Principal component analysis is a widely used technique. However, it is sensitive to noise and considers data samples to be linearly distributed globally. To tackle these challenges, a novel technique robust to noise termed deflated manifold embedding PCA is proposed. In this framework, we unify PCA with manifold embedding to preserve both global and local geometric structures of linear and non-linear data in sub-manifolds. Additionally, a scaling-factor is imposed in the instance space to mitigate the impact of noise in pursuing projections. By using cosine similarity and total distance approaches, we iteratively learn the relationships between instances and projections in order to discriminate between authentic and corrupt instances. Further, a deflation technique is applied to establish multi-relationships between instances and every pursued projection for thorough discrimination. Experimental evaluation of the proposed methods on five datasets show great improvements in their performances over six state-of-the-art techniques.

主成分分析是一种广泛使用的技术。但是，它对噪声敏感，并认为数据样本在全局范围内呈线性分布。为了解决这些挑战，提出了一种对噪声具有鲁棒性的新技术，称为放气歧管嵌入PCA。在此框架中，我们通过流形嵌入来统一PCA，以将线性和非线性数据的全局和局部几何结构保留在子流形中。另外，在实例空间中施加了比例因子，以减轻噪声对投影的影响。通过使用余弦相似度和总距离方法，我们可以迭代地学习实例与投影之间的关系，以便区分真实实例与损坏实例。进一步，使用通缩技术在实例与每个追求的投影之间建立多重关系，以进行全面的区分。对五个数据集上的拟议方法进行的实验评估表明，与六种最新技术相比，它们的性能有了很大的提高。