Large repositories of products, patents and scientific papers offer an opportunity for building systems that scour millions of ideas and help users discover inspirations. However, idea descriptions are typically in the form of unstructured text, lacking key structure that is required for supporting creative innovation interactions. Prior work has explored idea representations that were either limited in expressivity, required significant manual effort from users, or dependent on curated knowledge bases with poor coverage. We explore a novel representation that automatically breaks up products into fine-grained functional aspects capturing the purposes and mechanisms of ideas, and use it to support important creative innovation interactions: functional search for ideas, and exploration of the design space around a focal problem by viewing related problem perspectives pooled from across many products. In user studies, our approach boosts the quality of creative search and inspirations, substantially outperforming strong baselines by 50-60%.