Clustering algorithm for data analysis of the Fiber detectors of the HypHI project

The HypHI project aims to study hypernuclei by means of collisions of stable heavy ion and RI beams on stable target materials. As the first step (Phase 0), the feasibility of hypernuclear spectroscopy with heavy ion beams was investigated with a Li beam at 2 A GeV impinged on a C target by identifying ΛH, 4 ΛH and 5 ΛHe hypernuclei [1]. The Phase 0 experiment was performed in August and October 2009. In addition a new experiment has been performed in March 2010, in which a Ne beam was impinged on a C target at an energy of 2 A GeV. A dedicated algorithm for hit clustering has been considered to replace the current algorithm which is not flexible enough to handle the experimental behavior of the fiber detectors. The new algorithm should be able to handle channel gaps within a hit cluster which corresponds to the cross talk behavior of the PMT of the fiber detectors. As well outliners, corresponding to noisy channels, should not affect the clustering procedure and could be detected for possible rejection. The algorithm should also provide good clustering whatever is the detector occupancy, which is the fraction of fired channels over the total number of channels of considered fiber layer. The most important feature of the algorithm is that it should not require the number of clusters as an input since event by event the hit pattern on detectors are different, so that prior assumption is impossible. The proposed algorithm is based on Hierarchical clustering algorithm which consists in agglomerate fired channels using the distance matrix as clustering criteria. The definition of the distance gives different behavior on the clustering procedure. The complete-link method is used, in which the distance corresponds to the maximum euclidian distance between pairwise channels, producing compact clusters [2]. The use of a goodness criterion allows to assess the quality of each cluster and of the full hit partition. By using this kind of criteria, produced hit clusters can be merged in order to improve the global goodness of the clustering context. The number of clusters is then obtained when the criterion is optimal. The algorithm uses the silhouette factor, s(i), proposed in [3]. For each channel i: