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    政大機構典藏 > 商學院 > 統計學系 > 期刊論文 >  Item 140.119/139847


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    題名: 基於類別資訊的監督式t分布隨機鄰近嵌入法於維度縮減與視覺化之研究
    Supervised t-SNE for Dimension Reduction and Visualization Based on Class Information
    作者: 吳漢銘
    Wu, Han-Ming
    張一凡
    貢獻者: 統計系
    關鍵詞: 流形學習;監督式維度縮減
    t-SNE;Manifold learning;Supervised dimensionality reduction;t-SNE
    日期: 2021-06
    上傳時間: 2022-04-12
    摘要: 維度縮減是資料特徵擷取的一種方法，可幫助使用者在低維度空間中，以視覺化方式探索此高維度資料所隱含的內在結構與資訊，並且有利於接續的分析處理與應用。近年來，非線性維度縮減法相關的研究及應用蓬勃發展，其中t分佈隨機鄰近嵌入法（t-SNE）是目前最熱門的非監督式維度縮減法之一，它主要的創新之處是以機率分佈來當成距離尺度。近期，將類別資訊加入距離計算的監督式t-SNE（稱為S-tSNE）方法被發展出來。然而，S-tSNE所採用的距離計算公式有兩個主要缺點。第一，當資料的類別個數僅有一個的時候，S-tSNE演算法並不會回復到原來的t-SNE。第二，此距離的定義並沒有滿足距離三個公理。為克服上述缺點，本研究提出了另一個基於類別資訊的監督式t-SNE方法，稱為連結監督式t分佈隨機鄰近嵌入法（L-tSNE）。所提出的方法運用了聚合階層式分群法中的群間距離計算連結法則，可發展出不需要額外調整超參數的距離計算方式，有效降低計算成本。我們以六組模擬資料來測試t-SNE、S-tSNE及L-tSNE等方法，並以排列檢定驗證維度縮減結果的可靠度。同時，我們也採用數個實際資料，實現L-tSNE非線性維度縮減與視覺化結果比較。最後我們將降維後之資料應用於分類問題上，用以評估各種維度縮減的效果。
    The dimensionality reduction (DR) technique can be regarded as a feature extraction tool for the data, it assists users to explore the data structure embedded within higher dimensional space in the lower-dimensional DR subspace. The DR results are helpful for the subsequent analysis and application. Recently, with the flourish development of the researches and applications of the nonlinear dimensionality reduction (NLDR) techniques, t-distributed stochastic neighbor embedding (t-SNE) is the most popular unsupervised NLDR method. The novelty of t-SNE is that it employs the probability density as the distance metric. Most recent, a supervised t-SNE (S-tSNE) has been proposed to incorporate the class information into the distance calculation process. However, S-tSNE has two major drawbacks. Firstly, if the number of the classes is one, S-tSNE cannot be reduced to t-SNE. Secondly, the distance metric proposed by S-tSNE did not satisfy the three distance axioms. To overcome these drawbacks, we proposed an alternative method, called L-tSNE, to incorporate the class information into the distance calculation process according to the linkage criterion of the agglomerative hierarchical clustering. The proposed method reduces the computational cost without the needs of the extra hyperparameters tuning. We use the simulation data to evaluate the proposed method and compare it with t-SNE and S-tSNE. We also use the permutation test to validate the significance of the DR results. Also, we apply the proposed method to real datasets for visualization and classification problems. The results shows that L-tSNE is comparable to S-tSNE and is superior than t-SNE.
    關聯: 中國統計學報, Vol.59, No2, pp.53-97
    資料類型: article
    顯示於類別:[統計學系] 期刊論文

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