  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. To solve this problem,
this paper proposes a broad class of methods, which is referred to as
conditional multidimensional scaling (MDS). An algorithm for optimizing the
objective function of conditional MDS is also developed. The convergence of
this algorithm is proven under mild assumptions. Conditional MDS is illustrated
with kinship terms, facial expressions, textile fabrics, car-brand perception,
and cylinder machining examples. These examples demonstrate the advantages of
conditional MDS over conventional dimension reduction in improving the
estimation quality of the reduced-dimension space and simplifying visualization
and knowledge discovery tasks. Computer codes for this work are available in
the open-source cml R package.
