Tue Lehn-Schiøler

Vector quantization using information theoretic concepts

The process of representing a large data set with a smaller number of vectors in the best possible way, also known as vector quantization, has been intensively studied in the recent years. Very efficient algorithms like the Kohonen self-organizing map (SOM) and the Linde Buzo Gray (LBG) algorithm have been devised. In this paper a physical approach to the problem is taken, and it is shown that by considering the processing elements as points moving in a potential field an algorithm equally efficient as the before mentioned can be derived. Unlike SOM and LBG this algorithm has a clear physical interpretation and relies on minimization of a well defined cost function. It is also shown how the potential field approach can be linked to information theory by use of the Parzen density estimator. In the light of information theory it becomes clear that minimizing the free energy of the system is in fact equivalent to minimizing a divergence measure between the distribution of the data and the distribution of the processing elements, hence, the algorithm can be seen as a density matching method.

State-Space Models: From the EM Algorithm to a Gradient Approach

Slow convergence is observed in the EM algorithm for linear state-space models. We propose to circumvent the problem by applying any off-the-shelf quasi-Newton-type optimizer, which operates on the gradient of the log-likelihood function. Such an algorithm is a practical alternative due to the fact that the exact gradient of the log-likelihood function can be computed by recycling components of the expectation-maximization (EM) algorithm. We demonstrate the efficiency of the proposed method in three relevant instances of the linear state-space model. In high signal-to-noise ratios, where EM is particularly prone to converge slowly, we show that gradient-based learning results in a sizable reduction of computation time.

Vector-quantization by density matching in the minimum Kullback-Leibler divergence sense

Representation of a large set of high-dimensional data is a fundamental problem in many applications such as communications and biomedical systems. The problem has been tackled by encoding the data with a compact set of code-vectors called processing elements. In this study, we propose a vector quantization technique that encodes the information in the data using concepts derived from information theoretic learning. The algorithm minimizes a cost function based on the Kullback-Liebler divergence to match the distribution of the processing elements with the distribution of the data. The performance of this algorithm is demonstrated on synthetic data as well as on an edge-image of a face. Comparisons are provided with some of the existing algorithms such as LBG and SOM.

Nonlinear characteristics of randomly excited transonic flutter

The paper describes the effects of random external excitations on the onset and dynamical characteristics of transonic flutter (i.e. large-amplitude, self-sustained oscillations) for a high aspect ratio wing. Wind tunnel experiments performed at the National Aerospace Laboratory (NAL) in Japan have shown that the self-sustained oscillations arise in a subcritical Hopf bifurcation. However, analysis of the experimental data also reveals that this bifurcation is modified in various ways. We present an outline of the construction of a 6 DOF model of the aeroelastic behavior of the wing structure. When this model is extended by the introduction of nonlinear terms, it can reproduce the subcritical Hopf bifurcation. We hereafter consider the effects of subjecting simplified versions of the model to random external excitations representing the fluctuations present in the airflow. These models can reproduce several of the experimentally observed modifications of the flutter transition. In particular, the models display the characteristic phenomena of coherence resonance.

Parzen particle filters

Using a Parzen density estimator, any distribution can be approximated arbitrarily close by a sum of kernels. In particle filtering, this fact is utilized to estimate a probability density function with Dirac delta kernels; when the distribution is discretized it becomes possible to solve an otherwise intractable integral. In this work, we propose to extend the idea and use any kernel to approximate the distribution. The extra work involved in propagating small kernels through the nonlinear function can be made up for by decreasing the number of kernels needed, especially for high dimensional problems. A further advantage of using kernels with nonzero width is that the density estimate becomes continuous.

BLUES from music: BLind underdetermined extraction of sources from music

In this paper we propose to use an instantaneous ICA method (BLUES) to separate the instruments in a real music stereo recording. We combine two strong separation techniques to segregate instruments from a mixture: ICA and binary time-frequency masking. By combining the methods, we are able to make use of the fact that the sources are differently distributed in both space, time and frequency. Our method is able to segregate an arbitrary number of instruments and the segregated sources are maintained as stereo signals. We have evaluated our method on real stereo recordings, and we can segregate instruments which are spatially different from other instruments.

Nonlinear dynamics approach of modeling the bifurcation for aircraft wing flutter in transonic speed

The procedure of obtaining the two-degrees-of-freedom, finite dimensional. nonlinear mathematical model. which models the nonlinear features of aircraft flutter in transonic speed is reported. The model enables to explain every feature of the transonic flutter data of the wind tunnel tests conducted at National Aerospace Laboratory in Japan for a high aspect ratio wing. It explains the nonlinear features of the transonic flutter such as the subcritical Hopf bifurcation of a limit cycle oscillation (LCO), a saddle-node bifurcation, and an unstable limit cycle as well as a normal (linear) flutter condition with its linear pan. At a final procedure of improve a quantitative matching with the test data. the continuation method for analyzing the bifurcation is extensively used.