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Heterogeneity is a hallmark of cancer. For various cancer outcomes/phenotypes, supervised heterogeneity analysis has been conducted, leading to a deeper understanding of disease biology and customized clinical decisions. In the literature, such analysis has been oftentimes based on demographic, clinical, and omics measurements. Recent studies have shown that high-dimensional histopathological imaging features contain valuable information on cancer outcomes. However, comparatively, heterogeneity analysis based on imaging features has been very limited. In this article, we conduct supervised cancer heterogeneity analysis using histopathological imaging features. The penalized fusion technique, which has notable advantages-such as greater flexibility-over the finite mixture modeling and other techniques, is adopted. A sparse penalization is further imposed to accommodate high dimensionality and select relevant imaging features. To improve computational feasibility and generate more reliable estimation, we employ model averaging. Computational and statistical properties of the proposed approach are carefully investigated. Simulation demonstrates its favorable performance. The analysis of The Cancer Genome Atlas (TCGA) data may provide a new way of defining/examining breast cancer heterogeneity.