National Laboratory of Radar Signal Processing, Xidian University, Xi'an 710071, China.
Sensors (Basel). 2020 Aug 24;20(17):4778. doi: 10.3390/s20174778.
High-dimensional signals, such as image signals and audio signals, usually have a sparse or low-dimensional manifold structure, which can be projected into a low-dimensional subspace to improve the efficiency and effectiveness of data processing. In this paper, we propose a linear dimensionality reduction method-minimum eigenvector collaborative representation discriminant projection-to address high-dimensional feature extraction problems. On the one hand, unlike the existing collaborative representation method, we use the eigenvector corresponding to the smallest non-zero eigenvalue of the sample covariance matrix to reduce the error of collaborative representation. On the other hand, we maintain the collaborative representation relationship of samples in the projection subspace to enhance the discriminability of the extracted features. Also, the between-class scatter of the reconstructed samples is used to improve the robustness of the projection space. The experimental results on the COIL-20 image object database, ORL, and FERET face databases, as well as Isolet database demonstrate the effectiveness of the proposed method, especially in low dimensions and small training sample size.
高维信号，如图像信号和音频信号，通常具有稀疏或低维流形结构，可以将其投影到低维子空间中，以提高数据处理的效率和效果。在本文中，我们提出了一种线性降维方法——最小特征向量协同表示判别投影，以解决高维特征提取问题。一方面，与现有的协同表示方法不同，我们使用样本协方差矩阵的最小非零特征值对应的特征向量来减少协同表示的误差。另一方面，我们在投影子空间中保持样本的协同表示关系，以增强提取特征的可区分性。此外，还利用重构样本的类间散度来提高投影空间的鲁棒性。在 COIL-20 图像目标数据库、ORL 和 FERET 人脸数据库以及 Isolet 数据库上的实验结果表明了所提出方法的有效性，尤其是在低维度和小训练样本大小的情况下。
