Covariance Matrix Analysis Through Eigenvalues and Eigenvectors: Insights into Multivariate Data Structures
Keywords:
Principal Component Analysis (PCA), Dimensionality Reduction, Machine Learning Models, Variance Retention, Model Performance, Computational Efficiency
Abstract
This paper investigates the use of PCA for dimensionality reduction in multivariate datasets, focusing on its effect on machine learning model performance. The results show that PCA successfully preserves important variance and removes noise and redundancy, thus improving model accuracy, precision, recall, and F1-score. PCA enhances the efficiency and interpretability of models by reducing the dimensionality of high-dimensional datasets. This tool is invaluable in fields such as finance, healthcare, and image processing. PCA also contributes to faster training times and greater computational efficiency, supporting scalability for larger datasets. In general, this research affirms PCA's importance in optimizing machine learning workflows and generalizing models. It is a strong technique for handling complex data structures in real-world applications.
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2. Ernst, A. F., Timmerman, M. E., Jeronimus, B. F., & Albers, C. J. (2021). Insight into individual differences in emotion dynamics with clustering. Assessment, 28(4), 1186-1206.
3. Fan, J., Shu, L., Yang, A., & Li, Y. (2021). Phase I analysis of high-dimensional covariance matrices based on sparse leading eigenvalues. Journal of Quality Technology, 53(4), 333-346.
4. Frost, H. R. (2021). Eigenvectors from eigenvalues sparse principal component analysis (EESPCA). Journal of computational and graphical statistics: a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America, 31(2), 486.
5. Goldt, S., Mézard, M., Krzakala, F., & Zdeborová, L. (2020). Modeling the influence of data structure on learning in neural networks: The hidden manifold model. Physical Review X, 10(4), 041044.
6. Grotzinger, A. D., Rhemtulla, M., de Vlaming, R., Ritchie, S. J., Mallard, T. T., Hill, W. D., ... & Tucker-Drob, E. M. (2019). Genomic structural equation modelling provides insights into the multivariate genetic architecture of complex traits. Nature human behaviour, 3(5), 513-525.
7. Iacobucci, D., Ruvio, A., Román, S., Moon, S., & Herr, P. M. (2022). How many factors in factor analysis? New insights about parallel analysis with confidence intervals. Journal of Business Research, 139, 1026-1043.
8. Le Maître, A., & Mitteroecker, P. (2019). Multivariate comparison of variance in R. Methods in Ecology and Evolution, 10(9), 1380-1392.
9. Liu, L., Dong, Y., Kong, M., Zhou, J., Zhao, H., Tang, Z., ... & Wang, Z. (2020). Insights into the long-term pollution trends and sources contributions in Lake Taihu, China using multi-statistical analyses models. Chemosphere, 242, 125272.
10. Mardia, K. V., Kent, J. T., & Taylor, C. C. (2024). Multivariate analysis (Vol. 88). John Wiley & Sons.
11. New, W. K., Wong, K. K., Xu, H., Tong, K. F., & Chae, C. B. (2023). Fluid antenna system: New insights on outage probability and diversity gain. IEEE Transactions on Wireless Communications, 23(1), 128-140.
12. Pathare, A. R., & Joshi, A. S. (2023, March). Dimensionality reduction of multivariate images using the linear & nonlinear approach. In 2023 International Conference on Device Intelligence, Computing and Communication Technologies, (DICCT) (pp. 234-237). IEEE.
13. Santos, M. P. F., da Silva, J. F., da Costa Ilheu Fontan, R., Bonomo, R. C., Santos, L. S., & Veloso, C. M. (2020). New insight about the relationship between the main characteristics of precursor materials and activated carbon properties using multivariate analysis. The Canadian Journal of Chemical Engineering, 98(7), 1501-1511.
14. Scharf, F., & Nestler, S. (2018). Principles behind variance misallocation in temporal exploratory factor analysis for ERP data: Insights from an inter-factor covariance decomposition. International Journal of Psychophysiology, 128, 119-136.
15. Zhu, J., Ge, Z., Song, Z., & Gao, F. (2018). Review and big data perspectives on robust data mining approaches for industrial process modeling with outliers and missing data. Annual Reviews in Control, 46, 107-133.
Published
2024-12-21
How to Cite
Krishana, & Dr. Vinod Kumar. (2024). Covariance Matrix Analysis Through Eigenvalues and Eigenvectors: Insights into Multivariate Data Structures. Revista Electronica De Veterinaria, 25(2), 698-702. https://doi.org/10.69980/redvet.v25i2.1495
Section
Articles
