Toward a Quantitative Survey of Dimension Reduction Techniques.

Area of Science:

• Data Science
• Machine Learning
• Information Visualization

Background:

• Dimensionality reduction (projections) are crucial for exploring high-dimensional data.
• Numerous techniques exist, each with varying strengths in preserving data structure, neighborhoods, and scalability.
• Practitioners lack clear guidance on selecting appropriate projection methods for specific contexts.

Purpose of the Study:

• To provide a comprehensive survey and benchmark of dimensionality reduction techniques.
• To assist practitioners in choosing the most suitable projection method for their data exploration tasks.
• To offer a systematic framework for evaluating and comparing projection techniques.

Main Methods:

• Characterization of input data space, projection techniques, and projection quality using quantitative metrics.
• Sampling across these spaces to ensure broad coverage with efficient effort.
• Empirical measurement and analysis of dependencies between data characteristics, projection methods, and resulting quality.

Main Results:

• Observed dependencies between data properties, projection algorithms, and their performance metrics.
• Comparative analysis of various projection techniques based on defined quality criteria.
• Identification of factors influencing the effectiveness of different dimensionality reduction methods.

Conclusions:

• Provides actionable insights for comparing projection techniques across diverse datasets.
• Explains how different projection methods perform with various data types.
• Empowers practitioners to make informed decisions when selecting dimensionality reduction for their specific applications.
• The methodology, data, code, and results are publicly available for community use and extension.