Abstract: Most of existing manifold learning algorithms are not capable of dealing with new arrival samples. Although some incremental algorithms are developed via extending a specified manifold learning algorithm, most of them have some disadvantages more or less. In this paper, a novel and more Generalized Incremental Manifold Learning algorithm based on local smoothness is proposed (GIML). GIML algorithm first extracts the local smoothness structure of data set via local PCA. Then the optimal linear transformation, which transforms the local smoothness structure of new arrival sample’s neighborhood to its corresponded low-dimensional embedding coordinates, is computed. Finally the low-dimensinal embedding coordinates of new arrival samples are obtained by the optimal transformation. Extensive and systematic experiments are conducted on both artificial and real image data sets. Experimental results demonstrate that our GIML algotithm is an effective incremental manifold learning algorithm and outperforms other existing algirthms.

Key words: dimensionality reduction, manifold learning, manifold, incremental leaning, local tangent space aligment, local linear embedding

摘要： 目前大多数流形学习算法无法获取高维输入空间到低维嵌入空间的映射，无法处理新增数据，因此无增量学习能力。而已有的增量流形学习算法大多是通过扩展某一特定的流形学习算法使其具备增量学习能力，不具有通用性。针对这一问题，提出了一种通用的增量流形学习(GIML)算法。该方法充分考虑流形的局部平滑性这一本质特征，利用局部主成分分析法来提取数据集的局部平滑结构，并寻找包含新增样本点的局部平滑结构到对应训练数据的低维嵌入坐标的最佳变换。最后GIML算法利用该变换计算新增样本点的低维嵌入坐标。在人工数据集和实际图像数据集上进行了系统而广泛的比较实验，实验结果表明GIML算法是一种高效通用的增量流形学习方法，且相比当前主要的增量算法，能更精确地获取增量数据的低维嵌入坐标。

关键词: 维数归约, 流形学习, 流形, 增量学习, 局部切空间对齐, 局部线性嵌入