Summary: Non-negative matrix factorization and spectral clustering are widely recognized techniques in data analysis due to their distinctive geometric interpretation and proven effectiveness across various applications. However, despite their popularity, these methods are not without their limitations. Specifically, they are susceptible to noise (outliers), which can significantly impact their clustering performance. Furthermore, their ability to learn spatial information heavily relies on the quality of the initial adjacency matrix. To mitigate the mentioned limitations, this paper proposes a novel clustering approach that integrates non-negative matrix factorization with spectral clustering. The proposed method utilizes a novel robust loss function to quantify the reconstruction error of samples, thereby improving the model’s capacity to handle noise (outliers) and enhance clustering performance. Additionally, our method incorporates an adaptive-order graph learning strategy that enhances the model’s adaptability to initial adjacency matrices. To optimize the proposed model, we have devised a highly efficient algorithm and conducted a analysis of its convergence properties. Experimental results on diverse datasets substantiate the effectiveness of our method in robust clustering and spatial learning tasks.