Dimension Reduction With Prior Information for Knowledge Discovery.

Area of Science:

• Data science
• Machine learning
• Statistics

Background:

• High-dimensional data mapping is crucial in science and engineering.
• Existing dimension reduction methods often overlook known features.
• Controllable or measurable features are common in real-world applications.

Purpose of the Study:

• To propose a novel class of methods for dimension reduction called conditional multidimensional scaling (MDS).
• To develop and validate an optimization algorithm for conditional MDS.
• To demonstrate the advantages of conditional MDS over conventional methods.

Main Methods:

• Development of conditional multidimensional scaling (MDS) algorithms.
• Optimization of the objective function for conditional MDS.
• Theoretical convergence proof under mild assumptions.

Main Results:

• Conditional MDS effectively maps high-dimensional data to low-dimensional spaces while considering known features.
• Demonstrated improvements in estimation quality and visualization.
• Facilitated knowledge discovery across diverse examples like facial expressions and car perception.

Conclusions:

• Conditional MDS offers a significant advancement over conventional dimension reduction techniques.
• The proposed method simplifies complex data visualization and aids knowledge discovery.
• Open-source R package 'cml' provides accessible implementation.