Finding pre-images via evolution strategies

Kernel methods map, usually nonlinearly, the data from input space into a higher-dimensional feature space, in which linear algorithms are performed. In many applications, the inverse mapping is also useful, and the pre-images of some feature vectors need to be found in input space. However, finding pre-images is often a difficult optimization problem. This paper attempts to use evolution strategies (ES) to seek pre-images. This method firstly selects some of the nearest training patterns of an unknown pre-image as the initial group of the ES, then the ES carries out an iterative process to find the pre-images or approximate pre-images. Experimental results based on kernel principal component analysis (KPCA) for pattern denoising show that our proposed method outperforms some conventional techniques, including gradient descent technique, kernel ridge regression, and distance constraint method. Compared to these conventional techniques, the ES-based method is also straightforward to understand, and is easy to implement. (C) 2011 Elsevier B.V. All rights reserved.