This paper addresses one of the most common tasks in multimodal scientific data management: retrieving the k most similar items (or k-nearest neighbors, KNN) from a database given a new item. Recent advances in multimodal machine learning models provide semantic indices, called "embedding vectors," mapped from the original multimodal data. However, the resulting embedding vectors typically have hundreds or thousands of dimensions, making them impractically high for time-sensitive scientific applications. This paper proposes a method to reduce the dimensionality of the output embedding vector through order-preserving dimensionality reduction (OPDR), where the set of top k nearest neighbors remains unchanged in the low-dimensional space after dimensionality reduction. To achieve this, we establish the central hypothesis that by analyzing the intrinsic relationships among key parameters during dimensionality reduction, we can construct a quantitative function that reveals the correlation between the target (lower-dimensional) dimension and other variables. To prove this hypothesis, this paper first defines a formal metric function that quantifies KNN similarity for a given vector. It then extends this metric to aggregate accuracy in the global metric space, and then derives a closed-form function between the target (low-dimensional) dimensionality and other variables. Finally, it integrates this closed-form function into popular dimensionality reduction methods, various distance metrics, and embedding models.
