In order to improve the clustering accuracy and applicability of spectral clustering, a spectral clustering algorithm based on Fréchet distance (called FSC) is proposed. Firstly a similarity matrix is constructed by Fréchet distance, then the reconstructed similarity matrix is applied to the spectral clustering. Using Fréchet distance to measure the similarity of data feature dimensions can extend the applicability of typical spectral clustering algorithms. FSC is not only suitable for data with clear low-dimensional manifold structure, but also for high-dimensional or sparse data, such as hyperspectral images. The experimental results on three hyperspectral images show that the FSC algorithm effectively improves the accuracy of hyperspectral images clustering.

This paper proposes a new distance metric (NewDM) of categorical data based on the graph structure of ordinal and nominal attributes to address the poor effect of most existing measurement methods for categorical data. In NewDM, it first summarizes the basic framework formula of distance definition of categorical data and analyzes the challenges of measuring categorical data. Then, the graph structures of ordinal attributes and nominal ones are utilized to define the distance between two probability distribution columns. Finally, a new distance metric of categorical data is obtained through simultaneous weight. Experimental results on six public datasets show that the proposed NewDM is superior to the state-of-the-art approaches.

In multi-view clustering problems, the complementary information and difference information between views have impact on the clustering effect, while the importance conveyed by the sample points also affects the clustering effect. Some existing methods do not fully utilize the complementary information between views, some do not consider the difference information between views, and some do not utilize the importance of sample points, resulting in poor clustering performance. To address the above issues, an adaptive multi-view-fusion clustering algorithm based on self-correlative matrix (AMCSM) is proposed. Firstly, feature concatenating is used to better utilize complementary information between views; Secondly, the auto-weighted mechanism is introduced to adaptively assign appropriate weights to each view, to fully utilize the difference information between views; Finally, diagonal weighted matrices and self-correlative matrices are simultaneously utilized to mine important information conveyed by the sample points. A unified multi-step iterative framework is designed to integrate the above optimization solutions, so that complementary information, difference information, and important information of sample points can promote and learn from each other during the iteration process. The experimental results show that the proposed algorithm achieves excellent results in evaluation metrics such as sensitivity, precision, specificity, adjusted Rand Index, and Matthews correlation coefficient, which is more robust.