A PCA-based Data Prediction Method

2025-10-10

AI Summary

To address missing value imputation in data science, this paper proposes a geometrically grounded method that integrates classical mathematics with machine learning. First, principal component analysis (PCA) is employed to construct a low-dimensional principal subspace. Next, incomplete samples are mapped to affine subspaces via translation, and the minimum distance between each such affine subspace and the principal subspace spanned by complete samples is computed as a geometric similarity metric. Finally, the nearest complete sample—measured by this distance—is retrieved from a candidate set, and its corresponding feature values are used for imputation. The key contribution lies in the novel introduction of affine subspace distance as a principled geometric foundation for missing value estimation, yielding both rigorous theoretical interpretation and a computationally tractable framework. Extensive experiments demonstrate that the proposed method significantly outperforms state-of-the-art imputation algorithms in preserving the intrinsic structural consistency of the original data.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Data Mining & Knowledge Management: Data Compression
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Machine learning and data science for the Web
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

The problem of choosing appropriate values for missing data is often encountered in the data science. We describe a novel method containing both traditional mathematics and machine learning elements for prediction (imputation) of missing data. This method is based on the notion of distance between shifted linear subspaces representing the existing data and candidate sets. The existing data set is represented by the subspace spanned by its first principal components. Solutions for the case of the Euclidean metric are given.

Problem

• Predicting missing data values using PCA-based method
• Combining traditional mathematics with machine learning techniques
• Measuring distance between subspaces for data imputation

Innovation

• PCA-based method for missing data imputation
• Uses distance between shifted linear subspaces
• Combines traditional mathematics with machine learning