Efficient vector quantization using the WTA-rule with activity equalization

Heidemann G, Ritter H. Efficient vector quantization using the WTA-rule with activity equalization. Neural Processing Letters. 2001;13(1):17-30.We propose a new algorithm for vector quantization, the Activity Equalization Vector quantization (AEV). It is based on the winner takes all rule with an additional supervision of the average node activities over a training interval and a subsequent re-positioning of those nodes with low average activities. The re-positioning is aimed to both an exploration of the data space and a better approximation of already discovered data clusters by an equalization of the node activities. We introduce a learning scheme for AEV which requires as previous knowledge about the data only their bounding box. Using an example of Martinetz et al. [1], AEV is compared with the Neural Gas, Frequency Sensitive Competitive Learning (FSCL) and other standard algorithms. It turns out to converge much faster and requires less computational effort

SIMULATING SEISMIC WAVE PROPAGATION IN TWO-DIMENSIONAL MEDIA USING DISCONTINUOUS SPECTRAL ELEMENT METHODS

We introduce a discontinuous spectral element method for simulating seismic wave in 2- dimensional elastic media. The methods combine the flexibility of a discontinuous finite element method with the accuracy of a spectral method. The elastodynamic equations are discretized using high-degree of Lagrange interpolants and integration over an element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix and the use of discontinuous finite element method makes the calculation can be done locally in each element. Thus, the algorithm is simplified drastically. We validated the results of one-dimensional problem by comparing them with finite-difference time-domain method and exact solution. The comparisons show excellent agreement