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The concept of dimension is important because every mathematical equation linking physical quantities must be dimensionally consistent, implying that mathematical equations must meet the following two rules. The first rule is that, in an equation, the expressions on each side of the equal sign must have the same dimensions. This is fairly intuitive since we can only add or subtract quantities of the same type (dimension). The second rule states that, in an equation, the arguments of any of the...
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    This study introduces a quantitative method to evaluate dimensionality reduction embeddings, centering human perception. It uses machine learning to understand and rank embeddings based on user preferences, moving beyond qualitative assessments.

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    Area of Science:

    • Data Science
    • Computer Vision
    • Machine Learning

    Background:

    • Dimensionality reduction techniques offer numerous choices for data reduction.
    • Current evaluation of 2D embeddings is often qualitative, relying on human judgment.
    • Users frequently treat dimensionality reduction as a black box, ignoring method-specific properties.

    Purpose of the Study:

    • To develop a quantitative method for evaluating 2D embeddings that incorporates human perception.
    • To build a machine learning model that mimics human judgment in selecting high-quality embeddings.
    • To identify and quantify factors influencing human preference for specific embeddings.

    Main Methods:

    • A comparative study was conducted where participants identified "good" and "misleading" low-dimensional image embeddings.
    • A supervised machine learning model was trained using participant data as labels.
    • The trained model was used as a proxy for human judgment to rank and explain embedding relevance.

    Main Results:

    • A quantitative framework for embedding evaluation was established, grounded in human perception.
    • The developed model can effectively rank embeddings and provide explanations for their relevance.
    • The degree of subjectivity in human selection of preferred embeddings can be quantified.

    Conclusions:

    • This work provides a novel, quantitative approach to assessing dimensionality reduction embeddings.
    • The method bridges the gap between human perception and automated embedding evaluation.
    • It enables more objective and interpretable selection of dimensionality reduction techniques.