Many fundamental problems in machine learning require some form of dimensionality reduction. To this end, two different strategies were used: manifold learning and feature selection. Manifold learning (or data embedding) attempts to compute a subspace from original data by feature recombination/transformation. Feature selection aims to select the most relevant features in the original space. In this paper, we propose a novel cooperative manifold learning-feature selection that goes beyond the simple concatenation of these two modules. Our basic idea is to learn an embedding (or the subspace) by computing a cascade of embeddings in which each embedding undergoes feature selection and elimination. We use filter approaches in order to efficiently select irrelevant features at any stage of the process. For a case study, our proposed framework was used with two typical linear embedding algorithms: local discriminant embedding (a supervised technique) and locality preserving projections (unsupervised technique) on four challenging face databases and it has been conveniently compared with other cooperative schemes. Moreover, a comparison with several state-of-the-art manifold learning methods is provided. As it is exhibited by our experimental study, the proposed framework can achieve superior learning performance with respect to classic cooperative schemes and to many competing manifold learning methods.

机器学习中的许多基本问题都需要某种形式的降维。为此，使用了两种不同的策略：流形学习和特征选择。流形学习（或数据嵌入）尝试通过特征重组/变换从原始数据计算子空间。特征选择旨在选择原始空间中最相关的特征。在本文中，我们提出了一种新颖的协作流形学习特征选择，该选择超越了这两个模块的简单串联。我们的基本思想是通过计算级联的嵌入（每个嵌入都要进行特征选择和消除）来学习嵌入（或子空间）。我们使用过滤器方法，以便在流程的任何阶段有效选择不相关的功能。对于案例研究 我们提出的框架与两种典型的线性嵌入算法配合使用：在四个具有挑战性的人脸数据库上进行局部判别嵌入（一种监督技术）和局部保留投影（无监督技术），并且已与其他合作方案方便地进行了比较。此外，提供了与几种最新的流形学习方法的比较。正如我们的实验研究所展示的那样，相对于经典的合作方案和许多竞争性的多种学习方法，该框架可以实现卓越的学习性能。此外，提供了与几种最新的流形学习方法的比较。正如我们的实验研究所展示的那样，相对于经典的合作方案和许多竞争性的多种学习方法，该框架可以实现卓越的学习性能。此外，提供了与几种最新的流形学习方法的比较。正如我们的实验研究所展示的那样，相对于经典的合作计划和许多竞争性的多种学习方法，该框架可以实现卓越的学习性能。