基于稀疏回归和谱分析的无监督特征选择算法

Unsupervised Feature Selection Algorithm Based on Sparse Regression and Spectral Analysis

无监督特征选择是机器学习和计算机视觉等领域中的重要研究课题,可以降低数据维数,提高学习算法的性能。提出一种结合谱分析和稀疏回归的无监督特征选择算法。首先,利用经典最小二乘回归模型学习特征权重矩阵并结合谱分析探索数据的几何结构。其次,通过数据低维流形的最近邻概率自适应的构造相似矩阵。此外,为减少特征冗余,采用■2,1范数对模型正则化,使选择的特征更稀疏更有用。然后,通过交替迭代优化算法对模型求解并进行收敛性分析。最后,在四个数据集上与其他几种无监督特征选择算法对比,验证算法的有效性。

Unsupervised feature selection is an important research topic in the fields of machine learning and computer vision,which can reduce the dimension of data and improve the performance of learning algorithms.An unsupervised feature selection algorithm combining spectral analysis and sparse regression is proposed.Firstly,the classical least squares regression model is used to learn the feature weight matrix and spectral analysis is combined to explore the geometric structure of the data.Secondly,the similarity matrix is constructed adaptively by the nearest neighbor probability of the data low-dimensional manifold.In addition,in order to reduce feature redundancy,the■2,1norm is used to regularize the model,which makes the selected features more sparse and useful.Then,the model is solved by alternating iterative optimization algorithm and its convergence is analyzed.Finally,the effectiveness of the algorithm is verified by comparing with other unsupervised feature selection algorithms on four data sets.