Classical rough set theory is considered as a useful tool for dealing with the uncertainty of categorical data; the major deficiency of this model is that the classical rough set model is sensitive to noise in classification learning due to the stringent condition of equivalence relation. Thus, a class of fuzzy similarity relations was introduced to describe the similarity between samples with categorical attributes. However, these kinds of similarity relations also have deficiencies when they are used in fuzzy rough computation. In this paper, we propose a new fuzzy-rough-set model for categorical data by introducing a variable parameter to control the similarity of samples. This model employs the iterative computation strategy to define fuzzy rough approximations and dependency functions. It is proved that the proposed rough dependency function is monotonic. Finally, the proposed model is applied to the attribute reduction of categorical data. The experimental results indicate that the proposed model is more effective for categorical data than some existing algorithms.

The Adaptive Boosting (AdaBoost) algorithm is a widely used ensemble learning framework, and it can get good classification results on general datasets. However, it is challenging to apply the AdaBoost algorithm directly to imbalanced data since it is designed mainly for processing misclassified samples rather than samples of minority classes. To better process imbalanced data, this paper introduces the indicator Area Under Curve (AUC) which can reflect the comprehensive performance of the model, and proposes an improved AdaBoost algorithm based on AUC (AdaBoost-A) which improves the error calculation performance of the AdaBoost algorithm by comprehensively considering the effects of misclassification probability and AUC. To prevent redundant or useless weak classifiers the traditional AdaBoost algorithm generated from consuming too much system resources, this paper proposes an ensemble algorithm, PSOPD-AdaBoost-A, which can re-initialize parameters to avoid falling into local optimum, and optimize the coefficients of AdaBoost weak classifiers. Experiment results show that the proposed algorithm is effective for processing imbalanced data, especially the data with relatively high imbalances.

Raindrops adhered to a glass window or camera lens appear in various blurring degrees and resolutions due to the difference in the degrees of raindrops aggregation. The removal of raindrops from a rainy image remains a challenging task because of the density and diversity of raindrops. The abundant location and blur level information are strong prior guide to the task of raindrop removal. However, existing methods use a binary mask to locate and estimate the raindrop with the value 1 (adhesion of raindrops) and 0 (no adhesion), which ignores the diversity of raindrops. Meanwhile, it is noticed that different scale versions of a rainy image have similar raindrop patterns, which makes it possible to employ such complementary information to represent raindrops. In this work, we first propose a soft mask with the value in [-1,1] indicating the blurring level of the raindrops on the background, and explore the positive effect of the blur degree attribute of raindrops on the task of raindrop removal. Secondly, we explore the multi-scale fusion representation for raindrops based on the deep features of the input multi-scale images. The framework is termed uncertainty guided multi-scale attention network (UMAN). Specifically, we construct a multi-scale pyramid structure and introduce an iterative mechanism to extract blur-level information about raindrops to guide the removal of raindrops at different scales. We further introduce the attention mechanism to fuse the input image with the blur-level information, which will highlight raindrop information and reduce the effects of redundant noise. Our proposed method is extensively evaluated on several benchmark datasets and obtains convincing results.