Fernsel Pascal
Center for Industrial Mathematics, University of Bremen, 28359 Bremen, Germany.
J Imaging. 2021 Sep 28;7(10):194. doi: 10.3390/jimaging7100194.
Classical approaches in cluster analysis are typically based on a feature space analysis. However, many applications lead to datasets with additional spatial information and a ground truth with spatially coherent classes, which will not necessarily be reconstructed well by standard clustering methods. Motivated by applications in hyperspectral imaging, we introduce in this work clustering models based on Orthogonal Nonnegative Matrix Factorization (ONMF), which include an additional Total Variation (TV) regularization procedure on the cluster membership matrix to enforce the needed spatial coherence in the clusters. We propose several approaches with different optimization techniques, where the TV regularization is either performed as a subsequent post-processing step or included into the clustering algorithm. Finally, we provide a numerical evaluation of 12 different TV regularized ONMF methods on a hyperspectral dataset obtained from a matrix-assisted laser desorption/ionization imaging measurement, which leads to significantly better clustering results compared to classical clustering models.
聚类分析中的经典方法通常基于特征空间分析。然而，许多应用会产生具有额外空间信息的数据集以及具有空间连贯类别的真实情况，而标准聚类方法不一定能很好地重建这些。受高光谱成像应用的启发，我们在这项工作中引入了基于正交非负矩阵分解（ONMF）的聚类模型，该模型在聚类隶属矩阵上包括一个额外的全变差（TV）正则化过程，以在聚类中强制实现所需的空间连贯性。我们提出了几种采用不同优化技术的方法，其中TV正则化要么作为后续的后处理步骤执行，要么包含在聚类算法中。最后，我们对从矩阵辅助激光解吸/电离成像测量获得的高光谱数据集上的12种不同的TV正则化ONMF方法进行了数值评估，与经典聚类模型相比，这导致了显著更好的聚类结果。
