面向监督学习的稀疏平滑岭回归方法

摘要

岭回归是监督学习中的一个重要方法，被广泛用于多目标分类和识别。岭回归中一个重要的步骤是定义一个特殊的多变量标签矩阵，以实现对多类别样本的编码。通过将岭回归看作是一种基于图的监督学习方法，拓展了标签矩阵的构造方法。在岭回归的基础之上，进一步考虑投影中维度的平滑性和投影矩阵的稀疏性，提出稀疏平滑岭回归方法。对比一系列经典的监督线性分类算法，发现稀疏平滑岭回归在多个数据集上有着更好的表现。另外，实验表明新的标签矩阵构造方法不会降低原始岭回归方法的表现，同时还可以进一步提升稀疏平滑岭回归方法的性能。%Ridge regression is an important method in supervised learning.It is wide used in multi-class classification and recognition.An important step in ridge regression is to define a special multivariate label matrix,which is used to encode multi-class samples.By regarding the ridge regression as a supervised learning method based on graph,methods for constructing multivariate label matrix were extended.On the basis of ridge regression,a new method named sparse smooth ridge regression was proposed by considering the global dimension smoothness and the sparseness of the projection matrix.Experiments on several public datasets show that the proposed method performs better than a series of state-of-the-art supervised linear algorithms.Furthermore,experiments show that the proposed label matrix construction methods do not reduce the performance of the original ridge regression.Besides,it can further improve the performance of the proposed sparse smooth ridge regression.