Abstract
Fuzzy transform is a technique applied to approximate a function of one or more variables applied by researchers in various image and data analysis. In this work we present a summary of a fuzzy transform method proposed in recent years in different data mining disciplines, such as the detection of relationships between features and the extraction of association rules, time series analysis, data classification. After having given the definition of the concept of Fuzzy Transform in one or more dimensions in which the constraint of sufficient data density with respect to fuzzy partitions is also explored, the data analysis approaches recently proposed in the literature based on the use of the Fuzzy Transform are analyzed. In particular, the strategies adopted in these approaches for managing the constraint of sufficient data density and the performance results obtained, compared with those measured by adopting other methods in the literature, are explored. The last section is dedicated to final considerations and future scenarios for using the Fuzzy Transform for the analysis of massive and high-dimensional data.
Highlights
This paper presents a summary of the data analysis techniques proposed in the literature based on the use of the F-transform in one or more dimensions
We initially presented the definition of one-dimensional direct and inverse F-transform, showing how it can be used to approximate a continuous function on a real interval
We extended this concept to the multi-dimensional F-transform, showing how it can be used in regression analysis
Summary
Fuzzy Transform (for short, F-transform) [1,2] is a recent soft computing approximation technique, successfully used in numerous applications in image and data analysis (see, e.g., [3] for an in-depth discussion on this matter). The aim of this paper is to provide an in-depth overview of soft computing data analysis techniques based on the use of the F-transform proposed in the literature. We will discuss the techniques proposed in the literature that employ the direct and inverse zero-order F-transform in data mining problems, such as dependencies between attributes, time series analysis and data classification, analyzing their critical points and performance benefits. F-transform techniques were initially applied in image analysis in which the constraint of sufficient density described in Section 2 is always respected. A list with descriptions of all acronyms and abbreviations in the text is given in Appendix A
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