In this paper, the mathematical model used in finding the common vectors of classes in pattern recognition problems is reconsidered to obtain possible alternative solutions for the common vectors. Since the number of unknowns is always one larger than the number of equations in the mathematical model, the best solution to the problem seems to be the pseudo-inverse solutions. We obtained two forms of common vectors, called “pseudo-common vectors,” using the proposed idea. Computational simplifications are accomplished as shown in the paper since we know that taking pseudo-inverses is an exhaustive procedure especially in the high-dimensional vector spaces. The two forms of pseudo-common vectors obtained in the paper are used in the classification of the data given in TI-Digit, AR-Face, and MNIST databases separately in order to see their effectiveness.

在本文中，重新考虑了用于在模式识别问题中查找类的公共向量的数学模型，以获得公共向量的可能替代解决方案。由于未知数总是比数学模型中的方程数大一，因此，该问题的最佳解决方案似乎是伪逆解。使用提出的想法，我们获得了两种形式的通用矢量，称为“伪通用矢量”。如本文所示，可以实现计算简化，因为我们知道采用伪逆是穷举过程，尤其是在高维向量空间中。本文获得的两种形式的伪公共矢量被用于TI-Digit，AR-Face，