時間序列資料通常具有高維度、時間相依性、雜訊干擾與局部型態變化等特性，因此如何建立有效的特徵表示方式，對分類表現具有關鍵影響。Gramian Angular Field、Markov Transition Field 與 Recurrence Plot 等二維矩陣表示分類法，透過將一維時間序列轉換為二維矩陣，使分類器能夠從矩陣或影像紋理中學習序列結構。這些方法主要著重於原始時間點之間的數值關係、狀態轉移或相空間距離，但較少考慮局部序列分布之間的差異，且多數方法皆直接針對原始序列進行特徵擷取。因此，本研究提出一種結合三通道局部經驗分布與 Wasserstein 距離矩陣的時間序列分類方法，命名為 Empirical-Wasserstein with Support Vector Machine，簡稱 EW-SVM。本方法將原始序列、一階差分序列與去除趨勢後的序列視為三個通道，並以滑動視窗擷取各通道之局部子序列，將其視為經驗分布。接著，透過一維 Wasserstein 距離衡量子序列間的分布差異，形成 Empirical-Wasserstein 距離矩陣，並將三個通道之距離矩陣向量化後串接，作為支援向量機（support vector machine, SVM）分類器的輸入特徵。本研究透過七組二元分類模擬資料評估所提方法之表現，包含週期性背景下的兩種局部異常資料、AR(1) 模型下的兩種局部參數變動資料，以及 ARIMA(1,1,1) 模型下的三種局部參數變動資料。結果顯示，EW-SVM 在七組模擬資料中皆取得最佳分類表現。進一步以 UCR Time Series Classification Archive 中的 31 個二元分類資料集進行實證比較，並與七種方法進行比較。結果顯示，EW-SVM 的平均排名僅次於 miniROCKET，並在 9 個資料集上取得最佳 F1-score，其中 4 個為單獨最佳，5 個為並列最佳；相較於其他二維矩陣表示法，EW-SVM 亦具有較佳的分類表現。本研究所提出之三通道 Empirical-Wasserstein 表示法，整合了原始序列之局部分布、相鄰變化之局部分布，以及去除趨勢後之局部分布差異資訊，可提供一種適用於局部異常時間序列分類的特徵建構方法。

Time series data are often high-dimensional, temporally dependent, noisy, and affected by local pattern variations. Constructing an effective feature representation is therefore crucial for classification performance. Two-dimensional matrix representation methods, such as Gramian Angular Field, Markov Transition Field, and Recurrence Plot, transform one-dimensional time series into two-dimensional matrices, enabling classifiers to learn sequential structures from matrix or image textures. These methods mainly focus on pointwise numerical relationships, state transitions, or phase-space distances among the original time points. However, they pay relatively little attention to distributional differences among local subsequences, and most of them extract features directly from the original series. To address this issue, this study proposes a time series classification method that combines a three-channel local empirical-distribution representation with Wasserstein distance matrices. The method is named Empirical-Wasserstein with Support Vector Machine, abbreviated as EW-SVM. The raw series, first-order differenced series, and detrended series are treated as three channels. For each channel, sliding windows are used to extract local subsequences as empirical distributions. The one-dimensional Wasserstein distance is then used to construct Empirical-Wasserstein distance matrices, whose vectorized upper triangular elements from the three channels are concatenated as input features for a support vector machine (SVM) classifier. The proposed method is evaluated using seven binary classification simulation settings, including two types of local anomalies under periodic backgrounds, two types of local parameter changes under AR(1) models, and three types of local parameter changes under ARIMA(1,1,1) models. The results show that EW-SVM achieves the best classification performance across all seven simulation settings. Further experiments are conducted on 31 binary classification datasets from the UCR Time Series Classification Archive and compared with seven competing methods. The results show that EW-SVM achieves the second-best overall average rank, after miniROCKET, and obtains the best F1- score on 9 datasets, including 4 sole-best and 5 tied-best cases. Compared with other two-dimensional matrix representation methods, EW-SVM also demonstrates better classification performance. The proposed three-channel Empirical-Wasserstein representation integrates information from the local distribution of the raw series, the classification, particularly in settings involving local anomalies.

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