We describe an efficient algorithm for simultaneously extracting multiple smoothly-varying non-linear invariances from time-series data. The method exploits the concept of maximising temporal predictability introduced by Stone in the linear domain - we term this temporal component analysis (TCA). Our current work extends this linear method into the non-linear domain using kernel-based methods; it performs a non-linear projection of the input into an unknown high-dimensional feature space, computing a linear solution in this space. In this paper we describe the improved on-line version of this algorithm (KTCA) for working on very large data sets, and demonstrate its applicability for computer vision by extracting non-linear disparity directly from grey-level stereo pairs, without pre-processing.