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Several dimensionality-reduction techniques based on component analysis (CA) have been suggested for various data stream classification tasks and allow fast approximation. The variations of CA, such as PCA, KPCA and ICA, however, have limited dimensionality-reduction ability because of their high complexity or linear transformation scheme, etc. This paper proposes a fast iterative kernel principal component analysis algorithm: FIKDR, which non-linearly, iteratively extracts the kernel principal components with only linear order computation and storage complexity per iteration. On the basis of FIKDR, this paper proposes an online classification algorithm for data stream: FIKOCFrame. The convergence analysis confirms the validity of FIKDR and extensive experiments confirm the superiority of FIKOCFrame over recent classification schemes based on CA.