Incremental Learning of Bidirectional Principal Components for Face Recognition
首发时间:2009-06-25
Abstract:Recently, bidirectional PCA(BDPCA) has been proven to be an e眂ient tool for pattern recognition and image analysis. Encouraging experimental results have been reported and discussed in the literature. However, BDPCA has to be performed in batch mode, it means that all the training data has to be ready before we calculate the projection matrices. If there are additional samples need to be incorporated into an existing system, it has to be retrained with the whole updated training set. Moreover, the scatter matrices of BDPCA are formulated as the sum of K(samples size) image covariance matrices, this leads to the incremental learning directly on the scatters impossible, thus it presents new challenge for on-line training. In fact, there are two major reasons for building incremental algorithms. The 痳st reason is that in some cases, when the number of training images is very large, the batch algorithm can not process the entire training set due to large computational or space requirements of the batch approach. The second reason is when the learning algorithm is supposed to operate in a dynamical settings, that all the training data is not given in advance, and new training samples may arrive at any time, and they have to be processed in an online manner. Through matricizations of 3th-order tensor, we successfully transfer the eigenvalue decomposition problem of scatters to the SVD of corresponding unfolded matrices, followed by complexity and memory analysis on the novel algorithm. A theoretical clue for selecting suitable dimensionality parameters without losing classi痗ation information is also presented in this paper. Experimental results on FERET and CMU PIE databases show that the IBDPCA algorithm gives a close approximation to the BDPCA method, but using less time.
keywords: Incremental learning Bidirectional principal component analysis Singular value decomposition Tensor k-mode unfolding Face recognition
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双向主成分的在线学习与面像识别
摘要:双向主成分分析在模式识别与图像分析领域取得了重要的应用。然而,在投影矩阵的计算过程中,所有的图像都必须事先得到以求得协方差矩阵。当额外获取的图像进入系统时,已有的投影矩阵必须重新使用特征值分解来实现更新。同时,行散度矩阵与列散度矩阵分别表示为K(样本个数)个图像协方差矩阵之和,这是在线学习方法的主要瓶颈之一。通过高阶张量的矩阵化,我们将散度矩阵的特征值分解问题成功地转化为?#23637;开矩阵?#30340;奇异值分解,因此为双向主成分的在线学习提供了可行而高效的途径。本文同时给出了维数估计的理论依据。实验结果表明,新方法不仅可以得到较高的识别精度,而且在计算时间上具有明显优势。
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