This paper evaluates a segmentation technique for magnetic resonance (MR) images of the brain based on fuzzy algorithms for learning vector quantization (FALVQ). These algorithms perform vector quantization by updating all prototypes of a competitive network through an unsupervised learning process. Segmentation of MR images is formulated as an unsupervised vector quantization process, where the local values of different relaxation parameters form the feature vectors which are represented by a relatively small set of prototypes. The experiments evaluate a variety of FALVQ algorithms in terms of their ability to identify different tissues and discriminate between normal tissues and abnormalities.

This work evaluates the performance of an image compression system based on wavelet-based subband decomposition and vector quantization. The images are decomposed using wavelet filters into a set of subbands with different resolutions corresponding to different frequency bands. The resulting subbands are vector quantized using the Linde-Buzo-Gray (LBG) algorithm and various fuzzy algorithms for learning vector quantization (FALVQ). These algorithms perform vector quantization by updating all prototypes of a competitive neural network through an unsupervised learning process. The quality of the multiresolution codebooks designed by these algorithms is measured on the reconstructed images belonging to the training set used for multiresolution codebook design and the reconstructed images from a testing set.

First, we identify an algorithmic defect of the generalized learning vector quantization (GLVQ) scheme that causes it to behave erratically for a certain scaling of the input data. We show that GLVQ can behave incorrectly because its learning rates are reciprocally dependent on the sum of squares of distances from an input vector to the node weight vectors. Finally, we propose a new family of models-the GLVQ-F family-that remedies the problem. We derive competitive learning algorithms for each member of the GLVQ-F model and prove that they are invariant to all scalings of the data. We show that GLVQ-F offers a wide range of learning models since it reduces to LVQ as its weighting exponent (a parameter of the algorithm) approaches one from above. As this parameter increases, GLVQ-F then transitions to a model in which either all nodes may be excited according to their (inverse) distances from an input or in which the winner is excited while losers are penalized. And as this parameter increases without limit, GLVQ-F updates all nodes equally. We illustrate the failure of GLVQ and success of GLVQ-F with the IRIS data.

This paper presents the development of fuzzy algorithms for learning vector quantization (FALVQ). These algorithms are derived by minimizing the weighted sum of the squared Euclidean distances between an input vector, which represents a feature vector, and the weight vectors of a competitive learning vector quantization (LVQ) network, which represent the prototypes. This formulation leads to competitive algorithms, which allow each input vector to attract all prototypes. The strength of attraction between each input and the prototypes is determined by a set of membership functions, which can be selected on the basis of specific criteria. A gradient-descent-based learning rule is derived for a general class of admissible membership functions which satisfy certain properties. The FALVQ 1, FALVQ 2, and FALVQ 3 families of algorithms are developed by selecting admissible membership functions with different properties. The proposed algorithms are tested and evaluated using the IRIS data set. The efficiency of the proposed algorithms is also illustrated by their use in codebook design required for image compression based on vector quantization.

This paper presents the development and evaluation of fuzzy vector quantization algorithms. These algorithms are designed to achieve the quality of vector quantizers provided by sophisticated but computationally demanding approaches, while capturing the advantages of the frequently used in practice k-means algorithm, such as speed, simplicity, and conceptual appeal. The uncertainty typically associated with clustering tasks is formulated in this approach by allowing the assignment of each training vector to multiple clusters in the early stages of the iterative codebook design process. A training vector assignment strategy is also proposed for the transition from the fuzzy mode, where each training vector can be assigned to multiple clusters, to the crisp mode, where each training vector can be assigned to only one cluster. Such a strategy reduces the dependence of the resulting codebook on the random initial codebook selection. The resulting algorithms are used in image compression based on vector quantization. This application provides the basis for evaluating the computational efficiency of the proposed algorithms and comparing the quality of the resulting codebook design with that provided by competing techniques.