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.

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.

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.

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.