因科技快速進步以及企業全球化影響，如何有效控制製造系統是企業必須面對的重要課題。該如何在新產品開發初期利用有限的樣本量找出重要參數、減少試產次數以降低成本，成為相當重要的議題。針對小樣本問題的學習，過去研究中較常見的處理方法為虛擬樣本產生法(Virtual Sample Generation, VSG)，然而過去的產生法大多針對數值屬性的樣本資料，較少處理混合名目屬性及數值屬性之樣本資料。本研究提出名目屬性及數值屬性之間相依合成產生虛擬樣本的方法，首先考慮數值屬性的趨勢相似度，相依生成虛擬樣本中數值屬性部分的值。並依序建構每一個數值屬性和名目類別值之間的模糊關係函數；找出名目屬性的所有類別組合以及組合與每一數值屬性之間的模糊關係。最後在給定數值屬性值的情況下，計算名目屬性的所有類別組合之可能性值，並使用 篩選具有較高可能性值的組合為虛擬樣本中名目屬性的部分。
實驗中將利用五個公開的數據集進行有效性驗證，並將整合拔靴法(Bootstrap Aggregating, Bagging)及合成少數超採樣技術(Synthetic Minority Over-sampling Technique, SMOTE)兩種虛擬樣本產生法做為實驗對照組。利用支援向量迴歸(Support Vector Regression, SVR)以及倒傳遞類神經網路(Back-propagation Neural Network, BPN)兩種演算法進行模型建構。而實驗結果顯示利用本研究提出的方法學習具名目輸入屬性的小樣本資料，優於使用Bagging 及SMOTE方法。

Due to the rapid progress of technology and globalization, how to control the manufacturing system effectively is an important issue that companies must confront. It is important to find pivotal parameters in pilot-run of new product and to decrease the number of trials to reduce costs with limited sample size. Present research deal small data learning problem with virtual sample generation methods (VSG).
This study proposed a VSG method for generating virtual sample data with dependently synthesized samples that contain numerical and nominal attributes. Firstly, generate numerical virtual samples by considering trend similarity of numerical attributes in small dataset. Secondly, construct the fuzzy relations between each numerical attribute and nominal categories sequentially. And find all category combinations of all nominal attributes and their fuzzy relations with each numerical attributes. Calculate the possibility of all category combinations when numerical value is given. And filter the possibility of category combination with to be the nominal virtual samples.
Five public datasets and two learning models will be used to test the efficiency of proposed method, including support vector regression and back-propagation neural network. Take bootstrap aggregating and synthetic minority over-sampling technique as control group. The result of experiment shows that the propose method is better than other VSG methods.

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