Clustering is a fundamental approach to understanding data patterns, wherein the intuitive Euclidean distance space is commonly adopted. However, this is not the case for implicit cluster distributions reflected by qualitative attribute values, e.g., the nominal values of attributes like symptoms, marital status, etc. This paper, therefore, discovered a tree-like distance structure to flexibly represent the local order relationship among intra-attribute qualitative values. That is, treating a value as the vertex of the tree allows to capture rich order relationships among the vertex value and the others. To obtain the trees in a clustering-friendly form, a joint learning mechanism is proposed to iteratively obtain more appropriate tree structures and clusters. It turns out that the latent distance space of the whole dataset can be well-represented by a forest consisting of the learned trees. Extensive experiments demonstrate that the joint learning adapts the forest to the clustering task to yield accurate results. Comparisons of 10 counterparts on 12 real benchmark datasets with significance tests verify the superiority of the proposed method. Source code of the proposed method is available at [39].