IEEE Trans Pattern Anal Mach Intell. 2011 Oct;33(10):2013-25. doi: 10.1109/TPAMI.2011.44. Epub 2011 Mar 10.
In many information processing tasks, one is often confronted with very high-dimensional data. Feature selection techniques are designed to find the meaningful feature subset of the original features which can facilitate clustering, classification, and retrieval. In this paper, we consider the feature selection problem in unsupervised learning scenarios, which is particularly difficult due to the absence of class labels that would guide the search for relevant information. Based on Laplacian regularized least squares, which finds a smooth function on the data manifold and minimizes the empirical loss, we propose two novel feature selection algorithms which aim to minimize the expected prediction error of the regularized regression model. Specifically, we select those features such that the size of the parameter covariance matrix of the regularized regression model is minimized. Motivated from experimental design, we use trace and determinant operators to measure the size of the covariance matrix. Efficient computational schemes are also introduced to solve the corresponding optimization problems. Extensive experimental results over various real-life data sets have demonstrated the superiority of the proposed algorithms.
在许多信息处理任务中，人们经常面临非常高维的数据。特征选择技术旨在找到原始特征的有意义的特征子集，这可以促进聚类、分类和检索。在本文中，我们考虑了无监督学习场景中的特征选择问题，由于缺乏指导相关信息搜索的类别标签，因此该问题尤其困难。基于拉普拉斯正则化最小二乘法，它在数据流形上找到一个平滑的函数，并最小化经验损失，我们提出了两种新的特征选择算法，旨在最小化正则化回归模型的预期预测误差。具体来说，我们选择那些特征，使得正则化回归模型的参数协方差矩阵的大小最小化。受实验设计的启发，我们使用迹和行列式运算符来度量协方差矩阵的大小。还引入了有效的计算方案来解决相应的优化问题。在各种真实数据集上的广泛实验结果表明了所提出算法的优越性。
