We introduce a data-driven model approximation method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method is based on embedding the nonlinear system in a high (or infinite) dimensional reproducing kernel Hilbert space (RKHS) where linear balanced truncation may be carried out implicitly. This leads to a nonlinear reduction map which can be combined with a representation of the system belonging to a RKHS to give a closed, reduced order dynamical system which captures the essential input-output characteristics of the original model. Working in RKHS provides a convenient, general functional-analytical framework for theoretical understanding. Empirical simulations illustrating the approach are also provided. 1 2 U Z −1 . We also note that the problem of finding the coordinate change Q can be seen as an optimization problem [1] of the form min Q trace[QW c Q * + Q − * W o Q −1 ]. 5

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Drawing on recent progress in auditory neuroscience, we present a novel speech feature analysis technique based on localized spectrotemporal cepstral analysis of speech. We proceed by extracting localized 2D patches from the spectrogram and project onto a 2D discrete cosine (2D-DCT) basis. For each time frame, a speech feature vector is then formed by concatenating low-order 2D-DCT coefficients from the set of corresponding patches. We argue that our framework has significant advantages over standard onedimensional MFCC features. In particular, we find that our features are more robust to noise, and better capture temporal modulations important for recognizing plosive sounds. We evaluate the performance of the proposed features on a TIMIT classification task in clean, pink, and babble noise conditions, and show that our feature analysis outperforms traditional features based on MFCCs.

We propose a natural image representation, the neural response, motivated by the neuroscience of the visual cortex. The inner product defined by the neural response leads to a similarity measure between functions which we call the derived kernel. Based on a hierarchical architecture, we give a recursive definition of the neural response and associated derived kernel. The derived kernel can be used in a variety of application domains such as classification of images, strings of text and genomics data.