Improved Spectral Clustering Algorithm Based on Similarity Measure

Aimed at the Gaussian kernel parameter sigma sensitive issue of the traditional spectral clustering algorithm, this paper proposed to utilize the similarity measure based on data density during creating the similarity matrix, inspired by density sensitive similarity measure. Making it increase the distance of the pairs of data in the high density areas, which are located in different spaces. And it can reduce the similarity degree among the pairs of data in the same density region, so as to find the spatial distribution characteristics complex data. According to this point, we designed two similarity measure methods, and both of them didn't introduce Gaussian kernel function parameter sigma. The main difference between the two methods is that the first method introduces a shortest path, while the second method doesn't. The second method proved to have better comprehensive performance of similarity measure, experimental verification showed that it improved stability of the entire algorithm. In addition to matching spectral clustering algorithm, the final stage of the algorithm is to use the k-means (or other traditional clustering algorithms) for the selected feature vector to cluster, however the k-means algorithm is sensitive to the initial cluster centers. Therefore, we also designed a simple and effective method to optimize the initial cluster centers leads to improve the k-means algorithm, and applied the improved method to the proposed spectral clustering algorithm. Experimental results on UCI1 datasets show that the improved k-means clustering algorithm can further make cluster more stable.