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Abstract:
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It is often possible to use expert knowledge or other sources of information to obtain dissimilarity measures for pairs of objects, which serve as pseudo-distances between the objects. When dissimilarity information is available as the data, there are two types of problems of interest. The first is to estimate full position configuration for all objects in a low-dimensional space while respecting the data. In the second type of problem, the high-dimensional data points are assumed to lie on a low-dimensional manifold, and the goal is to unfold the manifold to recover the underlying intrinsic low-dimensional structure. We provide a novel, unified framework called Kernel Regularization that can be used to solve either problem. Various favorable operating characteristics and properties of the method will be illustrated via simulated and real data.
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