# An Adaptive Weighted Method for Remote Sensing Image Retrieval with Noisy Labels
## 1 Introduction  
The demand for the fast and efficient retrieval of images from large remote sensing databases has become increasingly urgent due to military and civilian needs in geospatial information science [1]. Content-based remote sensing image retrieval (CBRSIR) is an effective method to solve meet this demand [2] and has attracted an increasing amount of research interest. In recent years, various methods based on deep learning models, which can automatically learn the high-level semantic features of remote sensing images, have become the mainstream method for CBRSIR [3; 4; 5]. These deep learning model-based methods are data-driven and require large amounts of sample data. Therefore, to reduce the cost of labelling large datasets, many researchers have proposed clustering, semi-automatic labelling and crowdsourcing methods in real-world application scenarios [6; 7; 8]. However, these methods can introduce noisy labels into the sample datasets. According to the literature [9], existing datasets contain between 8.0% and 38.5% noisy labels. Such noisy labels may lead to overfitting of the deep learning-based methods [10], which can reduce the performance of remote sensing image retrieval. For example, [PERSON] et al. [11] found that noisy labels significantly affect the accuracy of deep learning-based classifiers, which can also negatively impact retrieval results. [PERSON] et al. [12] also confirmed that deep learningmodels are not robust enough in benchmarking datasets with noisy labels. Therefore, it is crucial to consider the effect of noisy labels during deep learning model training. To reduce the effect of noisy labels, several robust loss functions have been proposed. For example, [PERSON] et al. [13] proposed a mean absolute error (MAE) loss, which is more robust than cross-entropy (CE). However, it converges slowly due to gradient saturation. By combining the MAE with the faster converging CE, [PERSON] et al. [14] proposed a generalised cross-entropy (GCE). Inspired by the symmetry of Kullback-Leibler divergence, a robust symmetric cross-entropy (SCE) [15] is proposed by combining the robust reverse cross-entropy (RCE) and CE with two weighting hyperparameters. Additionally, [PERSON] et al. [16] proposed an adaptive cross-entropy (ACE) by replacing the two weighting parameters of the SCE with the output probability of the deep learning network. This approach can eliminate the need to manually select the weighting parameters for the SCE. Furthermore, [PERSON] et al. [17] categorised existing robust losses into active and passive losses and introduced an active passive loss (APL) by combining the two different types of robust losses with two weighting hyperparameters. This method provides a theoretical explanation for the effectiveness of the combination losses in combating noisy labels. Compared with other robust methods, the APL method has the best results. However, the APL method is time-consuming, and it may not always achieve optimal performance, as the two weighting parameters are typically determined manually or through a large number of experimental iterations. More unfortunately, the two weighting parameters vary with the dataset and the noise rate. This limitation restricts its widespread use in real-world applications, especially in contexts where noise levels in datasets are unknown. In addition, the ACE parameter replacement method is not applicable to APL. To solve this problem, we propose an adaptive weighted method for the robust APL method in remote sensing image retrieval. Specifically, a new metric based on the entropy and standard deviation of the predicted probabilities of the samples is developed to represent the complexity of the sample. Additionally, the predicted probability difference is chosen as a second metric of whether the sample has a noisy label. Then, an adaptive weighted learning network (AWNet) with one hidden layer is designed to dynamically learn the weighting parameters in each training batch using the above two metrics as inputs.