Nonparametric Cluster Analysis And Its Application

Cluster analysis is an unsupervised machine learning technique which can reveal the hidden patterns in datasets through their structure information.Clustering algorithm and cluster validity index are important parts of cluster analysis.They are introduced and improved by many researchers,and these algorithms are widely used in various fields.However,these algorithms and indices have their own drawbacks and are limited in practice.Most clustering algorithms need prior information provided by users.Most cluster validity indices depend on specific clustering algorithms,which is not completely unsupervised.Based on existing researches,this paper proposes novel cluster validity indices and clustering algorithm,and then applies cluster analysis to electrical tomography:1.A new cluster validity index based on hypervolume and hyper-surface area of the dataset.This index reveals the relation between cluster number and hypervolume and hyper-surface area of the dataset.This proposed index does not depend on specific clustering algorithms,and does not take the strategy of trial-and-error method.Thus,it has low computational complexity and can evaluate datasets with arbitrary-shaped clusters and noise points.2.A new cluster validity index based on boundary matching degree and interior connectivity degree.This index uses the matching degree and connectivity degree between the whole dataset and the clusters partitioned by clustering algorithms to compute cluster numbers.This index can evaluate clustering results given by C-means,FCM and DBSCAN algorithms.Thus,it does not depend on specific clustering algorithms.And this index can evaluate not only cluster numbers but also other parameters in the process of clustering.Moreover,this index can evaluate different clustering algorithms and then suggest the optimal algorithm.3.A clustering algorithm based on the adjacency matrix.This clustering algorithm takes full advantage of the relationships among points in the dataset.It uncovers the hidden structures in the dataset by updating the adjacency matrix.In order to deal with datasets with overlapped clusters,this index optimizes the adjacency relation among points in the overlapped area by using row operation.This index has faster execution speed and cannot affected by the distributions of datasets.Thus,it can evaluate datasets with density-skewed,size-diversity,arbitrary-shaped and overlapped clusters.4.An application in electrical tomography.This algorithm applies cluster analysis to electrical tomography to optimize image reconstruction resolution.This algorithm combines the existing image reconstruction algorithms by using cluster analysis firstly,and then identifies trail traces through cluster structures.The image reconstruction resolution can be improved by proper dispose of trail traces.