Spectral Clustering of Customer Transaction Data with a Two-Level Subspace Weighting Method

Finding customer groups from transaction data is very important for retail and e-commerce companies. Recently, a "Purchase Tree" data structure is proposed to compress the customer transaction data and a local PurTree spectral clustering method is proposed to cluster the customer transaction data. However, in the PurTree distance, the node weights for the children nodes of a parent node are set as equal and the differences between different nodes are not distinguished. In this paper, we propose a two-level subspace weighting spectral clustering (TSW) algorithm for customer transaction data. In the new method, a PurTree subspace metric is proposed to measure the dissimilarity between two customers represented by two purchase trees, in which a set of level weights are introduced to distinguish the importance of different tree levels and a set of sparse node weights are introduced to distinguish the importance of different tree nodes in a purchase tree. TSW learns an adaptive similarity matrix from the local distances in order to better uncover the cluster structure buried in the customer transaction data. Simultaneously, it learns a set of level weights and a set of sparse node weights in the PurTree subspace distance. An iterative optimization algorithm is proposed to optimize the proposed model. We also present an efficient method to compute a regularization parameter in TSW. TSW was compared with six clustering algorithms on ten benchmark data sets and the experimental results show the superiority of the new method.