最小二乘损失在多视角学习中的应用

Application of least squares loss in the multi-view learning algorithm

SVM-2K模型是一种采用了非光滑合页损失的多视角学习算法。由于非光滑模型的求解过程较为复杂,因此引入了光滑的最小二乘损失的最小二乘支持向量机作为一种经典的支持向量机算法。由于光滑的最小二乘损失的最小二乘支持向量机算法具有计算简单、运算速度快、精度高等优点,被广泛应用于科研领域。为了提高模型的训练速度,在SVM-2K模型中引入了最小二乘思想。首先,提出了完全应用最小二乘损失的LSSVM-2K模型,利用最小二乘损失替换SVM-2K模型中的合页损失,可通过求解线性方程组代替经典多视角学习模型的二次规划求解方法;其次,为探究最小二乘损失对SVM-2K模型的影响,提出了在另外两个部分应用最小二乘损失的模型——LSSVM-2KI和LSSVM-2KII。将新模型与其他多视角学习模型,如SVM_(+)(可分为SVM_(+A)和SVM_(+B))、MVMED、RMvLSTSVM和SVM-2K模型在同样条件下应用在动物特征数据集(AWA)、UCI手写数字集(Digits)和森林覆盖面积数据集上,以检验新模型的有效性。实验结果表明,3种新模型具有良好的分类表现。特别是LSSVM-2KI模型,在分类精度上更具优势;LSSVM-2K模型不仅在分类精度上效果较好,而且在计算速度上也具有较大的优势;LSSVM-2KII模型在分类效果和训练时间上介于两者之间。

The SVM-2K model is a multi-view learning algorithm using nonsmooth hinge loss.However,the solution process of nonsmooth model is more complex.The LSSVM with smooth least squares loss is introduced as a classical support vector machine algorithm which is widely used in the scientific research field because of its simple calculation,fast operation speed and high precision.In order to improve the training speed of the model,the least square idea is introduced into the SVM-2K.First,the LSSVM-2K model which fully applies the least square loss is proposed.The least square loss is used to replace the hinge loss in the SVM-2K model.The quadratic programming method of the classical multi-view learning model can be replaced by solving the linear equations;second,in order to explore the influence of least squares loss on the SVM-2K model,two other models using least squares loss are proposed,LSSVM-2KI and LSSVM-2KII.In this paper,the new model and other multi-view learning models:SVM_(+)(which can be divided into SVM_(+A) and SVM_(+B)),MVMED,RMvLSTSVM and SVM-2K are applied to three sets of data sets:animal feature data set(AWA),UCI handwritten digits(Digits)and forest coverage area to test the effectiveness of the new model.Experimental results show that the three new models have a good classification performance.In addition,the LSSVM-2KI model has more advantages in classification accuracy.The LSSVM-2K model not only has a better classification accuracy,but also has great advantages in calculation speed.The LSSVM-2KII model lies between the two in classification effect and training time.