一种基于ISOMAP的分类算法

An algorithm for classification based on ISOMAP

提出一种解决分类任务的等测距映射算法,该算法利用类标签信息指导高维数据的降维.首先根据类标签在属于某个类的数据集上构造类内邻域图;然后寻找类间最短距离相邻边,并将其乘以大于1的尺度变化因子,使得降维后的类内数据更加紧凑、类间数据更加分开;最后利用BP神经网络构建一个近似的从原始高维数据集到低维数据集之间的映射函数,通过遗传算法对BP神经网络的初始权值和阈值进行优化,以避免使用剃度下降算法所带来的局部最优问题.实验结果表明,分类性能有较大提高,并对噪声有一定的鲁棒性.

An improved isometric feature mapping（ISOMAP）algorithm for classification task, called ISOMAP-C, is proposed, which employs label information to guide the dimensionality reduction for high dimensional datasets. Firstly, within-class neighborhood graphs are constructed over each sub dataset belonging to the same class according to label information. Secondly, the between-class neighborhood edges with the shortest distance are searched for, which is multiplied by scaling factor greater than one so that low dimensional dataset after mapping become more compact within class and more separate between classes. Finally, the mapping function from original high dimensional space to low dimensional space can be approximately modeled by using Back-Propagation neural network, whose initial weights and thresholds are optimized by using genetic algorithms to avoid local minimum using gradient decent techniques. The experimental results show that the performance of classification is greatly enhanced and the alsorithm has robust for noisy data.