推薦系統中常見的算法，包含基於內存的協同過濾及基於模型的協同過濾，在成績矩陣作為輸入資料階段，我們主要探討基於模型協同過濾中的矩陣分解，如圖一。
SVD的結構是將矩陣進行分解，形成三個子矩陣U、Σ和V，其中Σ代表不同維度的重要特徵值，為一正交矩陣，且數值為降冪排列，Steven L. Brunton等人也提及特徵矩陣中數值皆為非負值，因此我們認為每一特徵值可對應到U及 中不同的行或欄，若針對Σ進行門檻的篩選，將矩陣還原後可表示為保留部分特徵值所獲得的訊息量，在相關論文中更以門檻測試來觀察奇異值門檻的保留，其目的為簡化數據，壓縮維度與去除數據噪音。
若將SVD應用於成績矩陣，在使用者登入後取得成績向量，與成績矩陣合併形成測試輸入，根據矩陣分解中的奇異直分解進行運算，可表示為圖三，課程與學生建立的成績矩陣可分解為課程對特徵、特徵對特徵、特徵對學生的子矩陣， 我們會針對特徵矩陣Σ進行門檻的篩選，保留測試學生與訓練學生合併後進行預測的訊息量。
實驗過程省略
我們可以從以上實驗過程中觀察，較佳的參數於SVD門檻介於0.7與0.9之間，因此選擇0.8作為SVD最佳門檻，而Jaccard門檻在各方法艱顯示較佳的門檻為0.6，因此我們將此兩數值做為最佳算法的參數組合
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