區間值觀測廣泛出現於象徵型資料分析、大型資料庫，以及具有測量不確定性的情境中。然而，針對此類資料所設計的可擴展非線性降維方法仍相對有限。本研究以t分配隨機鄰近嵌入法（t-distributed stochastic neighbor embedding, t-SNE）為基礎，提出區間值t分配隨機鄰近嵌入法（Interval t-SNE, I-tSNE），作為區間值資料探索性分析與視覺化的延伸方法。本文提出四種I-tSNE方法：其中兩種為展開式方法，分別以頂點法與分位點法為基礎；另外兩種則為直接區間最佳化方法，分別採用端點表示與中心–半徑表示。本文亦探討直接區間最佳化方法的理論性質，包括當區間退化為點時與標準t-SNE的一致性、中心半徑距離與Wasserstein 距離之間的關聯，以及低維區間表示的可行性問題。此外，本文提出一套適用於區間值資料的鄰域保留評估方式。此評估方式以局部連續性準則（localcontinuity meta-criterion）為基礎，並透過模擬資料與多組實際資料比較各方法的表現。研究結果顯示，各方法的表現會隨資料結構、區間生成機制與鄰域範圍而改變，並不存在單一方法在所有設定下皆占優。若僅以鄰域結構保留作為主要目標，部分既有區間值基準方法已能取得相當良好的效果；然而，這些方法多建立於線性投影或距離配置架構之上。相較之下，本文提出的I-tSNE將t-SNE的非線性鄰域機率架構延伸至區間值資料，使低維表示能從局部鄰近關係的角度呈現資料結構，同時保留觀測值的位置與範圍變化。因此，I-tSNE可作為區間值資料非線性探索性分析與視覺化的一項可行工具。

Interval-valued observations arise widely in symbolic data analysis, largedatabases, and settings involving measurement uncertainty. However, scalable nonlinear dimensionality reduction methods specifically designed for such data remain relatively limited. Building on t-distributed stochastic neighbor embedding (t-SNE), this study proposes Interval t-distributed Stochastic Neighbor Embedding (I-tSNE) as an extension for the exploratory analysis and visualization of interval-valued data. The proposed framework consists of four I-tSNE methods: two expansion-based approaches based on the vertices method and the quantile method, respectively, and two direct interval optimization approaches based on endpoint representation and center-radius representation, respectively. This study also examines the theoretical properties of the direct interval-optimization methods, including their consistency with standard t-SNE when intervals degenerate to points, the relationship between the center-radius distance and the Wasserstein distance, and the feasibility of low-dimensional interval representations. In addition, this study proposes a neighborhood-preservation assessment framework for interval-valued data based on the local continuity meta-criterion. The performance of the proposed methods is evaluated using simulated data and several real datasets. The results show that method performance varies with the data structure, the interval-generation mechanism, and the neighborhood scale, and that no single method uniformly dominates across all settings. When neighborhood preservation is the primary objective, some existing interval-valued benchmark methods can already achieve competitive performance. However, these methods are mostly built on linear projection or distance-configuration frameworks. In contrast, the proposed I-tSNE extends the nonlinear neighborhood-probability framework of t-SNE to interval-valued data, enabling the low-dimensional representation to capture local neighborhood relationships while simultaneously reflecting the location and range variation of the observations. Therefore, I-tSNE can serve as a feasible tool for nonlinear exploratory analysis and visualization of interval-valued data.

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