odinger equation allows to construct quantum trajectories describing the dynamics of the system…
Clustering points in a vector space or nodes in a graph is a ubiquitous primitive in statistical data analysis, and it is commonly used for exploratory data analysis. In practice, it is often of interest to "refine" or "improve" a given…
Numerous lines of experimental, numerical and analytical evidence indicate that it is surprisingly easy to locate optimal controls steering quantum dynamical systems to desired objectives. This has enabled the control of complex quantum…
A general dynamical system composed by two coupled sectors is considered. The initial time configuration of one of these sectors is described by a set of classical data while the other is described by standard quantum data. These dynamical…
Correlation clustering is a flexible framework for partitioning data based solely on pairwise similarity or dissimilarity information, without requiring the number of clusters as input. However, in many practical scenarios, these pairwise…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
We derive an efficient method to perform clustering of nodes in Gaussian graphical models directly from sample data. Nodes are clustered based on the similarity of their network neighborhoods, with edge weights defined by partial…
A new approach to clustering, based on the physical properties of inhomogeneous coupled chaotic maps, is presented. A chaotic map is assigned to each data-point and short range couplings are introduced. The stationary regime of the system…
Clustering artworks is difficult for several reasons. On the one hand, recognizing meaningful patterns in accordance with domain knowledge and visual perception is extremely difficult. On the other hand, applying traditional clustering and…