Clothing change person re-identification (CC-ReID) aims to match different images of the same person, even when the clothing varies across images. To reduce manual labeling costs, existing unsupervised CC-ReID methods employ clustering algorithms to generate pseudo-labels. However, they often fail to assign the same pseudo-label to two images with the same identity but different clothing—referred to as a clothing change positive pair—thus hindering clothing-invariant feature learning. To address this issue, we propose the identity-clothing similarity modeling (ICSM) framework. To effectively connect clothing change positive pairs, ICSM first performs clothing-aware learning to leverage all discriminative information, including clothing, to obtain compact clusters. It then extracts cluster-level identity and clothing features and performs inter-cluster similarity estimation to identify clothing change positive clusters, reliable negative clusters, and hard negative clusters for each compact cluster. During optimization, we design an adaptive version of existing optimization methods to enhance similarities of clothing change positive pairs, while also introducing text semantics as a supervisory signal to further promote clothing invariance. Extensive experimental results across multiple datasets validate the effectiveness of the proposed framework, demonstrating its superiority over existing unsupervised methods and its competitiveness with some supervised approaches.