| 摘要: | 在本文中，我們提出了幾種新方法 擴展矩陣分解，包括非負矩陣分解（NMF),、複數矩陣分解（CMF）、與主成分分析（PCA）相結合的捲積神經網絡（CNN)。我們的方法不僅僅適用於一般的數據表示，特別的是可用於圖像分析，同時超越了圖像處理領域的最新技術水準。
基於NMF模型的開發，論文設計了兩種約束NMF模型 為了獲得稀疏表示。特別是對於第一個型號我們構建了一個合適的單純錐底座，它結構緊湊且具有很高的泛化能力，我們將此模型命名為魯棒的最大體積約束圖非負矩陣分解（MV_GNMF）。第二，我們添加了新約束 增強稀疏性 代表權。在此，大基錐和稀疏表示 強加於非負矩陣分解 與Kullback-Leibler（KL）分歧（conespaNMF_KL），它通過基礎上的大型單純錐約束和提取特徵上的稀疏正則化來實現稀疏性。
复矩陣分解（CMF） 楷模 是自然延伸 NMF，其中處理複雜數據。這些型號具有廣泛的應用，例如 人臉識別 和臉部表情識別。最近，CMF和示例嵌入複雜矩陣分解（EE-CMF）[37]顯示了面部表情識別中強大的數據表示方法，其中像素密集的實際值轉化為複雜域。按照[37]中的工作，我們開發了CMF方法來增強數據顯示的能力，通過將更多約束集成到EE-CMF模型 中，以獲得圖正則化的示例嵌入复矩陣分解（gEE-CMF）和稀疏性分別用稀疏性約束（sEE-CMF）模型實現樣本嵌入複雜矩陣分解。此外，我們還提出了兩種複雜領域的數據學習方案，即 複雜域（PCMF）和（DPCMF）上的無監督和監督學習方法。
本文的另一個重點貢獻是提出了複雜域上的核方法，我們擴展了用於復雜矩陣分解（DKCMF）的深度核方法，以獲得有效的數據表示。在這項工作中，首先通過由採用的Euler內核定義的顯式映射，將實際數據投影到復雜字段中。然後，建立隱式希爾伯特核空間以將數據投影到高維空間。在特徵空間中，我們應用複雜矩陣因子分解來有效地減少高維數據點的維度，從而獲得新的數據描述符。
主成分分析（PCA）被稱為降維和多變量分析的強大技術，而卷積神經網絡（CNN）是強大的視覺模型，可產生特徵的層次結構。
人臉識別實驗中，人臉表情識別和人體動作識別的實驗表現與比較方法相比，所提出的方法提供更了強大的特徵，並獲得了一致且更好的識別結果。
;In this dissertation, we proposed several new approaches to extend matrix factorization including nonnegative matrix factorization (NMF), complex matrix factorization (CMF), and convolution neural networks (CNN) integrating with principal component analysis (PCA). Our approaches are not only specifically suited for data representation in general and for image analyzing in particular but also outperform to the state-of-the-art in image processing field.
Based on the development of NMF models, the thesis designed two constrained NMF models in order to obtain the sparsity representations. Particularly, for the first model, we constructed a proper simplicial cone base which is compact and has high generalization ability. We named this model is the robust maximum volume constrained graph nonnegative matrix factorization (MV_GNMF). For the second one, we added new constraints to enhance the sparseness of representation. In this, a large basis cone and sparse representation were imposed on non-negative matrix factorization with Kullback-Leibler (KL) divergence (conespaNMF_KL). It achieves sparseness from a large simplicial cone constraint on the base and sparse regularize on the extracted features.
Complex matrix factorization (CMF) models are natural extensions of NMFs, in which the complex data is treated. These models have a wide range of applications, e.g. face recognition and facial expression recognition. Recently, CMF and exemplar-embed complex matrix factorization (EE-CMF) [37] show the powerful data representation in facial expression recognition, in which the real value of pixel intensive is transformed into the complex domain. Follow the work in [37], we developed CMF approaches to enhance the ability of data display by integrating more constraints into EE-CMF model such as graph to obtain the graph regularized exemplar-embed complex matrix factorization (gEE-CMF), and sparsity to achieve the exemplar-embed complex matrix factorization with sparsity constraint (sEE-CMF) models, respectively. We also proposed two schemes of data learning on complex field, namely unsupervised and supervised learning methods on the complex domain (PCMF) and (DPCMF).
Principal component analysis (PCA) is known as a powerful technique for dimensionality reduction and multivariate analysis, whereas convolutional neural networks (CNNs) are powerful visual models that yield hierarchies of features. Taking the advances of these models, we proposed the model (CNN-PCA) by combining them together to acquire a discriminative data representation.
Experiments on face recognition, facial expression recognition, and human action recognition reveal that the proposed methods extract robust features and provide consistently better recognition results than compared methods. |
