The noise model based on σ trous wavelet algorithm produces a multi-scale expression of image through the combination of wavelet transform and a testing model of statistical significance. This kind of expression not only gives the formation and location of image structure on different scales, but also eliminates the influence of noise. Since the algorithm does not need any priori hypotheses, it is suitable for the data with complex structure. The research line is employed in this paper to analyze the spatial activity of earthquake. The method of how to recognize and describe the multi-scale space activity of earthquake is emphatically discussed in this paper. Taking typical sequences in Southwest China as research cases, we systematically study the structure characters of spatial activity of earthquake on different scales. Results show that multi-scale space structure to some extent possesses indicative effect on strong epicenters. And the foreshock anomalies of Songpan seismic sequence also reveal interesting pattern during the spatial-temporal evolvement.

针对常用时齐（比例选择下）遗传算法的强不收敛性和难以设置合理停机准则的弊端，提出一类非时齐（整体退火选择下）、保证收敛且容易判断收敛的新型遗传算法，证明允许父代参加竞争是这类新算法收敛的充要条件。数值实验表明：这类新算法收敛速度快，有极强的避免过早收敛及避免局部极值的全局优化能力。

给出一类基于奇异值软剔除的加权稳健支撑向量回归方法（WRSVR）。该方法的基本思想是首先由支撑向量回归方法（SVR）得到一个近似支撑向量回归函数，基于这个近似模型给出了加权SVR目标函数并利用高效的SVR求解技巧得到一个新的近似模型，然后再利用这个新的近似模型重新给出一个加权SVR目标函数并求解得到一个更为精确的近似模型，重复这一过程直至收敛。加权的目的是为了对奇异值进行软剔除。该方法具有思路简捷、稳健性强、容易实现等优点。实验表明，新算法WRSVR比标准SVR方法、稳健支撑向量网（RSVR）方法和加权最小二乘支撑向量机方法（WLS2SVM）更加稳健，算法的逼近精度受奇异值的影响远小于SVM、RSVR和WLS2SVM算法。

基于对生物复眼几何结构的模拟，提出一类新颖而有效的数据处理方法——方向量子化方法。该方法适宜于处理由高维数据所表示的凸体的几何外形，具有简洁有效、适用广泛、半动态维护简便和易于在各种并行计算模型上实现等优点。理论分析和数值模拟表明：这一方法理论基础坚实，计算稳定可靠，具有广阔的应用前景。