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Sea ice plays a critical role in the Earth's climate system, and its variations affect ecosystem stability. This study introduces a novel method for detecting sea ice in the Arctic Ocean using bidirectional radar reflections from the Global Navigation Satellite System (GNSS). Utilizing delay-Doppler maps (DDM) from the UK TechDemoSat-1 (TDS-1) satellite mission and surface data from the U.S. National Oceanic and Atmospheric Administration (NOAA), we employ the local linear embedding (LLE) algorithm for feature extraction. This approach notably reduces training costs and enhances real-time performance, while maintaining a high accuracy and robust noise immunity level. Focusing on the region above 70° north latitude throughout 2018, we aimed to distinguish between sea ice and seawater. The extracted DDM features via LLE are input into a support vector machine (SVM) for classification. The results indicate that our method achieves an accuracy of over 99% for selected low-noise data and a monthly average accuracy of 92.74% for data containing noise, while the CNN method has a monthly average accuracy of only 77.31% for noisy data. A comparative analysis between the LLE-SVM approach and the convolutional neural network (CNN) method demonstrated the superior anti-interference capabilities of the former. Additionally, the impact of the sea ice melting period on detection accuracy was analyzed. [ABSTRACT FROM AUTHOR]