隐式低秩表示(LatLRR)作为经典的无监督特征提取算法已应用于模式识别领域。然而该算法得到的特征维数无法降低,且由于算法分别学习2个低秩矩阵,因此无法保证整体最优;另外,算法忽略了样本在学习过程中存在的残差。为解决这些问题,提出了一种基于隐式低秩表示的联合投影学习算法。使用投影矩阵和恢复矩阵近似地表示隐式低秩表示中的投影矩阵,使算法在降维的同时可提取判别特征;联合学习投影矩阵、恢复矩阵和低秩矩阵,矩阵间相互提升,从获得的投影中可以提取出更多的判别特征,同时在算法模型中约束样本在投影学习中存在的残差;最后采用交替迭代方法求解该模型。在多个数据集上进行实验,结果说明算法在有效降维的同时能进一步提高判别能力。

The latent low-rank representation (LatLRR) is applied in the field of pattern recognition as a classical unsupervised feature extraction algorithm. However, the dimensions of the features obtained using the algorithm cannot be reduced. Two low-rank matrices are separately learned by the algorithm such that the overall optimality cannot be guaranteed. Furthermore, the algorithm ignores the samples' residuals in the learning process. This study proposes a joint projection learning algorithm based on the LatLRR to address these problems. First, projection and reconstruction matrices are used to approximate the low-rank projection matrix in the LatLRR such that the algorithm can extract discriminative features while reducing the samples' dimensions. Second, the projection, reconstruction, and low-rank matrices are jointly learned by the algorithm such that they can be mutually boosted. The obtained projection can extract more discriminative features. Simultaneously, the samples' residuals in the process of learning are constrained in the algorithm model. Third, the alternating iterative method is used to solve the model. Experiments on multiple datasets show that the algorithm can effectively reduce the samples' dimensions while further improving the discriminative ability.