球极平面逆投影迭代谱聚类算法

提出一种相似矩阵迭代修正并聚类算法, 分为偏振定理的谱分离数据和球极平面逆投影的几何分离数据两步. 首先将数据谱分解, 得到低维距离矩阵; 然后投影到双随机矩阵, 隐式进行一次球极平面逆投影, 几何对称分离数据; 最后解算投影后坐标, 得到新相似矩阵. 实验在人工合成数据和自然数据上进行, 结果表明所提出算法修正了数据的相似度, 并获得了正确的聚类个数, 对尺度参数变化有较强的鲁棒性, 聚类性能比修正前有较大提升.

Iterative spectral clustering by inverse stereographic projection

A method of iterative spectral clustering based on the inverse stereographic projection is proposed. The proposed method contains two steps for data clustering, one by the polarization theorem as the spectral clustering, the other by the inverse stereographic projection. Firstly, the affinity matrix of input data is eigen-decomposed, leading to the embedding of data in a low-dimensional space. The Euclidean distance matrix of the embedded data is then projected to its nearest doubly stochastic matrix. This approach is shown as a critical step to implicitly call the inverse stereographic projection that maps data into a hyper sphere. The last step is to solve the center and the scale factor of the hyper sphere. Experiments on the challenging synthetic data and the Iris and Wine data sets demonstrate the successful use of the proposed method in modifying the affinity matrix, and the modified affinity matrix can obtain better clustering results than the original one.