Dimension Reduction with Prior Information for Knowledge Discovery

This paper addresses the problem of mapping high-dimensional data to a low-dimensional space, in the presence of other known features. This problem is ubiquitous in science and engineering as there are often controllable/measurable features in most applications. Furthermore, the discovered features in previous analyses can become the known features in subsequent analyses, repeatedly. To solve this problem, this paper proposes a broad class of methods, which is referred to as conditional multidimensional scaling. An algorithm for optimizing the objective function of conditional multidimensional scaling is also developed. The proposed framework is illustrated with kinship terms, facial expressions, and simulated car-brand perception examples. These examples demonstrate the benefits of the framework for being able to marginalize out the known features to uncover unknown, unanticipated features in the reduced-dimension space and for enabling a repeated, more straightforward knowledge discovery process. Computer codes for this work are available in the open-source cml R package.