Principal Components on t-SNE

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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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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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