Data granulation by the principles of uncertainty

Researches in granular modeling produced a variety of mathematical models, such as intervals, (higher-order) fuzzy sets, rough sets, and shadowed sets, which are all suitable to characterize the so-called information granules. Modeling of the input data uncertainty is recognized as a crucial aspect in information granulation. Moreover, the uncertainty is a well-studied concept in many mathematical settings, such as those of probability theory, fuzzy set theory, and possibility theory. This fact suggests that an appropriate quantification of the uncertainty expressed by the information granule model could be used to define an invariant property, to be exploited in practical situations of information granulation. In this perspective, a procedure of information granulation is effective if the uncertainty conveyed by the synthesized information granule is in a monotonically increasing relation with the uncertainty of the input data. In this paper, we present a data granulation framework that elaborates over the principles of uncertainty introduced by Klir. Being the uncertainty a mesoscopic descriptor of systems and data, it is possible to apply such principles regardless of the input data type and the specific mathematical setting adopted for the information granules. The proposed framework is conceived (i) to offer a guideline for the synthesis of information granules and (ii) to build a groundwork to compare and quantitatively judge over different data granulation procedures. To provide a suitable case study, we introduce a new data granulation technique based on the minimum sum of distances, which is designed to generate type-2 fuzzy sets. We analyze the procedure by performing different experiments on two distinct data types: feature vectors and labeled graphs. Results show that the uncertainty of the input data is suitably conveyed by the generated type-2 fuzzy set models.Comment: 16 pages, 9 figures, 52 reference

A shadowing problem in the detection of overlapping communities: lifting the resolution limit through a cascading procedure

Community detection is the process of assigning nodes and links in significant communities (e.g. clusters, function modules) and its development has led to a better understanding of complex networks. When applied to sizable networks, we argue that most detection algorithms correctly identify prominent communities, but fail to do so across multiple scales. As a result, a significant fraction of the network is left uncharted. We show that this problem stems from larger or denser communities overshadowing smaller or sparser ones, and that this effect accounts for most of the undetected communities and unassigned links. We propose a generic cascading approach to community detection that circumvents the problem. Using real and artificial network datasets with three widely used community detection algorithms, we show how a simple cascading procedure allows for the detection of the missing communities. This work highlights a new detection limit of community structure, and we hope that our approach can inspire better community detection algorithms.Comment: 14 pages, 12 figures + supporting information (5 pages, 6 tables, 3 figures

Informational Paradigm, management of uncertainty and theoretical formalisms in the clustering framework: A review

Fifty years have gone by since the publication of the first paper on clustering based on fuzzy sets theory. In 1965, L.A. Zadeh had published “Fuzzy Sets” [335]. After only one year, the first effects of this seminal paper began to emerge, with the pioneering paper on clustering by Bellman, Kalaba, Zadeh [33], in which they proposed a prototypal of clustering algorithm based on the fuzzy sets theory

Fusion of aerial images and sensor data from a ground vehicle for improved semantic mapping

This work investigates the use of semantic information to link ground level occupancy maps and aerial images. A ground level semantic map, which shows open ground and indicates the probability of cells being occupied by walls of buildings, is obtained by a mobile robot equipped with an omnidirectional camera, GPS and a laser range finder. This semantic information is used for local and global segmentation of an aerial image. The result is a map where the semantic information has been extended beyond the range of the robot sensors and predicts where the mobile robot can find buildings and potentially driveable ground

IMPROVING UNDERSTANDABILITY AND UNCERTAINTY MODELING OF DATA USING FUZZY LOGIC SYSTEMS

The need for automation, optimality and efficiency has made modern day control and monitoring systems extremely complex and data abundant. However, the complexity of the systems and the abundance of raw data has reduced the understandability and interpretability of data which results in a reduced state awareness of the system. Furthermore, different levels of uncertainty introduced by sensors and actuators make interpreting and accurately manipulating systems difficult. Classical mathematical methods lack the capability to capture human knowledge and increase understandability while modeling such uncertainty. Fuzzy Logic has been shown to alleviate both these problems by introducing logic based on vague terms that rely on human understandable terms. The use of linguistic terms and simple consequential rules increase the understandability of system behavior as well as data. Use of vague terms and modeling data from non-discrete prototypes enables modeling of uncertainty. However, due to recent trends, the primary research of fuzzy logic have been diverged from the basic concept of understandability. Furthermore, high computational costs to achieve robust uncertainty modeling have led to restricted use of such fuzzy systems in real-world applications. Thus, the goal of this dissertation is to present algorithms and techniques that improve understandability and uncertainty modeling using Fuzzy Logic Systems. In order to achieve this goal, this dissertation presents the following major contributions: 1) a novel methodology for generating Fuzzy Membership Functions based on understandability, 2) Linguistic Summarization of data using if-then type consequential rules, and 3) novel Shadowed Type-2 Fuzzy Logic Systems for uncertainty modeling. Finally, these presented techniques are applied to real world systems and data to exemplify their relevance and usage