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中文摘要：
提出一种基于张量代数的核主成分分析方法来进行特征提取。该方法可以有效避免维数过高导致计算消耗过大，并合理利用已知训练样本的类别信息。算法先对每一类目标使用核主成分分析手段以形成其各自的特征空间；再通过张量积将所有的特征映射到一高维线性空间；随后直接在此空间上进行线性的主成分分析，即可构造出了适宜的特征空间。其既能有效反映各类样本特征，又能比直接使用核主成分的方法极大降低计算所需的消耗。目标识别实验表明，该方法与直接使用核主成分方法构造特征空间的方法进行比较，在保持识别效果的前提下，可以明显降低计算的消耗与存储的需求。
英文摘要：
A kernel principle component analysis method based on tensor algebra is proposed for feature extraction. It can reduce the huge computation cost due to increasing dimensions, while considering the information of known classes. First the kernel principle component analysis method is applied to each class of targets to build their corresponding feature spaces. Then,the collection of feature spaces is unified into a higher dimensional space after introducing the operation of the tensor product. Hence, a linear principle component analysis method can be directly applied on this feature space in order to construct the proper feature space to both retlect the characters of each class and lower the cost of computation. The recognition experiments showed that the cost of computation and memory can be decreased heavily compared to the approach that builds the feature space by using the kernel principle component analysis method directly.
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