16987880
Granular prototyping in fuzzy clustering
We introduce a logic-driven clustering in which prototypes are formed and evaluated in a sequential manner. The way of revealing a structure in data is realized by maximizing a certain performance index (objective function) that takes into consideration an overall level of matching (to be maximized) and a similarity level between the prototypes (the component to be minimized). The prototypes identified in the process come with the optimal weight vector that serves to indicate the significance of the individual features (coordinates) in the data grouping represented by the prototype. Since the topologies of these groupings are in general quite diverse the optimal weight vectors are reflecting the anisotropy of the feature space, i.e., they show some local ranking of features in the data space. Having found the prototypes we consider an inverse similarity problem and show how the relevance of the prototypes translates into their granularity.
19471846
Fuzzy clustering with a knowledge-based guidance
Fuzzy clustering becomes a broadly accepted synonym of fundamental endeavors aimed at finding structures in multidimensional data. In essence, these methods operate in unsupervised mode. This means that they act upon data while being directed by some predefined objective function (criterion) for which they "discover" a structure (clusters) that yields a minimal value of this criterion. In this study, we discuss an issue of exploiting and effectively incorporating auxiliary problem dependent hints being available as a part of the domain knowledge associated with the pattern recognition problem at hand. As such hints are usually expressed by experts/data analysts at the level of clusters (information granules) rather than individual data (patterns), we refer to them as knowledge-based indicators and allude to a set of them as a knowledge-based guidance available to fuzzy clustering. The proposed paradigm shift in which fuzzy clustering incorporates this type of knowledge-based supervision is discussed and contrasted with the "pure" (that is data-driven) version of fuzzy clustering. Several fundamental categories of the guidance mechanisms are introduced and discussed, namely partial supervision, proximity-based guidance and uncertainty driven knowledge hints. The details on how the guidance machinery translates into updates of the partition matrices are presented. We also present a number of practical scenarios in which the role of knowledge hints becomes evident and highly justifiable. This concerns Web exploration, exploitation of labeled patterns, issues of incomplete feature spaces, and constraints of typicality of patterns, to name a few representative applications.
2982088
Fuzzy Aggregation Method Using Fisherface and Wavelet Decomposition for Face Recognition
2312456
Two iterative methods of decomposition of a fuzzy relation for image compression/decompression processing
A decomposition problem of max–min type for a fuzzy relation is proposed. A fast method is derived by transforming slightly the derivatives in the traditional gradient algorithm and by updating simultaneously the prototype relation. The complexities of the proposed algorithm, with respect to the traditional gradient one, are decreased to approximately 1/c, where “c” denotes the Schein rank of the fuzzy relation involved. A dual decomposition problem of max–min type is also formulated and a similar fast method is presented. Both methods are applied to image compression/decompression processing.
20379804
Hybrid Fuzzy Polynomial Neural Networks
We propose a hybrid architecture based on a combination of fuzzy systems and polynomial neural networks. The resulting Hybrid Fuzzy Polynomial Neural Networks (HFPNN) dwells on the ideas of fuzzy rule-based computing and polynomial neural networks. The structure of the network comprises of fuzzy polynomial neurons (FPNs) forming the nodes of the first (input) layer of the HFPNN and polynomial neurons (PNs) that are located in the consecutive layers of the network. In the FPN (that forms a fuzzy inference system), the generic rules assume the form "if A then y = P(x)" where A is a fuzzy relation in the condition space while P(x) is a polynomial standing in the conclusion part of the rule. The conclusion part of the rules, especially the regression polynomial uses several types of high-order polynomials such as constant, linear, quadratic, and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership functions are considered. Each PN of the network realizes a polynomial type of partial description (PD) of the mapping between input and out variables. HFPNN is a flexible neural architecture whose structure is based on the Group Method of Data Handling (GMDH) and developed through learning. In particular, the number of layers of the PNN is not fixed in advance but is generated in a dynamic way. The experimental part of the study involves two representative numerical examples such as chaotic time series and Box-Jenkins gas furnace data.
41324764
Rule-based multi-FNN identification with the aid of evolutionary fuzzy granulation
Abstract In this paper, we introduce a category of Multi-Fuzzy-Neural Networks (Multi-FNNs) models, analyze the underlying architectures and propose a comprehensive identification framework. The proposed Multi-FNNs are based on a concept of fuzzy rule-based FNNs that use H ard C - M eans (HCM) clustering and evolutionary fuzzy granulation and exploit linear inference being treated as a generic inference mechanism of approximate reasoning. By this nature, this FNN model is geared toward capturing relationships between information granules–fuzzy sets. The form of the information granules themselves (in particular their distribution and a type of membership functions) becomes an important design feature of the FNN model that contributes to its structural and parametric optimization. The genetically guided global optimization is then augmented by more refined gradient-based learning mechanisms such as a standard back-propagation. The HCM algorithm, whose role is to carry out preprocessing of the experimental data, is utilized to determine the structure of Multi-FNNs. The detailed parameters of the Multi-FNN (such as apexes of membership functions, learning rates, and momentum coefficients) are adjusted using genetic algorithms. The proposed aggregate performance index helps achieve a sound balance between approximation and generalization (predictive) abilities of the model. To evaluate an effectiveness of the introduced model, several numeric data sets are experimented with. Those include a time-series data of gas furnace, NOx emission process of gas turbine power plant and some synthetic data.
34867589
Modeling temporal functions with granular regression and fuzzy rules
Modeling of temporal functions has been studied extensively in last few decades. Temporal functions or time series are found practically in the gamut of applications, ranging from engineering analysis to financial and commercial transactions.Numerous time series models been proposed, and they can be found in the relevant time series literature. Deterministic and stochastic models have dominated much of the research in this area. Nonetheless, these models have their limitations, and particularly specific models solve specific problem domains. Therefore, there is no general mechanism that can address the issues of modeling of temporal functions.Granular information is now being used to address a few of the problems in the theory of time series. This paper proposes two models that use the concepts of regression and interleaved information granules-intervals and fuzzy sets to identify the structure existing in a given time series. In brevity, we are attempting to combine regression and fuzzy rules to model temporal systems.
5269666
Conditional Fuzzy C-Means
A Fuzzy C-Means-based clustering method guided by an auxiliary (conditional) variable is introduced. The method reveals a structure within a family of patterns by considering their vicinity in a feature space along with the similarity of the values assumed by a certain conditional variable. The usefulness of the algorithm is exemplified in the problems of data mining.
22511023
Fuzzy clustering with partial supervision
Presented here is a problem of fuzzy clustering with partial supervision, i.e., unsupervised learning completed in the presence of some labeled patterns. The classification information is incorporated additively as a part of an objective function utilized in the standard FUZZY ISODATA. The algorithms proposed in the paper embrace two specific learning scenarios of complete and incomplete class assignment of the labeled patterns. Numerical examples including both synthetic and real-world data arising in the realm of software engineering are also provided.
37179983
Granular Regression
We augment a linear regression procedure by a thruth-functional method in order to identify a highly informative regression line. The idea is to use statistical methods to identify a confidence region for the line and exploit the structure of the sample data falling in this region for identifying the most fitting line. The fitness function is related to the fuzziness of the sampled points as a natural extension of the statistical criterion ruling the identification of the confidence region within the Algorithmic Inference approach. We tested the method on three well known benchmarks.