Dimension Reduction with Prior Information for Knowledge Discovery
This addresses a common issue in science and engineering for researchers and practitioners dealing with high-dimensional data with known features, offering an incremental improvement over conventional methods.
The paper tackles the problem of mapping high-dimensional data to a low-dimensional space when prior features are known, proposing conditional MDS to improve estimation quality and simplify visualization and knowledge discovery tasks, as demonstrated in examples like kinship terms and car-brand perception.
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.