基于多目标稀疏优化的多视图聚类方法

The feature space of big data consists of multiple feature subsets from difference views, which results in multi-view data. The main difficulties of multi-view clustering come from the view disagreement and high feature space, which make it essentially be a typical high-dimensional sparse optimization problem. From the sparse optimziation problem, the sparse optimization method based on multi-objective evolutionary algorithm is studied firstly in this project, then a multi-objective sparse model and optimization method for multi-view clustering are studied. Specifically, to solve sparse optimization problem, a multi-objective optimization model is constructed first, then a hybrid multi-objective evolutionary algorithm based on particle swarm optimization and iterative threshold algorithm is studied. In addition, to solve the multi-view clustering problem, the inter-relationship of clustering, view disagreement and feature selection are investigated firstly, then a two-level weighted multi-objetcive optimization model is proposed. Furthermore, a multi-view clustering algorithm based on multi-objective cooperation coevolution is studied. This project is an interdisciplinary research topic that have important theoretical significance and broad application prospects, because it provides not only the technique support for multi-view clustering but also the new thought for solving sparse optimization problem.

大数据的特征空间往往由来自不同视图的多个特征子集组合而成，因而呈现“多视图”特性。多视图聚类问题受限于视图非一致性和高维特征空间，本质上可归结为高维稀疏优化问题。本项目以稀疏优化问题为出发点，研究稀疏优化问题的多目标优化方法，进而构建多视图聚类的多目标稀疏优化模型，研究基于多目标稀疏优化的多视图聚类方法。针对稀疏优化问题，构建稀疏优化问题的多目标优化模型，给出多目标进化算法与迭代阈值算法的混合机制，研究粒子群优化算法的个体学习新机制，提出基于混合多目标进化的稀疏优化算法；针对多视图聚类问题，研究多视图聚类中簇分配、视图非一致性以及特征选择之间的内在联系，构建多视图聚类的多目标稀疏优化模型，研究基于多目标合作协同进化的多视图聚类算法。本项目是一个多学科交叉的研究课题，研究成果不仅为多视图聚类提供关键技术支撑，也为众多稀疏优化问题的高效求解提供一种新思路，具有重要的理论意义和广泛的应用前景。

本项目从函数优化的角度对多视图聚类问题进行了深入研究，构建了多视图聚类问题的多目标模型和同步加权模型，提出了基于多目标进化优化、梯度下降和混合优化等策略的模型求解方法，并将所提方法应用到多个实际应用问题。首先，将多视图问题看成是多个独立的子视图上的聚类任务，通过多目标优化模型建立跨越多个视图的多视图多目标优化模型，给出了基于多目标进化算法的模型求解方法，发现了优化效果与聚类性能的不对等性。其次，针对高维多视图聚类问题的函数优化本质，提出了基于问题分解、变量分解和多偏好引导等方法的高维目标进化优化方法，实验验证了所提分解方法的有效性。再次，建立多视图聚类问题的同步加权模型，通过同步加权同时识别视图不一致性和特征噪声，分别给出基于梯度下降和混合优化的求解算法，证明了算法收敛性。最后，将所提算法应用到图像处理、社区发现和学习行为挖掘等若干实际应用数据集上，验证了所提各类方法的有效性。本项目所提算法建立了多视图聚类和多目标优化之间的桥梁，为大数据中的多视图数据的分析提供了一种新的途径，并在数据挖掘的教育科学应用进行了探索研究。