Before revision:  The most success to date has come from finding methods for turning persistence diagrams into vectors in \mathbb{R in a way which preserves as much of the space of persistence diagrams as possible, commonly referred to as featurization.
After revision:  The most success to date has come from finding methods for turning persistence diagrams into vectors in \mathbb{R in a way which maximizes the structure preserved. This process is commonly referred to as featurization.