Related papers: Coreset Clustering on Small Quantum Computers
Clustering categorical data is an integral part of data mining and has attracted much attention recently. In this paper, we present k-histogram, a new efficient algorithm for clustering categorical data. The k-histogram algorithm extends…
Adiabatic quantum computers are a promising platform for approximately solving challenging optimization problems. We present a quantum approach to solving the balanced $k$-means clustering training problem on the D-Wave 2000Q adiabatic…
This paper introduces two techniques that make the standard Quantum Approximate Optimization Algorithm (QAOA) more suitable for constrained optimization problems. The first technique describes how to use the outcome of a prior greedy…
As quantum computing advances, quantum approximate optimization algorithms (QAOA) have shown promise in addressing combinatorial optimization problems. However, the limitations of Noisy Intermediate Scale Quantum (NISQ) devices hinder the…
In optimization or machine learning problems we are given a set of items, usually points in some metric space, and the goal is to minimize or maximize an objective function over some space of candidate solutions. For example, in clustering…
Over the past few years several quantum machine learning algorithms were proposed that promise quantum speed-ups over their classical counterparts. Most of these learning algorithms either assume quantum access to data -- making it unclear…
Machine Learning (ML) models are trained using historical data to classify new, unseen data. However, traditional computing resources often struggle to handle the immense amount of data, commonly known as Big Data, within a reasonable time…
We propose a new algorithm for k-means clustering in a distributed setting, where the data is distributed across many machines, and a coordinator communicates with these machines to calculate the output clustering. Our algorithm guarantees…
The efficient management of energy communities relies on the solution of the "prosumer problem", i.e., the problem of scheduling the household loads on the basis of the user needs, the electricity prices, and the availability of local…
Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…
Coresets for $k$-means and $k$-median problems yield a small summary of the data, which preserve the clustering cost with respect to any set of $k$ centers. Recently coresets have also been constructed for constrained $k$-means and…
Computational quantum technologies are entering a new phase in which noisy intermediate-scale quantum computers are available, but are still too small to benefit from active error correction. Even with a finite coherence budget to invest in…
Interconnecting clusters of qubits will be an essential element of scaling up future quantum computers. Operations between quantum processing units (QPUs) are usually significantly slower and costlier than those within a single QPU, so…
Quantum computing promises solutions to classically difficult and new-found problems through controlling the subtleties of quantum computing. The Quantum Approximate Optimisation Algorithm (QAOA) is a recently proposed quantum algorithm…
We study beyond worst case analysis for the $k$-means problem where the goal is to model typical instances of $k$-means arising in practice. Existing theoretical approaches provide guarantees under certain assumptions on the optimal…
This paper addresses the limitations of conventional vector quantization algorithms, particularly K-Means and its variant K-Means++, and investigates the Stochastic Quantization (SQ) algorithm as a scalable alternative for high-dimensional…
Kernel-based K-means clustering has gained popularity due to its simplicity and the power of its implicit non-linear representation of the data. A dominant concern is the memory requirement since memory scales as the square of the number of…
We give a quantum approximation scheme (i.e., $(1 + \varepsilon)$-approximation for every $\varepsilon > 0$) for the classical $k$-means clustering problem in the QRAM model with a running time that has only polylogarithmic dependence on…
Motivated by practical generalizations of the classic $k$-median and $k$-means objectives, such as clustering with size constraints, fair clustering, and Wasserstein barycenter, we introduce a meta-theorem for designing coresets for…
The K-Modes algorithm, developed for clustering categorical data, is of high algorithmic simplicity but suffers from unreliable performances in clustering quality and clustering efficiency, both heavily influenced by the choice of initial…