Related papers: Quantum spectral clustering algorithm for unsuperv…

This article introduces a novel approach to perform the simulation of a single qubit quantum algorithm using laser beams. Leveraging the polarization states of photonic qubits, and inspired by variational quantum eigensolvers, we develop a…

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…

Comparison of three kind of the clustering and find cost function and loss function and calculate them. Error rate of the clustering methods and how to calculate the error percentage always be one on the important factor for evaluating the…

Coresets have become an invaluable tool for solving $k$-means and kernel $k$-means clustering problems on large datasets with small numbers of clusters. On the other hand, spectral clustering works well on sparse graphs and has recently…

Nearest-neighbour clustering is a simple yet powerful machine learning algorithm that finds natural application in the decoding of signals in classical optical-fibre communication systems. Quantum k-means clustering promises a speed-up over…

A quantum computer promises efficient processing of certain computational tasks that are intractable with classical computer technology. While basic principles of a quantum computer have been demonstrated in the laboratory, scalability of…

Clustering, a fundamental activity in unsupervised learning, is notoriously difficult when the feature space is high-dimensional. Fortunately, in many realistic scenarios, only a handful of features are relevant in distinguishing clusters.…

A unitary coupled-cluster (UCC) form for the wavefunction in the variational quantum eigensolver has been suggested as a systematic way to go beyond the mean-field approximation and include electron correlation in solving quantum chemistry…

Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…

The analysis of continously larger datasets is a task of major importance in a wide variety of scientific fields. In this sense, cluster analysis algorithms are a key element of exploratory data analysis, due to their easiness in the…

Kernel-based clustering algorithm can identify and capture the non-linear structure in datasets, and thereby it can achieve better performance than linear clustering. However, computing and storing the entire kernel matrix occupy so large…

The $k$-means algorithm is a prevalent clustering method due to its simplicity, effectiveness, and speed. However, its main disadvantage is its high sensitivity to the initial positions of the cluster centers. The global $k$-means is a…

We propose a deep learning approach for discovering kernels tailored to identifying clusters over sample data. Our neural network produces sample embeddings that are motivated by--and are at least as expressive as--spectral clustering. Our…

Quantum processors may enhance machine learning by mapping high-dimensional data onto quantum systems for processing. Conventional feature maps, for encoding data onto a quantum circuit are currently impractical, as the number of entangling…

Spectral clustering techniques are valuable tools in signal processing and machine learning for partitioning complex data sets. The effectiveness of spectral clustering stems from constructing a non-linear embedding based on creating a…

We build upon recent advances in graph signal processing to propose a faster spectral clustering algorithm. Indeed, classical spectral clustering is based on the computation of the first k eigenvectors of the similarity matrix' Laplacian,…

We examine the efficiency of clustering a set of points, when the encompassing metric space may be preprocessed in advance. In computational problems of this genre, there is a first stage of preprocessing, whose input is a collection of…

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…

Color quantization is an important operation with numerous applications in graphics and image processing. Most quantization methods are essentially based on data clustering algorithms. However, despite its popularity as a general purpose…

Clustering is an unsupervised learning method that constitutes a cornerstone of an intelligent data analysis process. It is used for the exploration of inter-relationships among a collection of patterns, by organizing them into homogeneous…