博碩士論文 110225004 詳細資訊




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姓名 傅維康(Connor Wei Fu)  查詢紙本館藏   畢業系所 統計研究所
論文名稱
(Principal Components on t-SNE)
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檔案 [Endnote RIS 格式]    [Bibtex 格式]    [相關文章]   [文章引用]   [完整記錄]   [館藏目錄]   至系統瀏覽論文 (2026-7-1以後開放)
摘要(中) 在眾多視覺化方法中,t-隨機鄰近嵌入法 (t-SNE) 是相當有效且被廣泛使用的
技術之一。視覺上,t-SNE 有能力在 2 維或 3 維空間中呈現高維度資料集的結
構,然而,對資料進一步的解釋能力較弱。相對地,主成分分析 (PCA) 具有足
夠的解釋性,但視覺化效果較差。在本文中,我們提出一套新的方法。過程將
t-SNE 與 PCA 的概念做結合,旨在保留良好視覺化結果的同時,也提升資料的
解釋力。透過尋找與 t-SNE 分群相關的特徵,我們能夠得到用來解釋 t-SNE 映
射的主成分 (principal component)。這種方法除了提高 t-SNE 的解釋性以及應用
價值,也為資料視覺化研究提供了新的思路。在數值研究中,我們透過提出的
方法以及 PCA 方法獲得主成分進行資料降維,再重新執行 t-SNE 演算法進行視
覺化。視覺化的重建結果顯示,PCA 所找到的主成分無法有效還原 t-SNE 的映
射,而我們的方法不僅能夠重新還原,甚至能提供更優秀的視覺化效果。
摘要(英) t-distributed stochastic neighbor embedding (t-SNE) is one of highly effective and
widely used visualization methods. It is capable to visualize the structure of highdimensional data by giving each datapoint a location in a 2D or 3D map. However,
it lacks further interpretability of data. On the other hand, principal component analysis
(PCA) provides sufficient interpretability but yields inferior visualization. In this paper,
we propose a novel approach that combines the concepts of t-SNE and PCA to preserve
good visualizing results while keeping the interpretability of data. By searching for features that are correlated with the clustering performed by t-SNE, we can obtain dedicated
principal components for t-SNE. This method not only improves the interpretability and
applicability of t-SNE but also provides new insights for data visualization research. In
our numerical study, we use the principal components from our method and PCA method
to reapply the t-SNE algorithm for visualization. The reconstructed results demonstrate
that the principal components identified by PCA fail to effectively reproduce the mappings of t-SNE, while our method not only achieves successful reconstruction but also
offers superior visualization outcomes
關鍵字(中) ★ 高維度資料
★ 解釋性
★ 主成分分析
★ t-隨機鄰近嵌入法
★ 視覺化
關鍵字(英)
論文目次 1 Introduction 1
2 Review 3
2.1 Principal Component Analysis 3
2.2 t-Distributed Stochastic Neighborhood Embedding 4
3 Method 8
3.1 Minimization on the Stiefel manifold 9
3.2 Principal Components of t-SNE 12
4 Experiments 15
4.1 Experimental Setup 15
4.2 Simulated Data 16
4.3 Word Vector Data 19
4.4 MNIST Data 24
5 Conclusion 27
A Proofs 28
A.1 Properties of the Cayley Transform 28
A.1.1 28
A.1.2 30
A.2 Derivation of the Gradient 30
References 31
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指導教授 王紹宣 審核日期 2023-7-26
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