计算机工程与应用
計算機工程與應用
계산궤공정여응용
Computer Engineering and Applications
2015年
21期
6-11,47
,共7页
评分矩阵%低秩矩阵恢复%秩1矩阵%用户聚类数%奇异值分解
評分矩陣%低秩矩陣恢複%秩1矩陣%用戶聚類數%奇異值分解
평분구진%저질구진회복%질1구진%용호취류수%기이치분해
rating matrix%low-rank matrix completion%rank-one matrix%number of user clustering%singular value decomposition
评分矩阵（rating matrix）的特点是高维、稀疏、低秩，对其研究的主要方法是低秩矩阵恢复。对这些算法而言，不同评分矩阵的秩，会得到不同的恢复精度。但目前没有理论来研究评分矩阵秩的估计，从而影响了这些算法的应用。从理论上分析了用户聚类数与评分矩阵秩的关系，给出用户聚类数的计算方法，并在此基础上提出一种基于聚类数的秩1矩阵恢复（Clusters Number Rank-1 Matrix Completion，CN-R1MC）算法来恢复评分矩阵。通过在多个推荐系统数据集上的实验证明：用户聚类数能较好地近似评分矩阵的秩，这对提高评分矩阵的恢复精度有重要的作用。所提出的算法有较好的应用价值。
評分矩陣（rating matrix）的特點是高維、稀疏、低秩，對其研究的主要方法是低秩矩陣恢複。對這些算法而言，不同評分矩陣的秩，會得到不同的恢複精度。但目前沒有理論來研究評分矩陣秩的估計，從而影響瞭這些算法的應用。從理論上分析瞭用戶聚類數與評分矩陣秩的關繫，給齣用戶聚類數的計算方法，併在此基礎上提齣一種基于聚類數的秩1矩陣恢複（Clusters Number Rank-1 Matrix Completion，CN-R1MC）算法來恢複評分矩陣。通過在多箇推薦繫統數據集上的實驗證明：用戶聚類數能較好地近似評分矩陣的秩，這對提高評分矩陣的恢複精度有重要的作用。所提齣的算法有較好的應用價值。
평분구진（rating matrix）적특점시고유、희소、저질，대기연구적주요방법시저질구진회복。대저사산법이언，불동평분구진적질，회득도불동적회복정도。단목전몰유이론래연구평분구진질적고계，종이영향료저사산법적응용。종이론상분석료용호취류수여평분구진질적관계，급출용호취류수적계산방법，병재차기출상제출일충기우취류수적질1구진회복（Clusters Number Rank-1 Matrix Completion，CN-R1MC）산법래회복평분구진。통과재다개추천계통수거집상적실험증명：용호취류수능교호지근사평분구진적질，저대제고평분구진적회복정도유중요적작용。소제출적산법유교호적응용개치。
Rating matrix is high-dimensional, sparse and low rank. The low rank matrix recovery is the important method for rating matrix of research. For these algorithms, different scoring matrix rank will obtain different recovery precision. But there is no theory to study the score matrix rank, thus affecting the application of these algorithms. This paper analyzes the relationship between clustering number of user and rank of rating matrix, and then it presents the method of computing the cluster number of user, and on this basis, it proposes a number of clusters based on rank 1 matrix recovery(Clusters Number Rank-1 Matrix Completion, CN-R1MC)algorithm to recover rating matrix. Through a plurality of recommendation system data sets on the experiments, the cluster number of user can approximate rank of rating matrix better, which has an important role in improving recovery accuracy for the rating matrix. The proposed algorithm has good application value.
