Implementing Kernel Methods Incrementally by Incremental Nonlinear Projection Trick
提出增量非线性投影技巧（INPT），无需中心化步骤，可增量计算样本在再生核希尔伯特空间中的坐标，从而将任意增量算法扩展为核版本，应用于核矩阵重建、字母分类和人脸图像检索。
Recently, the nonlinear projection trick (NPT) was introduced enabling direct computation of coordinates of samples in a reproducing kernel Hilbert space. With NPT, any machine learning algorithm can be extended to a kernel version without relying on the so called kernel trick. However, NPT is inherently difficult to be implemented incrementally because an ever increasing kernel matrix should be treated as additional training samples are introduced. In this paper, an incremental version of the NPT (INPT) is proposed based on the observation that the centerization step in NPT is unnecessary. Because the proposed INPT does not change the coordinates of the old data, the coordinates obtained by INPT can directly be used in any incremental methods to implement a kernel version of the incremental methods. The effectiveness of the INPT is shown by applying it to implement incremental versions of kernel methods such as, kernel singular value decomposition, kernel principal component analysis, and kernel discriminant analysis which are utilized for problems of kernel matrix reconstruction, letter classification, and face image retrieval, respectively.