Dimension Reduction with Prior Information for Knowledge Discovery

TL;DR

This paper introduces conditional multidimensional scaling (MDS), a new dimension reduction method that incorporates prior known features to improve data visualization and knowledge discovery across various applications.

Contribution

The paper proposes a broad class of conditional MDS methods with an optimized algorithm and proves its convergence, enhancing dimension reduction with prior information.

Findings

Conditional MDS improves estimation quality over traditional methods.

It simplifies visualization and knowledge discovery tasks.

The method is demonstrated on diverse real-world examples.

Abstract

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.