A New Measure for Analyzing and Fusing Sequences of Objects.

Area of Science:

• Combinatorial Data Analysis
• Data Visualization
• Exploratory Data Analysis

Background:

• Seriation algorithms reorder data to place similar items adjacently, aiding visualization and analysis.
• Existing methods lack systematic approaches for comparing, analyzing, or fusing multiple seriation results.

Purpose of the Study:

• To develop a novel positional proximity measure for quantifying the similarity between arbitrary sequences.
• To introduce a consensus seriation procedure for fusing multiple sequences into a single representative one.
• To establish theoretical links with existing permutation distance functions.

Main Methods:

• A new positional proximity measure is proposed, evaluating sequence similarity based on pairwise object positions.
• Consensus seriation is formulated as a quadratic assignment problem with an efficient solution approximation.
• Statistical properties of the measure and its normalized version are derived, relating it to generalized correlation coefficients.

Main Results:

• The proposed proximity measure effectively quantifies sequence similarity.
• The consensus seriation procedure successfully fuses multiple sequences.
• Theoretical connections to permutation distances are established, offering new combinatorial optimization perspectives.

Conclusions:

• The developed methods provide a systematic framework for analyzing, comparing, and fusing seriation results.
• The approach enhances exploratory data analysis by enabling robust combination of multiple data visualizations.
• Demonstrated utility across diverse real-world datasets validates the proposed contributions.