Privacy-preserving nearest neighbor methods: comparing signals without revealing them

Comparing two signals is one of the most essential and prevalent tasks in signal processing. A large number of applications fundamentally rely on determining the answers to the following two questions: 1) How should two signals be compared? 2) Given a set of signals and a query signal, which signals are the nearest neighbors (NNs) of the query signal, i.e., which signals in the database are most similar to the query signal? The NN search problem is defined as follows: Given a set S containing points in a metric space M, and a query point x !M, find the point in S that is closest to x. The problem can be extended to K-NN, i.e., determining the K signals nearest to x. In this context, the points in question are signals, such as images, videos, or other waveforms. The qualifier closest refers to a distance metric, such as the Euclidean distance or Manhattan distance between pairs of points in S. Finding the NN of the query point should be at most linear in the database size and is a well-studied problem in conventional NN settings.