Analog feature extraction (AFE) is an appealing strategy for low-latency and efficient cognitive sensing systems since key features are much sparser than the Nyquist-sampled data. However, applying AFE to broadband radio-frequency (RF) scenarios is challenging due to the bandwidth and programmability bottlenecks of analog electronic circuitry. Here, we introduce a photonics-based scheme that extracts spatiotemporal features from broadband RF signals in the analog domain. The feature extractor structure inspired by convolutional neural networks is implemented on integrated photonic circuits to process RF signals from multiple antennas, extracting valid features from both temporal and spatial dimensions. Because of the tunability of the photonic devices, the photonic spatiotemporal feature extractor is trainable, which enhances the validity of the extracted features. Moreover, a digital-analog-hybrid transfer learning method is proposed for the effective and low-cost training of the photonic feature extractor. To validate our scheme, we demonstrate a radar target recognition task with a 4-GHz instantaneous bandwidth. Experimental results indicate that the photonic analog feature extractor tackles broadband RF signals and reduces the sampling rate of analog-to-digital converters to 1/4 of the Nyquist sampling while maintaining a high target recognition accuracy of 97.5%. Our scheme offers a promising path for exploiting the AFE strategy in the realm of cognitive RF sensing, with the potential to contribute to the efficient signal processing involved in applications such as autonomous driving, robotics, and smart factories.