Kernel functions based on triplet similarity comparisons

We propose two ways of defining a kernel function on a data set when the only available information about the data set are similarity triplets of the form "Object A is more similar to object B than to object C". Studying machine learning and data mining problems based on such restricted information has become very popular in recent years since it can easily be provided by humans via crowd sourcing. While previous approaches try to construct a low-dimensional Euclidean embedding of the data set that reflects the given similarity triplets, we aim at defining meaningful kernel functions on the data set that correspond to high-dimensional embeddings. These kernel functions can subsequently be used to apply all the standard kernel methods to solve tasks such as clustering, classification or principal component analysis on the data set.

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