Abstract
DBSCAN is a famous density-based clustering algorithm that can discover clusters with arbitrary shapes without the minimal requirements of domain knowledge to determine the input parameters. However, DBSCAN is not suitable for databases with different local-density clusters and is also a very time-consuming clustering algorithm. In this paper, we present a quantum mutual MinPts-nearest neighbor graph (MMNG)-based DBSCAN algorithm. The proposed algorithm performs better on databases with different local-density clusters. Furthermore, the proposed algorithm has a dramatic increase in speed compared to its classic counterpart.
Highlights
DBSCAN is a famous density-based clustering algorithm that can discover clusters with arbitrary shapes without the minimal requirements of domain knowledge to determine the input parameters
The distinguishing advantage of the DBSCAN algorithm is that it can be used to discover arbitrarily shaped clusters. It does not need the minimal requirements of domain knowledge to determine the input parameters, and can exclude outliers from the clusters
We propose a quantum mutual MinPts-nearest neighbor graph (MMNG)based DBSCAN algorithm
Summary
We design a quantum mutual MinPts-nearest neighbor graph algorithm and a quantum DBSCAN algorithm and present a quantum MMNG-based DBSCAN algorithm. To solve this problem, we intend to screen the points in the Eps-neighborhood of pi with quantum search. A quantum distance black box is proposed. The proposed black box can accept two types of inputs, as illustrated in Fig. 1.|i is a one-state input and the index of point pi ; j is a superposition of inputs and includes the indexes of all the points. Based on the aforementioned black box, we designed algorithm 2 (quant_find_Eps-neighborhood as described below) as a subroutine of the quantum-based DBSCAN algorithm. With the expanding methodology offered in the original DBSCAN algorithm, the quantum-based DBSCAN algorithm quant_DBSCAN(DN , Eps , MinPts ) is presented hereafter, as shown in algorithm 3. The proposed algorithm divides the database into subsets first and applies the quantum DBSCAN algorithm to each subset. We select the average MinPts distance as the Eps of the subset
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