<p>Non-negative matrix factorization (NMF) has demonstrated remarkable capabilities in data processing across various domains. As an important branch of NMF, separable non-negative matrix factorization (SNMF) has garnered significant attention from researchers, leading to the development of numerous variant algorithms. Among these, the successive projection algorithm (SPA) stands out due to its simplicity and computational efficiency. However, SPA’s inherent assumption that each vertex corresponds to a single data point often proves inadequate in the presence of noise and data sparsity, as noise introduces uncertainties and sparse data results in incomplete information. To address these limitations, we propose the adaptive smoothed successive projection algorithm (ASSPA). ASSPA relaxes the constraint of a fixed number of data points per vertex, allowing for a dynamic adjustment of the number of points used in each iteration. This approach is designed to tackle the challenges of noise distortion and sparse representation in real-world datasets. Guided by the cumulative distribution function (CDF), ASSPA adopts a data-driven strategy to dynamically select the number of points at each vertex based on the local data distribution, thereby enhancing its adaptability to diverse data conditions. Furthermore, ASSPA incorporates median aggregation and kernel density aggregation methods to smooth the selected data points, ensuring robustness against outliers and flexibility in handling various noise types. Experimental evaluations on hyperspectral and facial image datasets demonstrate that ASSPA consistently outperforms competing algorithms, underscoring its effectiveness and potential for applications in image analysis.</p>