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中文摘要：
针对现有图像识别中聚类数的确定算法存在的精度问题，本文研究了用谱图理论来确定图像聚类数的方法，即图像中赋权图的Laplace矩阵的零特征值和图像聚类数之间的关系．通过从理想状况、分块状况到一般状况的赋权图的普拉斯矩阵的讨论，运用矩阵论知识推证了若图像的赋权图的Laplace如上三种情形，则图像的聚类数是其对应赋权图的Laplace矩阵零特征值的重数．实例分析讨论了赋权图参数，发现参数位于0．4至0．6时能获得高的估计精度．同时采用我们的方法得到的聚类数，比利用图谱中权矩阵1特征值的重数的方法精度更高．
英文摘要：
According to spectral graph theory, a new method of determining the cluster number of image is proposed for resolving the accuracy problem in this paper. The relationship between the number of zeros eigenvalue of Laplace matrix of weighted graph and the cluster number of image is studied. By analyzing the ideal format, block format and general format of Laplace matrix of weighted graph, we have deduced that the cluster number of image is closed to the number of zeros eigenvalue of Laplace matrix of weighted graph via the matrix theory. In the numerical simulations, the parameter of weighted graph is discussed and it shows that we can get the accurate cluster number of image when the parameter is limited to 0.4 and 0.6. Meanwhile, the numerical result employing our method is better than that of using the number of one eigenvalue of weighted matrix.
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