High Dimensional Cluster Analysis Using Path Lengths

Abstract: A hierarchical scheme for clustering data is presented which applies to spaces with a high number of dimension ($N_{_{D}}>3$). The data set is first reduced to a smaller set of partitions (multi-dimensional bins). Multiple clustering techniques are used, including spectral clustering, however, new techniques are also introduced based on the path length between partitions that are connected to one another. A Line-Of-Sight algorithm is also developed for clustering. A test bank of 12 data sets with varying properties is used to expose the strengths and weaknesses of each technique. Finally, a robust clustering technique is discussed based on reaching a consensus among the multiple approaches, overcoming the weaknesses found individually.