Cross-entropy embedding of high-dimensional data using the neural gas model
✍ Scribed by Pablo A. Estévez; Cristián J. Figueroa; Kazumi Saito
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 830 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0893-6080
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✦ Synopsis
A cross-entropy approach to mapping high-dimensional data into a low-dimensional space embedding is presented. The method allows to project simultaneously the input data and the codebook vectors, obtained with the Neural Gas (NG) quantizer algorithm, into a low-dimensional output space. The aim of this approach is to preserve the relationship defined by the NG neighborhood function for each pair of input and codebook vectors. A cost function based on the cross-entropy between input and output probabilities is minimized by using a Newton-Raphson method. The new approach is compared with Sammon's non-linear mapping (NLM) and the hierarchical approach of combining a vector quantizer such as the self-organizing feature map (SOM) or NG with the NLM recall algorithm. In comparison with these techniques, our method delivers a clear visualization of both data points and codebooks, and it achieves a better mapping quality in terms of the topology preservation measure q(m).