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Hamiltonian-based data clustering and classification

基于哈密顿量的数据聚类和分类

基本信息

批准号：
EP/H011811/1
负责人：
Alessandro Astolfi
金额：
$ 13.92万
依托单位：
Imperial College London
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2009
资助国家：
英国
起止时间：
2009 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FH011811%2F1
关键词：
Hamiltonian based data clustering classification

项目摘要

For any extended entities such as convoys of vehicles, crowds of people, dust clouds or even rigid vehicles seen at close range, data clustering is an essential step in data processing and it is at the core of data recognition, classification and tracking procedures. Observations of such diffuse entities will generally be represented by points in a properly defined space. These points may represent observations of position, activity or other attributes, associated with the data. Over time, further points will be observed that need not necessarily correspond to any of the same features seen previously.Conventionally, the initial task in understanding such data is to find relations between the points to partition the observations into groups (i.e. the clusters) with similar features that define the entity to be tracked. Such clustering algorithms generally perform the classification on the basis of the relative displacements of the points in the observation space and/or on the basis of a library of known reference objects. Conventional clustering algorithms are easier to implement, and more reliable, if the number of clusters is known in advance, if the objects to be classified belong to a set of known objects, and if the cluster is stable in time. If this is not the case, the algorithm has to solve also the so-called cluster validation problem and has to adaptively generate a library of objects against which to perform the classification.Such convential approaches are sensitive to noise, under-sampling, presence of echoes and temporary data drop-outs, which would be typical of situations of uncooperative, diffuse observations. This proposal concerns a new approach to segmentation and tracking such extended objects characterised by sparse observations over extended times.We propose to develop a novel dynamic clustering algorithm: the clusters are identified as the level sets corresponding to a reference value of a clustering function.The core idea is to construct the clustering function from observations and to regard the clustering function as the generator of a Hamiltonian dynamical system, the trajectories of which describe the clusters. While the notion of clustering function is standard, the use of Hamiltonian dynamics provides an original perspective and several advantages. These include the possibility to compute on-line geometric features of the clusters, to represent their dynamics with reduced order models, and to identify their dynamical behaviour.

对于任何扩展的实体，例如车辆车队，人群，灰尘云甚至近距离看到的刚性车辆，数据聚类是数据处理的重要步骤，也是数据识别，分类和跟踪程序的核心。对这种扩散实体的观察通常由适当定义的空间中的点表示。这些点可以表示与数据相关联的位置、活动或其他属性的观察。随着时间的推移，将观察到更多的点，这些点不一定对应于先前看到的任何相同特征。传统上，理解此类数据的初始任务是找到点之间的关系，以将观察结果划分为具有定义待跟踪实体的相似特征的组（即，聚类）。这种聚类算法通常基于观察空间中的点的相对位移和/或基于已知参考对象的库来执行分类。如果预先知道簇的数量，如果待分类的对象属于一组已知对象，并且如果簇在时间上是稳定的，则传统的聚类算法更容易实现，也更可靠。如果不是这样的话，算法还必须解决所谓的聚类验证问题，并且必须自适应地生成一个对象库来执行分类。这种传统的方法对噪声，欠采样，回波的存在和临时数据丢失很敏感，这是典型的不合作，分散观测的情况。该建议涉及一种新的方法来分割和跟踪这样的扩展对象，其特征在于在扩展时间上的稀疏观测。我们提出开发一种新的动态聚类算法：该方法的核心思想是从观测值构造聚类函数，并将聚类函数看作是Hamilton动力学的生成元系统，其轨迹描述集群。虽然聚类函数的概念是标准的，但Hamilton动力学的使用提供了一个原始的视角和几个优点。这些措施包括可能性计算在线的几何特征的集群，以表示其动态与降阶模型，并确定其动态行为。