A non-linear partial least squares based on monotonic inner relation.

A novel regression model, monotonic inner relation-based non-linear partial least squares (MIR-PLS), is proposed to address complex issues like limited observations, multicollinearity, and nonlinearity in Chinese Medicine (CM) dose-effect relationship experimental data. MIR-PLS uses a piecewise mapping function based on monotonic cubic splines to model the non-linear inner relations between input and output score vectors. Additionally, a new weight updating strategy (WUS) is developed by leveraging the properties of monotonic functions. The proposed MIR-PLS method was compared with five well-known PLS variants: standard PLS, quadratic PLS (QPLS), error-based QPLS (EB-QPLS), neural network PLS (NNPLS), and spline PLS (SPL-PLS), using CM dose-effect relationship datasets and near-infrared (NIR) spectroscopy datasets. Experimental results demonstrate that MIR-PLS exhibits general applicability, achieving excellent predictive performances in the presence or absence of significant non-linear relationships. Furthermore, the model is not limited to CM dose-effect relationship research and can be applied to other regression tasks.

New research for detecting complex associations between variables with randomness.

Many correlation analysis methods can capture a wide range of functional types of variables. However, the influence of uncertainty and distribution status in data is not considered, which leads to the neglect of the regularity information between variables, so that the correlation of variables that contain functional relationship but subject to specific distributions cannot be well identified. Therefore, a novel correlation analysis framework for detecting associations between variables with randomness (RVCR-CA) is proposed. The new method calculates the normalized RMSE to evaluate the degree of functional relationship between variables, calculates entropy difference to measure the degree of uncertainty in variables and constructs the copula function to evaluate the degree of dependence on random variables with distributions. Then, the weighted sum method is performed to the above three indicators to obtain the final correlation coefficient R. In the study, which considers the degree of functional relationship between variables, the uncertainty in variables and the degree of dependence on the variables containing distributions, cannot only measure the correlation of functional relationship variables with specific distributions, but also can better evaluate the correlation of variables without clear functional relationships. In experiments on the data with functional relationship between variables that contain specific distributions, UCI data and synthetic data, the results show that the proposed method has more comprehensive evaluation ability and better evaluation effect than the traditional method of correlation analysis.

An improved particle swarm optimization combined with double-chaos search.

Particle swarm optimization (PSO) has been successfully applied to various complex optimization problems due to its simplicity and efficiency. However, the update strategy of the standard PSO algorithm is to learn from the global best particle, making it difficult to maintain diversity in the population and prone to premature convergence due to being trapped in local optima. Chaos search mechanism is an optimization technique based on chaotic dynamics, which utilizes the randomness and nonlinearity of a chaotic system for global search and can escape from local optima. To overcome the limitations of PSO, an improved particle swarm optimization combined with double-chaos search (DCS-PSO) is proposed in this paper. In DCS-PSO, we first introduce double-chaos search mechanism to narrow the search space, which enables PSO to focus on the neighborhood of the optimal solution and reduces the probability that the swarm gets trapped into a local optimum. Second, to enhance the population diversity, the logistic map is employed to perform a global search in the narrowed search space and the best solution found by both the logistic and population search guides the population to converge. Experimental results show that DCS-PSO can effectively narrow the search space and has better convergence accuracy and speed in most cases.

Feature selection based on neighborhood rough sets and Gini index.

Neighborhood rough set is considered an essential approach for dealing with incomplete data and inexact knowledge representation, and it has been widely applied in feature selection. The Gini index is an indicator used to evaluate the impurity of a dataset and is also commonly employed to measure the importance of features in feature selection. This article proposes a novel feature selection methodology based on these two concepts. In this methodology, we present the neighborhood Gini index and the neighborhood class Gini index and then extensively discuss their properties and relationships with attributes. Subsequently, two forward greedy feature selection algorithms are developed using these two metrics as a foundation. Finally, to comprehensively evaluate the performance of the algorithm proposed in this article, comparative experiments were conducted on 16 UCI datasets from various domains, including industry, food, medicine, and pharmacology, against four classical neighborhood rough set-based feature selection algorithms. The experimental results indicate that the proposed algorithm improves the average classification accuracy on the 16 datasets by over 6%, with improvements exceeding 10% in five. Furthermore, statistical tests reveal no significant differences between the proposed algorithm and the four classical neighborhood rough set-based feature selection algorithms. However, the proposed algorithm demonstrates high stability, eliminating most redundant or irrelevant features effectively while enhancing classification accuracy. In summary, the algorithm proposed in this article outperforms classical neighborhood rough set-based feature selection algorithms.