Visualized correlation and distance preserving dimensionality reduction method

Zhonghai He

doi:10.1016/j.chemolab.2025.105406

Visualized correlation and distance preserving dimensionality reduction method

2025-07-01

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DOI：10.1016/j.chemolab.2025.105406

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Abstract

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A large of existing dimensionality reduction methods are aimed at preserving some properties of data, which cannot take label information into account. With the aim of reduced low-dimensional coordinate is used as tool for timing judgment of model updating, the concentration information should be incorporated into dimensionality reduction procedure, which is presented and named as Visualized Correlation and Distance Preserving dimensionality reduction method. To address the difficulty of 2D coordinate and 1D label correlation computation, pairwise distance matrices in both the subspace and label space are computed and the strictly lower triangular parts of these matrices are extracted and vectorized in column-major order, resulting in two vectors so that correlation can be computed. Distance preservation term is included as sub-objective function to ensure the low distance dissimilarity between high and low coordinates. To reduce structural loss caused by sequential dimensionality reduction method, the projection matrix is concatenated to vector then optimized to ensure projection vectors are optimized synchronously. PCA transformation is continued to adjust the reduced coordinates to better suited for visual judgment.

Keywords:

Visualized dimensionality reduction

Combined objective function

Pairwise distance correlation

Synchronously optimized vectors

Visualized correlation and distance preserving dimensionality reduction method

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