近年來大數據以及機器學習技術的蓬勃發展，推薦系統被廣泛應用於各種資訊系( Information Systems )上。如何有效地利用這些巨量的資料增進推薦系統效能，成為具有挑戰的工作。圖形學習表示法( Graph Embedding )便是一種特徵提取 ( Feature Extraction ) 的技術，此方法目的在於如何有效的將不同節點以及節點間的關係投射到低維度向量空間並賦予特徵向量。因此，如何有效率且精準的描述這些向量空間的概念，也被加入到圖形學習表示法的領域。本論文基於非對稱常態分佈( Skew Normal Distribution)之特性，提出以機率分佈重新檢視表示法向量空間，並針對使用者與喜好物品在非對稱常態分佈上會趨向正向偏態( Positive Skewness )的特性，將偏態之概念加入目標函式中進行優化。特別的是，本論文所提出之偏態項優化式為一通用優化項，能適用於過去各種 State of The Art 推薦演算法上，進而重塑各種推薦演算法所構建之向量空間。從理論面來論述，我們證明了如何在優化各種推薦演算法上之餘，同時優化基於非對稱常態分佈之 Shape 參數，此參數與分佈之偏態值為正相關。此外，針對所提出之演算法能同時最大化接收者操作特徵曲線( Receiver Operating Characteristic Curve ( ROC Curve ) )之論述，我們也提出一數學證述來解釋與分析。在數據實驗上，本文以將此偏態優化項主要實驗於矩陣分解類之推薦算法上，且為了展示方法的一致性，我們也將此偏態優化項實驗在基於圖形學習表示法的推薦演算法上，來做驗證本方法的可行性與正確性。而為了驗證此方法，本文實驗於五種不同的真實世 界巨量資料上，並且針對兩種常見的推薦任務: Top-N 推薦任務以及 Query-based 推薦任務上皆有所比較與操作。最後，在實驗結果的部分，結果呈現出我們所提之演算法與過去各種 State of The Art 之推薦演算法中實際比較後皆取得更優的表現。

In recent years, machine learning technology has drastically improved in adapting big data among various fields, including commercial streaming online service and recommendation systems. Especially in recommendation systems case, the user-based recommendation systems or personalized recommendation is one of the most challenging tasks. In this paper, hence, we propose a novel optimization criterion that leverages features of the skew normal distribution to better model the problem of personalized recommendation. Specifically, the developed criterion borrows the concept and the flexibility of the skew normal distribution and also based on three hyper-parameters to not only provide the degree of freedom in optimization and also highly attached to the optimization criterion. Moreover, we both provide the relation of optimization of the proposed criterion and the shape parameter in the skew normal distribution from theoretical point of view and provide the analogies and provide the theoretical proof on asymptotic analysis of the area under the ROC curve to our proposed method. Experimental results conducted on five large-scale real-world datasets reveal that our proposed optimization criterion significantly achieve the best performance of the state of the art and yields consistently on all tested datasets.

致謝 1

中文摘要 2

Abstract 3

第一章 緒論....................................... 1
1.1 前言..................................... 1
1.2 研究目的.................................. 3
1.3 研究動機詳述 ............................... 4
第二章 相關文獻探討.................................. 5
2.1 圖形學習表示法.............................. 5
2.2 推薦系統.................................. 6
2.3 表示法空間調整.............................. 8
第三章 研究方法..................................... 9
3.1 個人化推薦系統.............................. 9
3.1.1 問題定義.............................. 9
3.1.2 先備相關知識 ........................... 10
3.2 偏態排序優化(SkewnessRankingOptimization) ...... 12
3.2.1 觀察與動機 ............................ 13
3.2.2 優化準則.............................. 14
3.2.3 模型理論敘述與證明 ....................... 16
3.2.4 AUC分析.............................. 19
第四章 實驗結果與討論................................ 21
4.1 資料集 ................................... 21
4.2 比較基準模型 ............................... 22
4.3 實驗設定與驗證標準 ........................... 23
4.3.1 實驗設定.............................. 23
4.3.2 驗證標準.............................. 23
4.4 實驗結果.................................. 24
4.4.1 Top-N推薦任務表現 ....................... 24
4.4.2 敏感度分析 ............................ 26
4.4.3 機率分佈之討論.......................... 30
4.4.4 估計量之差異分析 ........................ 32
第五章 結論....................................... 34
參考文獻.......................................... 35

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