融合稀疏性與相關性的降維方法及其在 t-SNE 中的應用;A Dimensionality Reduction Method Integrating Sparsity and Correlation for t-SNE

Please use this identifier to cite or link to this item: https://ir.lib.ncu.edu.tw/handle/987654321/97990

Title:	融合稀疏性與相關性的降維方法及其在 t-SNE 中的應用;A Dimensionality Reduction Method Integrating Sparsity and Correlation for t-SNE
Authors:	陳威谷;Chen, Wei-Gu
Contributors:	統計研究所
Keywords:	高維度資料;拉普拉斯矩陣;t-隨機鄰近嵌入法;視覺化;High-dimensional data;Laplacian Matrix;t-SNE;Visualization
Date:	2025-06-26
Issue Date:	2025-10-17 12:14:03 (UTC+8)
Publisher:	國立中央大學
Abstract:	在高維資料盛行的時代，降維技術對於提升計算效率至關重要。其中，t-SNE 因其能有效避免視覺化時的擁擠問題，而被廣泛應用。然而，傳統的 t-SNE 缺乏解釋能力，且對於大規模資料來說，計算成本相當高。本研究提出一種新的降維方法，將稀疏性與特徵之間的相關性結構整合進 t-SNE 的核心最佳化框架中。具體來說，我們透過最小化 Kullback-Leibler (KL) 散度，並加入兩個正則化項來建構降維矩陣 B：其中包含 ℓ1 懲罰項以鼓勵稀疏性，以及拉普拉斯懲罰項，用以捕捉基於精確矩陣所估計之特徵間的條件相依性。所建構出的 B 矩陣能保留關鍵資料結構並提供高品質的視覺化效果，並降低計算成本。本方法在具有獨立與相關結構的模擬資料集上進行驗證，並應用於實際的 MNIST 資料集中。結果顯示，該方法甚至在以少量樣本估計出轉換矩陣 B 的情況下，也能應用於大規模資料，展現出優異的穩健性。整體而言，將結構性正則化整合至 t-SNE 演算法中，不僅提升了整體的解釋性，亦滿足了降維矩陣 B 對於具有相似結構資料降維的重複使用性。 ;In the era of high-dimensional data, dimensionality reduction techniques are essential for improving computational efficiency. Among these methods, t-SNE is widely used due to its ability to effectively alleviate the crowding problem in data visualization. However, traditional t-SNE lacks interpretability and incurs high computational costs when applied to large-scale datasets.This study proposes a novel dimensionality reduction method that in tegrates sparsity and feature correlation structures into the core optimization framework of t-SNE. Specifically, we construct a transformation matrix B by minimizing the Kullback Leibler (KL) divergence with two regularization terms: an ℓ1 penalty to promote sparsity, and a Laplacian penalty to capture conditional dependencies among features, estimated via the precision matrix.The resulting matrix B preserves essential data structures and en ables high-quality visualizations, while also reducing computational burden. The proposed method is evaluated on simulated datasets with both independent and correlated structures, as well as on the real-world MNIST dataset. Results demonstrate that even when the trans formation matrix B is estimated from a small number of samples, the method can still be effectively applied to large-scale data, exhibiting strong robustness. Overall, incorporating structured regularization into the t-SNE algorithm enhances interpretability and supports the reuse of the transformation matrix B for dimensionality reduction on structurally simi lar datasets.
Appears in Collections:	[Graduate Institute of Statistics] Electronic Thesis & Dissertation

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