Pearson's $r$, the most widely-used correlation coefficient, is traditionally regarded as exclusively capturing linear dependence, leading to its discouragement in contexts involving nonlinear relationships. However, recent research challenges this notion, suggesting that Pearson's $r$ should not be ruled out a priori for measuring nonlinear monotone relationships. Pearson's $r$ is essentially a scaled covariance, rooted in the renowned Cauchy-Schwarz Inequality. Our findings reveal that different scaling bounds yield coefficients with different capture ranges, and interestingly, tighter bounds actually expand these ranges. We derive a tighter inequality than Cauchy-Schwarz Inequality, leverage it to refine Pearson's $r$, and propose a new correlation coefficient, i.e., rearrangement correlation. This coefficient is able to capture arbitrary monotone relationships, both linear and nonlinear ones. It reverts to Pearson's $r$ in linear scenarios. Simulation experiments and real-life investigations show that the rearrangement correlation is more accurate in measuring nonlinear monotone dependence than the three classical correlation coefficients, and other recently proposed dependence measures.

The critical aspects of risk management include hazard identification, risk assessment, and risk control. Timely risk management is critical to company decision‐making, but the process of acquiring risk management knowledge is often time‐consuming and labor‐intensive. Knowledge graph question answering (KGQA) provides an effective solution by delivering knowledge through accurate reasoning. However, existing KGQA methods do not cover the critical risk management aspects and are difficult to retrieve quickly and accurately from large knowledge graphs. This study describes a complex question answering method for intelligently generating risk management knowledge, specifically through multi‐intent information retrieval based on knowledge subgraphs. The proposed method comprises three main modules. First, in the question understanding module, we propose an intent recognition method that integrates topic entity extraction with convolutional neural networks (CNNs) to identify eleven different user intents. To enhance the retrieval efficiency, we propose a hierarchical knowledge‐embedding subgraph constructed based on company and hazard descriptions. Once user intent is identified, the information retrieval module based on a novel approximate nearest neighbor (ANN) algorithm achieves deep semantic feature matching of company and hazard expressions from the knowledge embedding subgraph. After obtaining these two deep semantic features, in the answer generation module, we propose a rule‐based knowledge subgraph reasoning method to answer complex questions including single‐hop, multihop, constraints, and numerical calculations. On the real risk management dataset, the precision of the intent recognition module reaches 91.3% and the information retrieval module spends only 0.36 ms, verifying that the model outperforms the existing state‐of‐the‐art models. Meanwhile, a question answering system based on the proposed method is developed to acquire risk management knowledge: Xiao An. Compared to the popular search engine and expert system for acquiring knowledge, Xiao An achieves the best results regarding ease of use, time spent, and overall performance.

Fully supervised object detection needs to use the data set with object category annotation and location annotation to train the model. In contrast, weak supervised object localisation only needs to use the data set with object category annotation to train the model, but it can complete the classification task and object localisation task at the same time. Inspired by the attention‐based dropout layer (ADL) method, this study designs a category‐wise feature extractor (CFE), which can explicitly obtain the localisation map used to indicate the object location, and it is directly related to the category output of the classification task. Although its amount of calculation is slightly larger than that of the ADL method, the performance is better than ADL in some tasks. In addition to the standard CFE method mentioned above, this study also designs a lightweight CFE‐tiny method, which adopts split‐attention mechanism, and the calculation amount of this method is much smaller than that of ADL method.