We develop a comprehensive and original methodology of data compression realized in the setting of granular computing. It is advocated that a compression process is inherently associated with the emergence of information granules forming compressed data. This entails that compression goes hand-in-hand with the elevated level of abstraction of the generated results. The performance of the method is evaluated with the aid of the indexes of coverage and specificity commonly encountered when processing and describing information granules. A two-phase design environment is systematically established along with the detailed algorithmic layer exploring mechanisms of fuzzy clustering and the principle of justifiable granularity and its generalizations. Reconstruction error and granular reconstruction error criteria are introduced and analyzed. Experimental studies carried out on publicly available data are reported and illustrate the process of granular compression and analyze the performance of the obtained results.
Many of the industrial and research databases are plagued by the problem of missing values. Some evident examples include databases associated with instrument maintenance, medical applications, and surveys. One of the common ways to cope with missing values is to complete their imputation (filling in). Given the rapid growth of sizes of databases, it becomes imperative to come up with a new imputation methodology along with efficient algorithms. The main objective of this paper is to develop a unified framework supporting a host of imputation methods. In the development of this framework, we require that its usage should (on average) lead to the significant improvement of accuracy of imputation while maintaining the same asymptotic computational complexity of the individual methods. Our intent is to provide a comprehensive review of the representative imputation techniques. It is noticeable that the use of the framework in the case of a low-quality single-imputation method has resulted in the imputation accuracy that is comparable to the one achieved when dealing with some other advanced imputation techniques. We also demonstrate, both theoretically and experimentally, that the application of the proposed framework leads to a linear computational complexity and, therefore, does not affect the asymptotic complexity of the associated imputation method.
We introduce a concept of fuzzy polynomial neural networks (FPNNs), a hybrid modeling architecture combining polynomial neural networks (PNNs) and fuzzy neural networks (FNNs). The development of the FPNNs dwells on the technologies of computational intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms. The structure of the FPNN results from a synergistic usage of FNN and PNN. FNNs contribute to the formation of the premise part of the rule-based structure of the FPNN. The consequence part of the FPNN is designed using PNNs. The structure of the PNN is not fixed in advance as it usually takes place in the case of conventional neural networks, but becomes organized dynamically to meet the required approximation error. We exploit a group method of data handling (GMDH) to produce this dynamic topology of the network. The performance of the FPNN is quantified through experimentation that exploits standard data already used in fuzzy modeling. The obtained experimental results reveal that the proposed networks exhibit high accuracy and generalization capabilities in comparison to other similar fuzzy models.
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A very important issue faced by researchers and practitioners who use industrial and research databases is incompleteness of data, usually in terms of missing or erroneous values. While some of data analysis algorithms can work with incomplete data, a large portion of them require complete data. Therefore, different strategies, such as deletion of incomplete examples, and imputation (filling) of missing values through variety of statistical and machine learning (ML) procedures, are developed to preprocess the incomplete data. This study concentrates on performing experimental analysis of several algorithms for imputation of missing values, which range from simple statistical algorithms like mean and hot deck imputation to imputation algorithms that work based on application of inductive ML algorithms. Three major families of ML algorithms, such as probabilistic algorithms (e.g. Naive Bayes), decision tree algorithms (e.g. C4.5), and decision rule algorithms (e.g. CLIP4), are used to implement the ML based imputation algorithms. The analysis is carried out using a comprehensive range of databases, for which missing values were introduced randomly. The goal of this paper is to provide general guidelines on selection of suitable data imputation algorithms based on characteristics of the data. The guidelines are developed by performing a comprehensive experimental comparison of performance of different data imputation algorithms.
