Spectral rotation for deep one-step clustering

•Similarity matrix is obtained from the low-dimensional feature space of original data where both the influence of noise and the issue of high-dimensional data are considered.•Optimized K-means clustering rotates original result of K-means clustering to search optimized clustering hyperplane which partition data points into clusters.•Each of four parts (similarity matrix learning, spectral representation learning, optimized K-means clustering, and transformation matrix learning) is iteratively updated until convergence criteria is met. Previous spectral clustering methods sequentially conduct three steps, i.e., similarity matrix learning from original data, spectral representation learning, and K-means clustering on spectral representation, respectively, to difficultly output robust clustering result even though each of three steps achieves individual optimization. The reason is that each goal of former two steps is not focused on achieving optimal clustering result. Moreover, original data usually contains noise to affect the clustering result, as well as has high-dimensional representation to easily result in the curse of dimensionality. In this paper, we propose a deep spectral clustering method which embeds four parts (i.e., similarity matrix learning, spectral representation learning, optimized K-means clustering, and transformation matrix learning) in a unified framework with the following advantages: 1) similarity matrix is obtained from the low-dimensional feature space of original data where the influence of both noise and high-dimensional data are considered; 2) optimized K-means clustering rotates original result of K-means clustering to search optimized clustering hyperplane which partitions data points into clusters; and 3) each of four parts is iteratively updated so that the clustering result is obtained based on the feedback of other three parts. As a result, our proposed framework develops a two-task deep clustering model with linear activation functions to output effective clustering result. Experimental results on real data sets show the effectiveness of our method in terms of four clustering evaluation metrics, compared to state-of-the-art clustering methods.