摘要
稀疏向量特征提取是指在优化时利用各种范数对解进行约束,从而获得带有稀疏特征的最优解,其广泛应用于复杂系统中的机器学习、深度学习和大数据分析等领域的特征提取问题.大量的研究表明各种范数如L_(0)范数、L_(1)范数和L_(2)范数的方法都存在各自的缺点,主要表现在越容易求解的范数越不精准稀疏,越精准稀疏的范数越难求解.文章提出了一种基于SCN函数共轭梯度方向的稀疏向量特征发现算法(CGDL),稀疏向量特征发现可以用一个稀疏特征提取优化模型建立,其目标函数是一个SCN函数,对其中的L_(0)范数进行转换,形成一个具有特殊结构优化问题,这个问题等价于双层规划的凸-凹极小极大化问题,这类问题可以解决稀疏回归、图像特征和压缩感知等问题.文章给出了上述模型的稀疏特征提取算法的详细计算步骤和收敛性分析证明,并且对给定的实际数据集和高维模拟数据集对算法的有效性、复杂性和收敛速度进行了数值对比实验,表明了该算法在精准度和稀疏性上显著优于其他对比方法,并且具有较好的收敛速度.
Sparse vector feature extraction refers to the use of various paradigms to constrain the solution during optimization,and to obtain a solution with sparse features,which is widely used in complex systems in machine learning,deep learning,big data analysis and other fields of feature extraction problems.A large number of studies have shown that some norms such as L_(0)norm,Li norm,and L_(2)norm,have their own problems.The less accurate and sparse the norm is easier to solute,and the more accurate and sparser the norm is more difficult to solve.In this paper,a sparse vector feature discovery algorithm(CGDL)based on the conjugate gradient direction of SCN function is proposed.The sparse vector feature discovery can be established by a sparse feature extraction optimization model.Its objective function is a SCN function,and the L_(0)norm is transformed to form a convex-concave minimax problem with special structure equivalent to bilevel programming.This kind of problem can solve the problems of sparse regression,image feature,and compression perception.This paper gives the detailed calculation steps and convergence analysis proof of the sparse feature extraction algorithm of the above model.A numerical comparison experiment is carried out on the effectiveness,complexity and convergence speed of the algorithm between the given real data set and the high-dimensional simulation data set.It is proved that this method is significantly superior to other comparison methods in accuracy and sparsity,and has a good convergence rate.
作者
温国栋
孟志青
蒋敏
潘阳
WEN Guodong;MENG Zhiqing;JIANG Min;PAN Yang(School of Management,Zhejiang University of Technology,Hangzhou 310023)
出处
《系统科学与数学》
CSCD
北大核心
2024年第2期355-372,共18页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金面上项目(11871434)资助课题。
