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PCA by Shrinkage Estimation: A Comprehensive Mathematical and Statistical Analysis | ||
| Journal of Data Science and Modeling | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 15 آبان 1404 اصل مقاله (1.76 M) | ||
| نوع مقاله: Research Manuscript | ||
| شناسه دیجیتال (DOI): 10.22054/jdsm.2025.86705.1074 | ||
| نویسندگان | ||
| Parviz Nasiri* 1؛ Heydar Mokhtari Farivar2 | ||
| 1Payam Noor uinversity | ||
| 2Department of Mathematics and Computer Sciences, Iran University of Science and Technology, P.O. Box 16846, Tehran, Iran | ||
| چکیده | ||
| Principal Component Analysis (PCA) is a cornerstone technique for dimensionality reduction and data analysis. However, classic PCA can exhibit instability in high-dimensional settings where the number of variables significantly exceeds the number of observations. Shrinkage-based PCA addresses this limitation by incorporating regularization into the covariance matrix estimation process, leading to more stable and interpretable results. This paper provides a robust mathematical and statistical foundation for shrinkage-based PCA, compares its performance with classic PCA, and demonstrates its advantages through theoretical analysis, numerical simulations, and real-world data experiments. It is important to note that using the idea of a contraction estimator increases the efficiency of the estimator. mean time in this paper, it is shown that the covariance matrix estimator resulting from the contraction estimator is very efficient. It is also worth mentioning that to increase the efficiency of the contraction estimator, the recently discussed interval contraction estimator can be used. keywords: principal component analysis, Shrinkage-based, Estimation, Covariance Structures, Simulation. | ||
| کلیدواژه‌ها | ||
| Principal Component Analysis (PCA)؛ Estimation؛ Mean square error | ||
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