Shallow and ensemble deep randomized neural network for anomaly detection.

Anomaly detection or one-class classification (OCC) plays a vital role in real-world applications. Traditional support vector machine-based OCC models often face challenges with large-scale datasets and are sensitive to the choice of kernel functions. To overcome these limitations and enhance the generalization of OCC, we propose the one-class random vector functional link (OC-RVFL) network, which fuses linear and nonlinear patterns through a combination of original and randomized features. Although the proposed OC-RVFL efficiently computes output weights by solving linear equations, its single hidden layer restricts its ability to capture complex patterns. To address this, we introduce the one-class ensemble deep RVFL (OC-edRVFL), a fusion of deep learning and ensemble learning principles with OC-RVFL as the base model in each layer. The proposed OC-edRVFL, a novel model with multiple output layers for OCC provides improved stability, robustness, and generalization compared to the proposed OC-RVFL. The proposed models employ a closed-form solution approach for output weights computation, reducing the training time. We also derive an upper bound on the generalization error for these models. Experiments on artificial, UCI, NDC, and MNIST datasets demonstrate that the proposed OC-edRVFL outperforms baseline models, showcasing its superior performance with dataset of up to 5 million samples.