Personal credit scoring is a challenging issue. In recent years, research has shown that machine learning has satisfactory performance in credit scoring. Because of the advantages of feature combination and feature selection, decision trees can match credit data which have high dimension and a complex correlation. Decision trees tend to overfitting yet. eXtreme Gradient Boosting is an advanced gradient enhanced tree that overcomes its shortcomings by integrating tree models. The structure of the model is determined by hyperparameters, which is aimed at the time-consuming and laborious problem of manual tuning, and the optimization method is employed for tuning. As particle swarm optimization describes the particle state and its motion law as continuous real numbers, the hyperparameter applicable to eXtreme Gradient Boosting can find its optimal value in the continuous search space. However, classical particle swarm optimization tends to fall into local optima. To solve this problem, this paper proposes an eXtreme Gradient Boosting credit scoring model that is based on adaptive particle swarm optimization. The swarm split, which is based on the clustering idea and two kinds of learning strategies, is employed to guide the particles to improve the diversity of the subswarms, in order to prevent the algorithm from falling into a local optimum. In the experiment, several traditional machine learning algorithms and popular ensemble learning classifiers, as well as four hyperparameter optimization methods (grid search, random search, tree-structured Parzen estimator, and particle swarm optimization), are considered for comparison. Experiments were performed with four credit datasets and seven KEEL benchmark datasets over five popular evaluation measures: accuracy, error rate (type I error and type II error), Brier score, and score. Results demonstrate that the proposed model outperforms other models on average. Moreover, adaptive particle swarm optimization performs better than the other hyperparameter optimization strategies.

CNN is particularly effective in extracting spatial features. However, the single-layer classifier constructed by activation function in CNN is easily interfered by image noise, resulting in reduced classification accuracy. To solve the problem, the advanced ensemble model XGBoost is used to overcome the deficiency of a single classifier to classify image features. To further distinguish the extracted image features, a CNN-XGBoost image classification model optimized by APSO is proposed, where APSO optimizes the hyper-parameters on the overall architecture to promote the fusion of the two-stage model. The model is mainly composed of two parts: feature extractor CNN, which is used to automatically extract spatial features from images; feature classifier XGBoost is applied to classify features extracted after convolution. In the process of parameter optimization, to overcome the shortcoming that traditional PSO algorithm easily falls into a local optimal, the improved APSO guide the particles to search for optimization in space by two different strategies, which improves the diversity of particle population and prevents the algorithm from becoming trapped in local optima. The results on the image set show that the proposed model gets better results in image classification. Moreover, the APSO-XGBoost model performs well on the credit data, which indicates that the model has a good ability of credit scoring.

In this paper, we constructed a new rational fractal interpolation model with scale factors and shape parameters. The model obtains different expressions by changing the scale factor, according with the diversity of image features. On the basis of the constructed model, this paper presents a novel adaptive rational fractal magnification (ARFM) algorithm based on local fractal feature analysis. Firstly, the image is divided into different regions according to an adaptive threshold determined by a calculated fractal dimension, and the scaling factor is calculated based on the relationship between global fractal dimension (GFD) and local fractal dimension (LFD). Secondly, for different regions, different interpolation forms are selected according to regional characteristics. Thirdly, parameter optimization and sub-block selection are studied to further enhance the quality of the magnified image. The experimental results illustrate that the performance of the proposed ARFM algorithm is very competitive compared with the latest magnification algorithms.

Option pricing based on data-driven methods is a challenging task that has attracted much attention recently. There are mainly two types of methods that have been widely used, respectively, the neural network method and the ensemble learning method. The option pricing model based on the neural network has high complexity, and a large number of hyper-parameters will be generated during training, resulting in difficult model adjustment. Furthermore, a lot of training data are needed. The option pricing model based on ensemble learning is not ideal for data feature extraction, because each calculation of the ensemble learning method is mainly to reduce the final residual. Therefore, this paper adopts a learning framework that embeds the modular ensemble learning methods into the network learning structure, and an option pricing model based on deep ensemble learning is proposed. The model is mainly composed of two parts: features reorganization based on random forest, used to calculate the importance of features, combined with the original data as training input; the multilayer ensemble data training structure is based on network learning structure and embeds two ensemble learning methods as network modules, and it also designs a stop algorithm to automatically determine the number of layers. This enables the model to retain the effect of data feature extraction and adapt to small and medium data sets without generating many hyper-parameters. Moreover, in order to make the model fully absorb the advantages of the two ensemble learning methods, we adopt cross-training for data. From the experimental results, it can be concluded that compared with the current optimal method, the prediction performance of the proposed model is improved by 36% in the root mean square error (RMSE), which proves the superiority of the proposed model from the quantitative direction.

Unbalanced data classification is a major challenge in the field of data mining. Random forest, as an ensemble learning method, is usually used to solve the problem of unbalanced data classification. For the existing random forest-based classification prediction model, its hyperparameters are dependent on empirical settings, which leads to the problem of unsatisfactory model performance. In order to make random forest find the optimum modelling corresponding to the character of unbalanced data sets and improve the accuracy of prediction, we apply the improved particle swarm optimization to set reasonable hyperparameters of the model. This paper proposes a random forest-based adaptive particle swarm optimization on data classification, and an adaptive particle swarm used to optimize the hyperparameters in the random forest to ensure that the model can better predict the unbalanced data accurately. Aiming at the premature convergence that appears in the particle swarm optimization algorithm, the population is adaptively divided according to the population fitness and the adaptive update strategy is introduced to enhance the ability of particles to jump out of the local optimum. Experimental results show that our proposed algorithms outperform the traditional ones, especially regarding the evaluation criterion of F1-measure and accuracy. The results on the six keel unbalanced data set the advantages of our proposed algorithms are presented.