面向等维独立多流形的增量学习算法IMM-ISOMAP

摘要

流形学习是机器学习与数据挖掘领域的一个重要研究方向.其经典算法总是假设高维数据批量存在于单一流形,且不能有效处理增量式出现的高维多流形数据.针对等维独立多流形提出一种增量学习算法IMM-ISOMAP.首先在对新样本增量地更新动态邻域时,仅修改关键路径,避免重新计算全部邻域关系,以提高算法整体效率.然后通过扩展切空间的方法将新样本依次划分到各子流形,实现新样本的增量式分类算法.最后对各子流形计算低维嵌入并进行合并.实验结果表明,该算法可以有效地应用于人造多流形数据和实际得多流形图像数据.%Manifold learning is an important research issne in the fields of machine learning and data mining.The classical algorithms always assume that the high dimensional batched data exist in a single manifold,and can not effectively deal with the high dimensional multi-manifold data.We propose an incremental learning algorithm IMM-ISOMAP for equal dimension independent multi-manifolds.The algorithm computes the dynamic neighborhood of the new sample,and then divides the new samples into sub-manifolds by extending the tangent space.Finally it realizes the classification of the new samples and calculates the final low dimensional embedding.The experimental results show that the proposed algorithm can be effectively applied to artificial data and real image data.