论文标题
量子密度峰簇
Quantum density peak clustering
论文作者
论文摘要
在处理大型非结构化数据集并发现其中的新模式和相关性时，聚类算法至关重要，从科学研究到医学成像和营销分析，应用程序中的新模式和相关性至关重要。在这项工作中，我们介绍了密度峰值聚类算法的量子版本，该算法是基于量子例程，以最小发现。我们证明，根据数据集的结构，对密度峰值聚类的决策版本具有量子加速。具体而言，加速度取决于诱导图的树的高度，即与密度较高的连接图与最近元素的连接图。我们讨论了这种情况，表明我们的算法特别适用于高维数据集。最后，我们在真正的量子设备上使用玩具问题对我们的建议进行了基准测试。
Clustering algorithms are of fundamental importance when dealing with large unstructured datasets and discovering new patterns and correlations therein, with applications ranging from scientific research to medical imaging and marketing analysis. In this work, we introduce a quantum version of the density peak clustering algorithm, built upon a quantum routine for minimum finding. We prove a quantum speedup for a decision version of density peak clustering depending on the structure of the dataset. Specifically, the speedup is dependent on the heights of the trees of the induced graph of nearest-highers, i.e., the graph of connections to the nearest elements with higher density. We discuss this condition, showing that our algorithm is particularly suitable for high-dimensional datasets. Finally, we benchmark our proposal with a toy problem on a real quantum device.
