In this study, we present an automated approach to classify prostate cancer (PCa) whole slide images (WSIs) as high or low cancer aggressiveness using features derived from persistent homology, a tool of topological data analysis (TDA). This extends previous work on the use of these features for representing the characteristics of prostate cancer architecture in region of interest (ROI) images, and demonstrates the value of features derived from persistent homology to predict cancer aggressiveness of WSIs on an ROI basis. We compute persistence on ROI images and summarize persistence as a persistence image. Using this summary we construct a random forest classifier to predict cancer aggressiveness. We demonstrate the potential of persistent homology to capture the architectural differences between low and high grade prostate cancers in a feature representation that lends itself well to machine learning approaches.