Distributed multiple-input multiple-output (MIMO), also known as cell-free massive MIMO, emerges as a promising technology for sixth-generation (6G) systems to support uniform coverage and reliable communication. For the design and optimization of such systems, measurement-based investigations of real-world distributed MIMO channels are essential. In this paper, we present an indoor channel measurement campaign, featuring eight distributed antenna arrays with 128 elements in total. Multi-link channels are measured at 50 positions along a 12-meter user route. A clustering algorithm enabled by interacting objects is proposed to identify clusters in the measured channels. The algorithm jointly clusters the multipath components for all links, effectively capturing the dynamic contributions of common clusters to different links. In addition, a Kalman filter-based tracking framework is introduced for cluster prediction, tracking, and updating along the user movement. Using the clustering and tracking results, cluster-level characterization of the measured channels is performed. First, the number of clusters and their visibility at both link ends are analyzed. Next, a maximum-likelihood estimator is utilized to determine the entire cluster visibility region length. Finally, key cluster-level properties, including the common cluster ratio, cluster power, shadowing, spread, among others, are statistically investigated. The results provide valuable insights into cluster behavior in typical multi-link channels, necessary for accurate modeling of distributed MIMO channels.