Summary: As one popular clustering algorithm in the last few years, spectral clustering is advantageous over most existing clustering algorithms. Although spectral clustering can perform well in many instances, the algorithm still has some problems. The clusters obtained by spectral clustering have crisp boundaries, which cannot reflect the fact that one cluster may not have a well-defined boundary in the real situations. Furthermore, the frequently-used distance measures in spectral clustering cannot satisfy both global and local consistency, especially for the data with multi-scale. In order to address the above limitations, we firstly present a three-way density-sensitive spectral clustering algorithm, which uses the core region and the fringe region to represent a cluster. In the proposed algorithm, we use density-sensitive distance to produce a similarity matrix, which can well capture the real data structures. An overlap clustering is introduced to obtain the upper bound (unions of the core regions and the fringe regions) of each cluster and perturbation analysis is applied to separate the core regions from the upper bounds. The fringe region of the specific cluster is the differences between the upper bound and the core region. Because a single clustering algorithm cannot always achieve a good clustering result, we develop an improved ensemble three-way spectral clustering algorithm based on ensemble strategy. The proposed ensemble algorithm randomly extracts feature subset of sample and uses the three-way density-sensitive clustering algorithm to obtain the diverse base clustering results. Based on the base clustering results, voting method is used to generate a three-way clustering result. The experimental results show that the three-way density-sensitive clustering algorithm can well explain the data structure and maintain a good clustering performance at the same time, and the ensemble three-way density-sensitive spectral clustering can improve the robustness and stability of clustering results.