基于带偏倚最大间隔二值矩阵分解的多值矩阵分层填充

Maximum margin matrix factorization is an important method for solving matrix completion. It completes matrix completion by projecting each item into a low-dimensional feature space, constructing a hyperplane for each user, and classifying each item. However, when decomposing a binary matrix, traditional maximum margin matrix factorization methods assume that the constructed hyperplane passes through the origin. In order to make the hyperplane more universal and improve the classification effect, a certain bias amount is added to the hyperplane, and a maximum margin binary matrix factorization method with bias is proposed. For the problem of multi-valued matrix completion, the above improved binary matrix factorization method is used multiple times to perform hierarchical completion on the multi-valued matrix, and an alternating optimization method is used for solution. The experimental results on the real dataset Movielens are better than the existing methods, and matrix factorization can be completed in a lower-dimensional feature space, which can effectively improve the speed of matrix factorization and reduce the computing memory.

最大间隔矩阵分解是解决矩阵填充的重要方法,它通过将每个项目投影到低维特征空间,构建出每个用户的超平面,对每个项目进行分类来完成矩阵填充.然而传统的最大间隔矩阵分解方法对二值矩阵进行分解时都假设所构造的超平面经过原点.为了使超平面具有普适性,提高分类效果,将超平面移动一定的偏倚量,提出了带偏倚的最大间隔二值矩阵分解方法.对于多值矩阵的填充问题,通过多次采用上述改进的二值矩阵分解方法,对多值矩阵进行分层填充,并采用交替优化的方法进行求解.在真实数据集Movielens上的实验结果优于目前已有的方法,并且在较低维的特征空间中就能够完成矩阵分解,能有效提高矩阵分解速度,减少计算内存.