Shukla Prashant, Verma Shekhar, Kumar Manish
Department of Information Technology, Indian Institute of Information Technology Allahabad, Deoghat, Jhalwa, Allahabad, U.P. 211012 India.
Pattern Anal Appl. 2021;24(3):887-905. doi: 10.1007/s10044-020-00947-9. Epub 2021 Jan 4.
In manifold learning, the intrinsic geometry of the manifold is explored and preserved by identifying the optimal local neighborhood around each observation. It is well known that when a Riemannian manifold is unfolded correctly, the observations lying spatially near to the manifold, should remain near on the lower dimension as well. Due to the nonlinear properties of manifold around each observation, finding such optimal neighborhood on the manifold is a challenge. Thus, a sub-optimal neighborhood may lead to erroneous representation and incorrect inferences. In this paper, we propose a rotation-based affinity metric for accurate graph Laplacian approximation. It exploits the property of aligned tangent spaces of observations in an optimal neighborhood to approximate correct affinity between them. Extensive experiments on both synthetic and real world datasets have been performed. It is observed that proposed method outperforms existing nonlinear dimensionality reduction techniques in low-dimensional representation for synthetic datasets. The results on real world datasets like COVID-19 prove that our approach increases the accuracy of classification by enhancing Laplacian regularization.
在流形学习中，通过识别每个观测值周围的最优局部邻域来探索和保留流形的内在几何结构。众所周知，当一个黎曼流形被正确展开时，在空间上靠近该流形的观测值在低维空间中也应保持接近。由于每个观测值周围流形的非线性特性，在流形上找到这样的最优邻域是一项挑战。因此，次优邻域可能会导致错误的表示和不正确的推断。在本文中，我们提出了一种基于旋转的亲和度度量，用于精确的图拉普拉斯近似。它利用最优邻域中观测值对齐的切空间的特性来近似它们之间的正确亲和度。我们对合成数据集和真实世界数据集都进行了广泛的实验。结果表明，对于合成数据集，所提出的方法在低维表示方面优于现有的非线性降维技术。在COVID - 19等真实世界数据集上的结果证明，我们的方法通过增强拉普拉斯正则化提高了分类的准确性。
