在許多研究報告中，虛擬樣本生成法經常被用於提高小資料學習性能。適當地估計資料的分佈在虛擬樣本生成過程中扮演一個重要的角色，通常面對具有簡單分佈的資料則該方法假定資料為一個簡單的分佈確實可以獲得較佳性能，但是資料可能是一個複雜的分佈。通常混合的資料集具有多峰分佈，也就是資料的分佈並不是一個簡單且單峰的分佈。為了解決這個問題，本研究假設資料來自一個兩參數型的韋伯分佈並且提出最大P值法來估計兩參數值以用來建構一個非線性且非對稱形狀的小資料分佈。更進一步地，本研究提出新的方法來偵測多峰資料集，以避免不當地假設資料為單峰分佈的問題。本研究利用常見的k-means分群方法來找出可能的群集，並且針對每個群內的樣本使用已估計韋伯變量來產生多峰性虛擬樣本。在提出的方法提出一個準則來決定虛擬樣本數的大小，該準則為測量原本樣本和虛擬樣本之間的Weibull偏斜之誤差的變化程度。本研究提供模擬的資料集與兩個實例來驗證最大P值法在小樣本數量下是一個更適當的技術來提升資料分佈估計的正確性。此外，本研究運用六個資料集來驗證提出所提出方法的性能，並在不同的訓練資料數量下比較分類的正確性。最後的實驗結果使用一個無母數檢定法來檢定所提出的方法比整體趨勢擴散法具有更佳的分類性能。

Virtual sample generation approaches have been used with small data sets to enhance learning performance in a number of reports. The appropriate estimation of the data distribution plays an important role in this process, and the resulting performance is usually better for data sets that have a simple distribution rather than a complex one. However, mixed-type data sets often have a multi-modal distribution instead of a simple, uni-modal one. In order to solve this problem, this study assumes that a data set follows a two-parameter Weibull distribution, and proposes the Maximal P-Value method to estimate two parameters of a Weibull distribution to construct a nonlinear and asymmetrical small data distribution. Further, this study thus proposes a new approach to detect multi-modality in data sets, to avoid the problem of inappropriately using a uni-modal distribution. This work utilizes the common k-means clustering method to detect possible clusters, and, based on the clustered sample sets, a Weibull variate is estimated for each of these to produce multi-modal virtual data. In this approach, the degree of error variation in the Weibull skewness between the original and virtual data is measured and used as the criterion for determining the sizes of virtual samples. This study provides simulated data sets and two practical examples to demonstrate that the Maximal P-Value method is a more appropriate technique to increase estimation accuracy of data distribution with small sample sizes. In addition, six data sets with different training data sizes are employed to check the performance of the proposed method, and comparisons are made based on the classification accuracy. Finally, the experimental results using non-parametric testing show that the proposed method has better classification performance than that of the Mega-Trend-Diffusion method.

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