Quantum Clustering

Güleser Kalaycı Demir

Rupam Bhagawati, Sahinur Rahman Laskar, Bhagaban Swain

In the domain of Quantum Information processing (QIP), quantum clustering approach plays a vital role for processing information. The quantum clustering technique is basically used for providing effective information navigation and browsing mechanism. There are many classical approach of clustering the documents like k-means clustering algorithm, hierarchical clustering algorithm, information bottleneck clustering algorithm and many more. In this paper we proposed a clustering method which is based on quantum theory. For clustering the documents, such that which provides an agreeable result in comparison of existing classical approach.

Gonçalo Sousa, Duarte Magano

Clustering is a fundamental task in unsupervised learning. The goal is to partition unlabeled data into clusters such that similar elements are assigned to the same cluster, while elements in different clusters are dissimilar. We propose a quantum Monte Carlo approach to density estimation, a key routine in density peak clustering. Building on this approach, we develop quantum algorithms for the full clustering problem and three related tasks: decision clustering, cluster counting, and heavy cluster counting. For each one, we establish a polynomial quantum query speedup under assumptions on the scaling of dataset-dependent parameters. Numerical experiments suggest that these conditions are satisfied for several practically relevant settings.

Günter Mahler A, Volker A. Weberruß

Fengbo Kong, Hong Lai, Hailing Xiong

It is getting harder to deal with the large data sets by the classical hierarchical clustering algorithm, so we propose an efficient quantum hierarchical clustering algorithm, in which the quantum bit (qubit) is used to represent the data point in the space.For quantum entanglement, the distance between two data points is calculated through adding an auxiliary particle to construct the entangled state.Then a projective measurement is performed on the auxiliary particle alone.The distance between two points is acquired by the projective measurement.We use the distance of the cluster centroids as a measure of similarity between clusters.Also, based on the principle of the minimum cluster centroids distance, the nearest two clusters are merged.We aim at improving time and space complexity and effect of the clustering of the hierarchical clustering algorithm.

Günter Mahler A, Volker A. Weberruß