Abstract: Supervised locality preserving projection (SLPP) seeks to find the projection which efficiently preserves the local structure of data points embedded in high-dimensional data space. However, it has the over-learning problem and does not preserve the diversity information of data which is also useful for data recognition. A novel feature extraction method based on manifold learning, namely supervised local structure and diversity projection (S-LSDP), is presented to address this problem. The S-LSDP introduces the diversity of data points from the perspective of statistic and then calculates diversity scatter via the diversity of data points to measure the diversity information of data. A concise feature extraction criterion is raised by minimizing the local scatter, which efficiently preserves the local structure and simultaneously maximize the diversity scatter. Different from the most existing manifold learn methods, the S-LSDP not only preserves both the local structure and diversity information of data, but also avoids the data over-fitting problem. Extensive experiments in UMIST, Yale, PIE, and AR face database show the efficiency of the proposed method.