The existing unsupervised feature extraction methods frequently explore low-redundant features by an uncorrelated constraint. However, the constrained models might incur trivial solutions, due to the singularity of scatter matrix triggered by high-dimensional data. In this paper, we propose a regularized regression model with a generalized uncorrelated constraint for feature selection, which leads to three merits: 1) exploring the low-redundant and discriminative features; 2) avoiding the trivial solutions and 3) simplifying the optimization. Besides that, the local cluster structure is achieved via a novel constrained spectral analysis for the unsupervised learning, where Must-Links and Cannot-Links are transformed into a intrinsic graph and a penalty graph respectively, rather than incorporated into a mixed affinity graph. Accordingly, a discriminative and uncorrelated feature selection with constrained spectral analysis (DUCFS) is proposed with adopting σ -norm regularization for interpolating between F-norm and l2,1 -norm. Due to the flexible gradient and global differentiability, our model converges fast. Extensive experiments on benchmark datasets among several state-of-the-art approaches verify the effectiveness of the proposed method.

中文翻译：

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无监督学习中具有约束频谱分析的判别和不相关特征选择。

现有的无监督特征提取方法经常通过不相关的约束来探索低冗余特征。但是，由于高维数据触发的散射矩阵的奇异性，受约束的模型可能会产生平凡的解。在本文中，我们提出了一种具有广义不相关约束的正则化回归模型用于特征选择，该模型具有三个优点：1）探索低冗余和区分特征。2）避免琐碎的解决方案，3）简化优化。除此之外，通过针对无监督学习的新型约束谱分析来实现局部聚类结构，其中必须链接和不能链接分别转换为内在图和惩罚图，而不是合并为混合亲和图。因此，提出了采用σ范数正则化对F范数和l2,1范数进行插值的具有约束性的频谱分析（DUCFS）的判别和不相关特征选择。由于灵活的梯度和全局可微性，我们的模型快速收敛。在几种最先进的方法中对基准数据集进行的大量实验证明了该方法的有效性。