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. To solve this problem, this paper pro...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence 2024-05, Vol.46 (5), p.3625-3636
Main Author: Bui, Anh Tuan
Format: Article
Language:English
Subjects:
Algorithms
Controllability
Data visualization
Dimensionality reduction
Distance scaling
ISOMAP
Knowledge discovery
Machining
Manifolds
Measurement
Multidimensional methods
multidimensional scaling
Principal component analysis
Reduction
Sammon mapping
SMACOF
Task analysis
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Summary: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.
ISSN:0162-8828
1939-3539
2160-9292
DOI:10.1109/TPAMI.2023.3346212