Neural networks and adaptive wavelets for vector quantization, function approximation, and classification

This dissertation develops neural network models for function approximation, classification, and vector quantization. These models perform code compression of data and are used for efficient transmission of images, medical diagnosis; customer profiling, and data visualization. Code compression reduces the amount of data in a problem by using prototypical values from a codebook to summarize a database, or by representing complex functions as combinations of basis functions.; The first part of the work introduces two models that define basis functions adapted to given data distributions. The Continuous Self-Organizing Map (CSOM) is a new, distributed version of the discrete Self-Organizing Map (SOM) network. Applications of SOM have included the visualization of high dimensional datasets and function approximation. CSOM outperforms the SOM algorithm in function approximation and data visualization tasks. The second model, the Wavelet Self-Organizing Map (WSOM) implements discrete approximations using wavelets for basis functions. Wavelets represent functions concisely and are useful in separating signal from noise. The WSOM model creates wavelet bases adapted to the distribution of input data, achieving improved performance with fewer wavelets compared to non-adaptive methods. The model also provides an efficient online way to construct, iv high-dimensional wavelet bases.; The second part of the dissertation builds hierarchical representations of data and applies the resulting systems to vector quantization and clustering problems. Hierarchical architectures break down complex and difficult problems into smaller ones. This dissertation introduces S-TREE (Self-Organizing Tree), a competitive learning neural network tree. S-TREE is an online method that can learn codebooks for data compression with small numbers of passes through large databases of examples. The performance of the algorithm is illustrated with an image compression application. On this task, S-TREE's image reconstruction quality approaches that of the standard generalized Lloyd algorithm (a non-hierarchical method) while taking less than 10% of the computer time of the generalized Lloyd algorithm. S-TREE also compares favorably with the standard Tree-Structured Vector Quantizer algorithm in both the time needed to create the codebook and quality of image reconstruction.