Abstract A kernel-based algorithm is proposed to solve the nonlinear expansion problem of slow feature analysis (SFA). By using the kernel trick, the difficulties of computing directly in high dimensional space are avoided. Because of the full use of nonlinear information of the data, its output is steady. Meanwhile, based on the objective analysis of the proposed algorithm, a formula is put forward to estimate the output slowness of the signal and it is utilized as a guide line to select parameters of the kernel functions. Experimental results show the effectiveness of the proposed algorithm.
[1] Wiskott L, Sejnowski T. Slow Feature Analysis: Unsupervised Learning of Invariances. Neural Computation, 2002, 14(4): 715-770 [2] Berkes P, Wiskott L. Slow Feature Analysis Yields a Rich Repertoire of Complex Cell Properties. Journal of Vision, 2005, 5(6): 579-602 [3] Franzius M, Sprekeler H, Wiskott L. Slowness and Sparseness Lead to Place, Head-Direction and Spatial-View Cells. PLoS Computational Biology, 2007, 3(8): 1605-1622 [4] Blaschke T, Zito T, Wiskott L. Independent Slow Feature Analysis and Nonlinear Blind Source Separation. Neural Computation, 2007, 19(4): 994-1021 [5] Franzius M, Wilbert N, Wiskott L. Unsupervised Learning of Invariant 3D-Object Representations with Slow Feature Analysis // Proc of the 3rd Bernstein Symposium for Computational Neuroscience. Gttingen, Germany, 2007: 105-112 [6] Franzius M, Wilbert N, Wiskott L. Invariant Object Recognition with Slow Feature Analysis // Proc of the 18th International Conference on Artificial Neural Networks. Prague, Czech Republic, 2008: 961-970 [7] Courant R, Hilbert D. Methods of Mathematical Physics. New York, USA: Wiley-Interscience, 1989 [8] Vapnik V N. The Nature of Statistical Learning Theory. New York, USA: Springer-Verlag, 1995 [9] Schlkopf B, Smola A. Nonlinear Component Analysis as a Kernel Eigenvalue Problem. Neural Computation, 1998, 10(5): 1299-1319 [10] Schlkopf B, Mika S, Burges C J C, et al. Input Space vs. Feature Space in Kernel-Based Methods. IEEE Trans on Neural Networks, 1999, 10(5): 1000-1017 [11] Wiskott L. Slow Feature Analysis: A Theoretical Analysis of Optimal Free Responses. Neural Computation, 2003, 15(9): 2147-2177 [12] Sprekeler H, Wiskott L. Understanding Slow Feature Analysis: A Mathematical Framework [EB/OL]. [2008-10-10]. http://cogprints.org/6223/2/Sprekeler wiskotl08.pdf [13] Harmeling S, Ziehe A, Kawanabe M, et al. Kernel-Based Nonlinear Blind Source Separation. Neural Computation, 2003, 15(5): 1089-1124 [14] Duda R O, Hart P E, Stork D G. Pattern Classification. 2nd Edition. New York, USA: Wiley-Interscience, 2001 [15] Bray A, Martinez D. Kernel-Based Extraction of Slow Features: Complex Cells Learn Disparity and Translation Invariance from Natural Images // Becker S, Thrun S, Obermayer K, eds. Advances in Neural Information Processing Systems. Cambridge, USA: MIT Press, 2002: 269-276
2011, Vol. 24 
