軟體品質保證在軟體開發中期中佔有很重要的部分，而錯誤預測是提升軟體品質保證的一個好方法，他常被用來找出有錯誤傾向的程式以幫助使用者分配品質保證的資源（如測試及除錯的資源），精準的錯誤預測系統可以帶來可觀的利益，然而現今的系統仍有許多地方有待改進，如使用不同層級的特徵資料或使用當今先進的技術來建立預測模型。
錯誤預測可以根據分析資料的密度與分類器分成許多種類，其中分析資料的密度決定了使用者需要花多少資源去檢查被預測為有錯誤的資料，即時錯誤預測是使用修改層級的特徵資料來建立預測模型，此種方法可以幫助品質保證工程師更精確地找出錯誤，他們可以藉由查找特徵資料中的修改紀錄來檢查程式碼，此種方法可以有效地減少需要檢查的範圍。近來深度學習可謂電腦科學中新興的研究領域，他藉由強大的資料分類能力解決的許多領域各式各樣的問題，此外有許多研究指出深度學習也可以適當地應用於軟體工程相關的資料集，使用深度學習建立錯誤預測模型或許能有效地提升預測的表現。
在本篇論文中，我們提出了激活函數的加權組合來改善錯誤預測模型，當有許多種模型或分類器的時候，加權組合常被用來結合各個種類的特性並且創造出一個新的模型或分類器，他們結合了不同激活函數的優點來建立深度學習中的神經網路。深度置信網路被稱為最適合軟體工程資料集的神經網路，我們透過二元和三元加權組合六種最先進的激活函數，建立了41種即時錯誤預測模型期望能改進預測的表現，我們使用了六個大型開源專案來評估我們所提出的方法，一共包含了227,417筆特徵資料，而實驗結果顯示二元的激活函數加權組合表現結果優於單一的激活函數。
為了找出錯誤預測模型中最關鍵的參數，我們利用一次一因子方法進行敏感度分析，結果顯示微調丟棄數和有限波茲曼狀態機的世代數量是精準度和時間的關鍵參數，如果精準度被視為最重要的結果，則應該優先調整微調丟棄數、相對地如果時間為優先考量，則應該先調整有限波茲曼狀態機的世代數量。

Software quality assurance is an essential part of the Software Development Life Cycle (SDLC). Defect prediction is a prominent approach to enhance software quality assurance. It is a common technique for identifying defect-prone programs, which help the practitioners allocate their quality assurance efforts (e.g., testing and debugging). An accurate prediction may bring significant benefits. However, there is still space for improvements by applying different levels of instances or using some state-of-the-art techniques to construct the prediction models.
There are several kinds of defect predictions which vary from granularity to classifier during the SDLC. The prediction granularity determines the efforts that practitioners take to inspect the buggy instances. Just-In-Time defect prediction, which uses change-level instances to train the prediction model, helps the quality assurance engineers discover the defects precisely. They can inspect the code by reading the change log reported in the instances, which would minimize the range of the defective area. Recently, deep learning is a promising research domain in computer science. It can solve or improve versatile problems in a wide range of fields by its powerful ability for data classification. Besides, there are several researches showing that datasets related to software engineering can be applied to deep learning appropriately. It may improve the performance to construct defect prediction models based on deep learning.
In this study, we propose several kinds of weighted combinations of activation functions to improve the defect prediction models, comprising of arithmetic, geometric, harmonic, contra-harmonic, and cubic weighted combinations. When there are several kinds of models or classifiers, weighted combinations are always applied to combine the strengths and create a new model or classifier. They can combine the advantage of different activation functions to train the neural network in deep learning. Deep belief network is claimed to be the most suitable neural network for software engineering datasets. We construct 41 kinds of Just-In-Time defect prediction models by deep belief networks built with dual and ternate combination of six kinds of state-of-the-art activation functions to improve the predictions. We use six large open source projects, including 227,417 instances, to evaluate the performance of our approach. The experimental result shows that dual weighted combinations of activation function perform better than single activation function.
In order to find the most critical parameter in the defect prediction model, in this study we plan to use the One-factor-at-a-time approach to perform sensitivity analysis. It can be figured out that fine-tuning dropout and number of RBM epochs are the critical parameters for accuracy and time. If accuracy is identified as the first priority, fine-tuning dropout should be set in advance. Number of RBM epochs should be set first if time takes precedence.

Abstract i
中文摘要 iii
List of Tables vii
List of Figures viii
List of Symbols ix
Acronyms and Abbreviations ix
Notation x
Chapter 1 Introduction 1
Chapter 2 Background and Related Work 5
2.1 Defect Prediction 5
2.2 Deep Learning Techniques 8
2.3 Activation Function 11
2.3.1 Saturated Activation Function 12
2.3.1.1 Sigmoid 12
2.3.1.2 TanH 14
2.3.2 Unsaturated Activation Function 15
2.3.2.1 ReLU 15
2.3.2.2 Leaky ReLU 17
2.3.2.3 ELU 18
2.3.2.4 Softplus 19
Chapter 3 Incorporation of Weighted Combination into Defect Prediction in Deep Learning 21
3.1 Weighted Activation Function 21
3.2 Ingredients of Deep Belief Network 25
3.2.1 Applied Features 25
3.2.2 Preprocessing 27
3.3 Architecture of Deep Belief Network 28
3.4 Methodology 31
Chapter 4 Experimental Results and Analysis 36
4.1 Datasets 36
4.2 Evaluation Metrics 38
4.3 Defect Prediction Result 40
4.4 More Observation and Discussion 48
Chapter 5 Sensitivity Analysis 52
5.1 One-factor-at-a-time (OFAT) method 52
5.2 The most sensitive parameter 53
Chapter 6 Discussion 56
6.1 RQ1: Could Deep Learning Technique Be Applied to Defect Prediction? 56
6.2 RQ2: How Is the Effect of Weighted Combination On Defect Prediction? 56
6.3 RQ3: What is the best kind of the weighted combination for defect prediction? 58
6.4 RQ4: What Is the Major Factor of Defect Prediction Based On Deep Learning? 58
6.5 Threat to Validity 58
Chapter 7 Conclusion and Future Work 62

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