In this paper we propose a framework inspired by interacting particle physics and devised to perform clustering on multidimensional datasets. To this end, any given dataset is modeled as an interacting particle system, under the assumption that each element of the dataset corresponds to a different particle and that particle interactions are rendered through gaussian potentials. Moreover, the way particle interactions are evaluated depends on a parameter that controls the shape of the underlying gaussian model. In principle, different clusters of proximal particles can be identified, according to the value adopted for the parameter. This degree of freedom in gaussian potentials has been introduced with the goal of allowing multiresolution analysis. In particular, upon the adoption of a standard community detection algorithm, multiresolution analysis is put into practice by repeatedly running the algorithm on a set of adjacency matrices, each dependent on a specific value of the parameter that controls the shape of gaussian potentials. As a result, different partitioning schemas are obtained on the given dataset, so that the information thereof can be better highlighted, with the goal of identifying the most appropriate number of clusters. Solutions achieved in synthetic datasets allowed to identify a repetitive pattern, which appear to be useful in the task of identifying optimal solutions while analysing other synthetic and real datasets.
Dynamic clustering and chemotactic collapse of self-phoretic active particles
最近的实验表明，在低浓度下的自泳粒子显着的动态聚类[I]。Theurkauff \emph{et al.}，物理学\修订版本\ Lett. \textbf{108}，268303（2012）]。我们模拟这种情况，考虑到平移和旋转的扩散泳运动，活性粒子在其自生的化学领域进行。我们的布朗动力学模拟表明，只有当这两个泳的贡献引起竞争的吸引力和排斥力的相互作用，分别显着的动态聚类。我们确定了两个动态聚类状态，并通过幂律指数分布来表征它们。在仅仅吸引力的情况下，趋化性的的发生直接从气体样到崩溃的状态，我们也预测映射我们的Langevin动力学的Keller-Segel模型的细菌趋化性。
