| Title: | A vector algebra perspective on data dimensionality reduction |
| Authors: | Harbar, A. E. |
| Keywords: | материалы конференций;vector algebra;Gram matrix;singular value decomposition;principal component analysis;primary data analysis;multicollinearity;condition number;Eckart-Young theorem |
| Issue Date: | 2026 |
| Publisher: | БГУИР |
| Citation: | Harbar, A. E. A vector algebra perspective on data dimensionality reduction / A. E. Harbar // Компьютерные системы и сети : сборник материалов 62-й научной конференции аспирантов, магистрантов и студентов БГУИР, Минск, 13–17 апреля 2026 г. / Белорусский государственный университет информатики и радиоэлектроники. – Минск, 2026. – С. 367–370. |
| Abstract: | The paper studies methods of applying vector algebra to optimize machine learning tasks. Using the Human Activity Recognition dataset, a mathematically rigorous primary data analysis is conducted: the Gram matrix and correlation structure are examined, positive semi-definiteness of the correlation matrix is proved, and multicollinearity is quantified via the condition number 𝑘(XᵀX) ≈ 9.56 ∙ 10⁴ and median VIF = 22.4. Principal Component Analysis is examined through the lens of singular value decomposition; the orthogonality of principal components is proved. Projection onto k = 20 components increases classifier accuracy from 62.8 % to 65.5 %. |
| URI: | https://libeldoc.bsuir.by/handle/123456789/64060 |
| Appears in Collections: | Компьютерные системы и сети : материалы 62-й научной конференции аспирантов, магистрантов и студентов : сборник статей (2026)
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