Unsupervised Optimal Fuzzy Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Why triangular membership functions?
Fuzzy Sets and Systems
Two soft relatives of learning vector quantization
Neural Networks
Large-Scale Parallel Data Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fuzzy equalization in the construction of fuzzy sets
Fuzzy Sets and Systems
The LBG-U Method for Vector Quantization – an Improvement over LBGInspired from Neural Networks
Neural Processing Letters
Clustering based on conditional distributions in an auxiliary space
Neural Computation
Generalized relevance learning vector quantization
Neural Networks - New developments in self-organizing maps
Soft learning vector quantization
Neural Computation
A vector quantization method for nearest neighbor classifier design
Pattern Recognition Letters
On the use of the weighted fuzzy c-means in fuzzy modeling
Advances in Engineering Software
A generalized multiple projection axes method for fast encoding of vector quantization
Pattern Recognition Letters
Toward a generalized theory of uncertainty (GTU): an outline
Information Sciences—Informatics and Computer Science: An International Journal
An overview of scalar quantization based data hiding methods
Signal Processing
Differential evolution and particle swarm optimisation in partitional clustering
Computational Statistics & Data Analysis
Vector quantization: a weighted version for time-series forecasting
Future Generation Computer Systems
An image zooming technique based on vector quantization approximation
Image and Vision Computing
Competitive learning and soft competition for vector quantizerdesign
IEEE Transactions on Signal Processing
Optimum design of vector-quantized subband codecs
IEEE Transactions on Signal Processing
An efficient vector quantizer providing globally optimal solutions
IEEE Transactions on Signal Processing
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Analysis of the weighting exponent in the FCM
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
An integrated approach to fuzzy learning vector quantization and fuzzy c-means clustering
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
Optimality test for generalized FCM and its application to parameter selection
IEEE Transactions on Fuzzy Systems
Conditional fuzzy clustering in the design of radial basis function neural networks
IEEE Transactions on Neural Networks
A dynamic data granulation through adjustable fuzzy clustering
Pattern Recognition Letters
Saliency-directed image interpolation using particle swarm optimization
Signal Processing
Use of a fuzzy granulation--degranulation criterion for assessing cluster validity
Fuzzy Sets and Systems
Type-2 fuzzy neural networks with fuzzy clustering and differential evolution optimization
Information Sciences: an International Journal
Fuzzy linear regression based on Polynomial Neural Networks
Expert Systems with Applications: An International Journal
Some concepts of the fuzzy multicommodity flow problem and their application in fuzzy network design
Mathematical and Computer Modelling: An International Journal
Information Sciences: an International Journal
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Vector quantization (VQ) is a fundamental and omnipresent mechanism of data compression with various conceptual underpinnings and diversified algorithmic realizations. The objective of this study is to investigate the concept of VQ in the setting of fuzzy sets by forming a coherent algorithmic framework referred to as a fuzzy VQ (FVQ). Given the nature of the framework of VQ in which fuzzy sets are involved, we may refer to the discussed processes of FVQ as a fuzzy granulation and fuzzy degranulation. In comparison to the winner-takes-all strategy encountered in VQ where a result of decoding typically arises as a single element of the codebook, in the FVQ we exploit an efficient usage of all components of the codebook (fuzzy sets) in the reconstruction of the original data. In this study, we present a complete development scheme of the FVQ and elaborate on its essential features. Its main design phases involve: (a) an encoding in which we encode data in terms of the elements of the given codebook; (b) a decoding during which we reconstruct the original data; and (c) a development of the codebook. The mechanisms of encoding and decoding are created as a result of some well-formed optimization tasks. The buildup of the codebook is completed through a mechanism of global optimization realized in the form of the particle swarm optimization (PSO). We offer a collection of experiments using synthetic data by focusing on and quantifying the role of fuzzy sets in VQ. While FVQ outperforms VQ (which seems to be an intuitively appealing finding), we also show that this improvement could be achieved through a careful optimization of the elements of the granulation scheme. It is also shown that without optimization of the FVQ scheme, the enhancements could not be possible or may become very much limited. A series of experiments involving synthetic data and data sets coming from the Machine Learning repository is included as well.