Multiplex immunohistochemistry (mIHC) is an innovative method that simultaneously labels multiple biomarkers in the same tissue section with different colored stains. However, analyzing these complex images is a challenging task for current image processing methods. In order to efficiently process these images, it may be beneficial to employ an effective representation of the data. The component-tree is known to facilitate the representation of images containing sparse objects, which necessitate representation at a higher scale, as opposed to large background regions that can be represented at a lower scale without loss of fidelity. In this paper, we present how a multi-scale version of the component-tree can be effectively utilized to represent this type of data, drawing inspiration from the approach a pathologist might take when analyzing these images (initially identifying objects of interest via a specific nuclear channel, such as DAPI, and then associating each object with a spectral signature based on the intensities of other channels). We demonstrate this method on an unsupervised analysis of 9-channel multiplexed glioblastoma data.