本研究的目的是研究最大邊際分類限制對於約束非負矩陣分解目標函數的影響。 非負矩陣分解（NMF）是基於特徵空間的降維技術。不幸的是，大多數現有NMF的方法並不足以編碼高階數據信息，且忽略了數據集中的局部幾何結構。此外，在以往的方法中分類步驟和矩陣分解步驟為獨立分開進行。第一個執行數據轉換，第二個利用支持向量機（SVM）分類那些轉換後的數據。 因此，在這項研究中，我們使用統一最大化邊際分類限制於限制型NMF的最佳化以結合SVM與限制型NMF。所提出的演算法是從NMF算法通過利用空間屬性和保護圖型結構屬性所推導出來的。還提出了一種乘法演算法來更新，並解決對應的最佳化問題。 基準圖像數據集的實驗結果證明了該方法的有效性。結果說明，我們提出的算法提供了更好的臉部表示，並且比標準非負矩陣分解及其變體獲得更高的識別率。 ;The purpose of this study is to investigate the effects of merging maximum margin classification constraints on the constrained non-negative matrix factorization objective function. Non-negative matrix factorization (NMF) is a dimension-reduction technique based on a low-rank approximation of the feature space. Unfortunately, most existing NMF based methods are not ready for encoding higher-order data information and ignore the local geometric structure contained in the data set. Furthermore, the previous classification approaches which the classification and matrix factorization steps are separated independently. The first one performs data transformation and the second one classifies the transformed data using classification methods as support vector machine (SVM). In this research, therefore, we joint SVM and constrained NMF into one by uniting maximum margin classification constraints into the constrained NMF optimization. The proposed algorithm is derived from NMF algorithm by exploiting both spatial and graph-preserving properties. A multiplicative updating algorithm is also proposed to solve the corresponding optimization problem. Experimental results on benchmark image data sets demonstrate the effectiveness of the proposed method. The results show that our proposed algorithm provides better facial representations and achieves higher recognition rates than standard non-negative matrix factorization and its variants.
