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

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

Hematological image analysis for acute lymphoblastic leukemia detection and classification

Microscopic analysis of peripheral blood smear is a critical step in detection of leukemia.However, this type of light microscopic assessment is time consuming, inherently subjective, and is governed by hematopathologists clinical acumen and experience. To circumvent such problems, an efficient computer aided methodology for quantitative analysis of peripheral blood samples is required to be developed. In this thesis, efforts are therefore made to devise methodologies for automated detection and subclassification of Acute Lymphoblastic Leukemia (ALL) using image processing and machine learning methods.Choice of appropriate segmentation scheme plays a vital role in the automated disease recognition process. Accordingly to segment the normal mature lymphocyte and malignant lymphoblast images into constituent morphological regions novel schemes have been proposed. In order to make the proposed schemes viable from a practical and real–time stand point, the segmentation problem is addressed in both supervised and unsupervised framework. These proposed methods are based on neural network,feature space clustering, and Markov random field modeling, where the segmentation problem is formulated as pixel classification, pixel clustering, and pixel labeling problem respectively. A comprehensive validation analysis is presented to evaluate the performance of four proposed lymphocyte image segmentation schemes against manual segmentation results provided by a panel of hematopathologists. It is observed that morphological components of normal and malignant lymphocytes differ significantly. To automatically recognize lymphoblasts and detect ALL in peripheral blood samples, an efficient methodology is proposed.Morphological, textural and color features are extracted from the segmented nucleus and cytoplasm regions of the lymphocyte images. An ensemble of classifiers represented as EOC3 comprising of three classifiers shows highest classification accuracy of 94.73% in comparison to individual members. The subclassification of ALL based on French–American–British (FAB) and World Health Organization (WHO) criteria is essential for prognosis and treatment planning. Accordingly two independent methodologies are proposed for automated classification of malignant lymphocyte (lymphoblast) images based on morphology and phenotype. These methods include lymphoblast image segmentation, nucleus and cytoplasm feature extraction, and efficient classification

On Information Granulation via Data Filtering for Granular Computing-Based Pattern Recognition: A Graph Embedding Case Study

Granular Computing is a powerful information processing paradigm, particularly useful for the synthesis of pattern recognition systems in structured domains (e.g., graphs or sequences). According to this paradigm, granules of information play the pivotal role of describing the underlying (possibly complex) process, starting from the available data. Under a pattern recognition viewpoint, granules of information can be exploited for the synthesis of semantically sound embedding spaces, where common supervised or unsupervised problems can be solved via standard machine learning algorithms. In this companion paper, we follow our previous paper (Martino et al. in Algorithms 15(5):148, 2022) in the context of comparing different strategies for the automatic synthesis of information granules in the context of graph classification. These strategies mainly differ on the specific topology adopted for subgraphs considered as candidate information granules and the possibility of using or neglecting the ground-truth class labels in the granulation process and, conversely, to our previous work, we employ a filtering-based approach for the synthesis of information granules instead of a clustering-based one. Computational results on 6 open-access data sets corroborate the robustness of our filtering-based approach with respect to data stratification, if compared to a clustering-based granulation stage

Fuzzy Techniques for Decision Making 2018

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches

An Intelligent Decision Support System for Leukaemia Diagnosis using Microscopic Blood Images

This research proposes an intelligent decision support system for acute lymphoblastic leukaemia diagnosis from microscopic blood images. A novel clustering algorithm with stimulating discriminant measures (SDM) of both within- and between-cluster scatter variances is proposed to produce robust segmentation of nucleus and cytoplasm of lymphocytes/lymphoblasts. Specifically, the proposed between-cluster evaluation is formulated based on the trade-off of several between-cluster measures of well-known feature extraction methods. The SDM measures are used in conjuction with Genetic Algorithm for clustering nucleus, cytoplasm, and background regions. Subsequently, a total of eighty features consisting of shape, texture, and colour information of the nucleus and cytoplasm subimages are extracted. A number of classifiers (multi-layer perceptron, Support Vector Machine (SVM) and Dempster-Shafer ensemble) are employed for lymphocyte/lymphoblast classification. Evaluated with the ALL-IDB2 database, the proposed SDM-based clustering overcomes the shortcomings of Fuzzy C-means which focuses purely on within-cluster scatter variance. It also outperforms Linear Discriminant Analysis and Fuzzy Compactness and Separation for nucleus-cytoplasm separation. The overall system achieves superior recognition rates of 96.72% and 96.67% accuracies using bootstrapping and 10-fold cross validation with Dempster-Shafer and SVM, respectively. The results also compare favourably with those reported in the literature, indicating the usefulness of the proposed SDM-based clustering method

Granular Fuzzy Regression Domain Adaptation in Takagi-Sugeno Fuzzy Models

© 1993-2012 IEEE. In classical data-driven machine learning methods, massive amounts of labeled data are required to build a high-performance prediction model. However, the amount of labeled data in many real-world applications is insufficient, so establishing a prediction model is impossible. Transfer learning has recently emerged as a solution to this problem. It exploits the knowledge accumulated in auxiliary domains to help construct prediction models in a target domain with inadequate training data. Most existing transfer learning methods solve classification tasks; only a few are devoted to regression problems. In addition, the current methods ignore the inherent phenomenon of information granularity in transfer learning. In this study, granular computing techniques are applied to transfer learning. Three granular fuzzy regression domain adaptation methods to determine the estimated values for a regression target are proposed to address three challenging cases in domain adaptation. The proposed granular fuzzy regression domain adaptation methods change the input and/or output space of the source domain's model using space transformation, so that the fuzzy rules are more compatible with the target data. Experiments on synthetic and real-world datasets validate the effectiveness of the proposed methods

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

The application of remote sensing to identify and measure sealed soil and vegetated surfaces in urban environments

Soil is an important non-renewable source. Its protection and allocation is critical to sustainable development goals. Urban development presents an important drive of soil loss due to sealing over by buildings, pavements and transport infrastructure. Monitoring sealed soil surfaces in urban environments is gaining increasing interest not only for scientific research studies but also for local planning and national authorities. The aim of this research was to investigate the extent to which automated classification methods can detect soil sealing in UK urban environments, by remote sensing. The objectives include development of object-based classification methods, using two types of earth observation data, and evaluation by comparison with manual aerial photo interpretation techniques. Four sample areas within the city of Cambridge were used for the development of an object-based classification model. The acquired data was a true-colour aerial photography (0.125 m resolution) and a QuickBird satellite imagery (2.8 multi-spectral resolution). The classification scheme included the following land cover classes: sealed surfaces, vegetated surfaces, trees, bare soil and rail tracks. Shadowed areas were also identified as an initial class and attempts were made to reclassify them into the actual land cover type. The accuracy of the thematic maps was determined by comparison with polygons derived from manual air-photo interpretation; the average overall accuracy was 84%. The creation of simple binary maps of sealed vs. vegetated surfaces resulted in a statistically significant accuracy increase to 92%. The integration of ancillary data (OS MasterMap) into the object-based model did not improve the performance of the model (overall accuracy of 91%). The use of satellite data in the object-based model gave an overall accuracy of 80%, a 7% decrease compared to the aerial photography. Future investigation will explore whether the integration of elevation data will aid to discriminate features such as trees from other vegetation types. The use of colour infrared aerial photography should also be tested. Finally, the application of the object- based classification model into a different study area would test its transferability