基于广义分形插值理论的多尺度分类尺度下推算法

多尺度数据挖掘多应用于空间遥感图像数据,以图像的分辨率或者区域分割为依据进行尺度划分,然后在每个尺度层进行分析。近期,有不少学者将多尺度数据挖掘应用于一般数据集上,以等级理论、概念分层和包含度理论尺度划分等为尺度划分依据,研究不同尺度层的分布规律,进而发现有意义的事实,如多尺度关联规则以及多尺度聚类。但是在一般数据集下,很少将多尺度数据挖掘应用于分类算法领域。本文定义了广义分形插值理论的概念,打破了局限于迭代函数系统IFS(Iterative Function Systems)的缺憾,拓展了分形插值的应用；提出了基于广义分形插值理论的多尺度分类尺度下推算法MSCSDA(Multi-Scale Classification Scaling-Down Algorithm)；仿真实验建立在4个UCI基准数据集和1个H省部分人口真实数据集上,并将MSCSDA与KNN、Decision Tree以及Libsvm算法进行对比分析；实验结果表明,MSCSDA算法在不同的数据集上,均优于其他算法。

Scaling-down Algorithm of Multi-scale Classification Based on Generallized Fractal Interpolation Theory

The research of multi-scale data mining mainly applied to space remote sensing image data sets, and conduct scale division based on the resolution or regional segmentation of the images, then analysis knowledge on each scale layer. Recently, there are quite a few learners applied the multi-scale data mining to general data sets, and conduct scale division based on the level theory, concept hierarchy and inclusion degree etc., study the distribution rule on different scale layers, and then found significant facts. For example, multi-scale association rules, multi-scale clustering. But it has not been involved in the field of the classification mining. This paper defines the concept of generalized fractal interpolation theory, break the situation that limited to the use of the iteration function system(IFS), and extend the application of the fractal interpolation. Then, a multi-scale classification scaling-down algorithm based on the generalized fractal interpolation theory named MSCSDA (Multi-Scale Classification Scaling-Down Algorithm) is proposed. This paper performs experiments on four UCI benchmark data sets, and one real data set (H province part of the population). Then analysis the experimental results compare MSCSDA with KNN, Decision Tree and LIBSVM algorithms on different data sets. The experimental results show that the MSCSDA algorithm gives better results in terms of classification than the others.