导　　师： 蒋静坪

学科专业： H08

授予学位： 博士

作　　者： ;

机构地区： 浙江大学电气工程学院

摘　　要： 数据聚类是模式识别的重要分支，它在模式分析、数据挖掘、信息获取、图像分割、决策等领域都有重要的应用。而这些领域的问题，通常都没有关于数据的先验知识可供利用。正是由于实际问题存在这些难以逾越的限制条件，因此，数据聚类应运而生，它特别适合对未标记数据点间的关系进行探索。数据聚类就是研究如何对未标记的数据进行分组或分类的学科，它不需要事先提供任何标记的样本，聚类的任务就是找出大量数据的内在结构，将这些未标记的数据点聚合成有意义的类别，以对它们的结构进行评价。在典型的聚类算法中，用于聚类的数据点是固定不动的，通过设计函数找到聚类中心或边界。然而，近年来，一些研究者提出动点聚类的新思想，他们将数据点考虑为自身可移动的AGENT，通过设计简单规则，让数据点自动完成聚类。
　　 另一方面，量子计算的研究方兴未艾，在过去十年间，量子计算取得了一系列惊人的成就，以奇特的量子效应，如量子内在并行性、量子纠缠等为基础的量子算法，已经提供了量子计算可能比经典计算更强大的有力证据。如SHOR的大数质因子分解量子算法，将经典计算中的NP完全问题转化为一个P问题，以多项式时间完成经典算法指数时间才能完成的任务。这些成就让我们意识到量子算法可能比已知最好的经典算法更快更好地解决问题，甚至解决某些经典计算无法有效解决的问题。更重要的是，它提供了一条寻找潜在算法加速的新途径。
　　 本文的研究主要分为两个部分：(1)经典世界中的动点聚类算法。受近年来兴起的动点聚类思想的启发，本文提出基于改进随机游动模型，基于复杂网络上的FLOCKING，基于演化网络上的博弈等几种动点聚类算法。(2)量子世界中的聚类算法。受量子计 Cluster analysis is a main branch of Pattern Recognition, which is widely used in many fields such as pattern analysis, data mining, information retrieval and image segmen-tation. In these fields, however, there is usually little priori knowledge available about the data. In response to these restrictions, clustering methodology come into being, which is particularly appropriate for the investigation of interrelationships between unlabeled data points. In other words, Cluster analysis is the formal study of algorithms and methods for grouping or classifying unlabeled data points, and its task is to find the inherent structure of a given collection of unlabeled data points and group them into meaningful clusters. In the typical clustering algorithms, data points for clustering are fixed in their positions, and they are grouped by designing different functions to find the clustering centers or bound-aries. In recent years, however, a new idea has emerged in clustering algorithms that some researchers begin to consider data points as movable agents or the like. They move in space according to some simple rules and form clusters automatically. In addition, Quantum Computation is an extremely exciting and rapidly growing field. More recently, an increasing number of researchers with different backgrounds, ranging from physics, computer sciences and information theory to mathematics and philosophy, are involved in researching properties of quantum-based computation. During the last decade, a series of significant breakthroughs have been made. One was that Peter Shor surprised the world by proposing a polynomial-time quantum algorithm for integer factor-ization in 1994, while in the classical world the best-known classical factoring algorithm works in exponential time. Three years later, Lov Grover proved that a quantum computer could search an unsorted database in the square root of the time. These successes make us realize that powerful quantum computers can figure out solutions faster and better than the best kn

关 键 词： 模式识别 无监督学习 数据聚类 随机游动 复杂网络 量子博弈

领　　域： [自动化与计算机技术] [自动化与计算机技术] [自动化与计算机技术] [自动化与计算机技术]