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Distance metrics and their nonlinear variant play a crucial role in machinelearning based real-world problem solving. We demonstrated how Euclidean andcosine distance measures differ not only theoretically but also in real-worldmedical application, namely, outcome prediction of drug prescription. Euclideandistance exhibits favorable properties in the local geometry problem. To thisregard, Euclidean distance can be applied under short-term disease withlow-variation outcome observation. Moreover, when presenting to highly variantchronic disease, it is preferable to use cosine distance. These differentgeometric properties lead to different submanifolds in the original embeddedspace, and hence, to different optimizing nonlinear kernel embeddingframeworks. We first established the geometric properties that we needed inthese frameworks. From these properties interpreted their differences incertain perspectives. Our evaluation on real-world, large-scale electronichealth records and embedding space visualization empirically validated ourapproach.

The Analysis from Nonlinear Distance Metric to Kernel-based Drug Prescription Prediction System