Order Is All You Need for Categorical Data Clustering

Categorical data composed of nominal valued attributes are ubiquitous in knowledge discovery and data mining tasks. Due to the lack of well-defined metric space, categorical data distributions are difficult to intuitively understand. Clustering is a popular technique suitable for data analysis. However, the success of clustering often relies on reasonable distance metrics, which happens to be what categorical data naturally lack. Therefore, the cluster analysis of categorical data is considered a critical but challenging problem. This paper introduces the new finding that the order relation among attribute values is the decisive factor in clustering accuracy, and is also the key to understanding the categorical data clusters. To automatically obtain the orders, we propose a new learning paradigm that allows joint learning of clusters and the orders. It turns out that clustering with order learning achieves superior clustering accuracy, and the learned orders provide intuition for understanding the cluster distribution of categorical data. Extensive experiments with statistical evidence and case studies have verified the effectiveness of the new ``order is all you need'' insight and the proposed method.