State Key Laboratory of Integrated Services Networks, Xidian University, Shaanxi 710071, China.
Center for OPTical Imagery Analysis and Learning, Northwestern Polytechnical University, Shaanxi 710065, China.
Neural Netw. 2019 Jul;115:65-71. doi: 10.1016/j.neunet.2019.03.008. Epub 2019 Mar 27.
Dimensionality reduction is one of the fundamental and important topics in the fields of pattern recognition and machine learning. However, most existing dimensionality reduction methods aim to seek a projection matrix W such that the projection Wx is exactly equal to the true low-dimensional representation. In practice, this constraint is too rigid to well capture the geometric structure of data. To tackle this problem, we relax this constraint but use an elastic one on the projection with the aim to reveal the geometric structure of data. Based on this context, we propose an unsupervised dimensionality reduction model named flexible unsupervised feature extraction (FUFE) for image classification. Moreover, we theoretically prove that PCA and LPP, which are two of the most representative unsupervised dimensionality reduction models, are special cases of FUFE, and propose a non-iterative algorithm to solve it. Experiments on five real-world image databases show the effectiveness of the proposed model.
降维是模式识别和机器学习领域的基本和重要主题之一。然而，大多数现有的降维方法旨在寻求投影矩阵 W，使得投影 Wx 恰好等于真实的低维表示。在实践中，这种约束过于严格，难以很好地捕获数据的几何结构。为了解决这个问题，我们放松了这个约束，但对投影使用了一个弹性约束，旨在揭示数据的几何结构。基于此，我们提出了一种用于图像分类的无监督降维模型，名为灵活无监督特征提取（FUFE）。此外，我们从理论上证明了 PCA 和 LPP，这两个最具代表性的无监督降维模型，是 FUFE 的特例，并提出了一种非迭代算法来求解它。在五个真实图像数据库上的实验表明了所提出模型的有效性。
