Abstract: Aiming at the default that when the traditional spectral clustering algorithm is applied to?image segmentation, it only uses the feature similarity information to construct similarity matrix and ignores the spatial adjacency information defect of spatial distribution of pixels, this paper presents a new similarity measure formula—weighted euclidean distance of the Gaussian kernel function, making full use of image feature similarity information and spatial adjacency information to structure similarity matrix. In the spectral mapping process, using Nystrom approximation strategy to approximate similarity matrix and eigenvectors, it greatly reduces the computational complexity to solve similarity matrix and reduces the memory consumption. This paper applies a new clustering algorithm—Affinity?Propagation to the low-dimensional subspace. It avoids the defect that traditional spectral clustering using K-means algorithm can not automatically determine the number of clusters and it is sensitive to initial value and easy to fall into local optimum. The experiments prove that the proposed algorithm obtains better segmentation results than the traditional spectral clustering algorithm.

Key words: spectral clustering, spatial adjacency information, similarity matrix, Nystrom approximation, Affinity Propagation（AP） algorithm

摘要： 针对传统谱聚类算法应用于图像分割时仅采用特征相似性信息构造相似性矩阵，而忽略了像素分布的空间临近信息的缺陷，提出一种新的相似性度量公式——加权欧氏距离的高斯核函数，充分利用图像特征相似性信息和空间临近信息构造相似性矩阵。在谱映射过程中，采用Nystrom逼近策略近似估计相似性矩阵及其特征向量，大大减少了求解相似性矩阵的运算复杂度，降低了内存消耗。对得到的低维向量子空间采用一种新型的聚类算法——近邻传播聚类算法进行聚类，避免了传统谱聚类采用K-means算法对初始值敏感，易陷入局部最优的缺陷。实验表明该算法获得了比传统谱聚类算法更好的分割效果。

关键词: 谱聚类, 空间临近信息, 相似性矩阵, Nystrom逼近策略, 近邻传播聚类算法