Approximation operators via TD-matroids on two sets

Rough set theory is an extension of set theory with two additional unary set-theoretic operators known as approximation in order to extract information and knowledge. It needs the basic, or say definable, knowledge to approximate the undefinable knowledge in a knowledge space using the pair of approximation operators. Many existed approximation operators are expressed with unary form. How to mine the knowledge which is asked by binary form with rough set has received less research attention, though there are strong needs to reveal the answer for this challenging problem. There exist many information with matroid constraints since matroid provides a platform for combinatorial algorithms especially greedy algorithm. Hence, it is necessary to consider a matroidal structure on two sets no matter the two sets are the same or not. In this paper, we investigate the construction of approximation operators expressed by binary form with matroid theory, and the constructions of matroidal structure aided by a pair of approximation operators expressed by binary form.

First, we provide a kind of matroidal structure—TD-matroid defined on two sets as a generalization of Whitney classical matroid.

Second, we introduce this new matroidal construction to rough set and construct a pair of approximation operators expressed with binary form.

Third, using the existed pair of approximation operators expressed with binary form, we build up two concrete TD-matroids.

Fourth, for TD-matroid and the approximation operators expressed by binary form on two sets, we seek out their properties with aspect of posets, respectively.

Through the paper, we use some biological examples to explain and test the correct of obtained results. In summary, this paper provides a new approach to research rough set theory and matroid theory on two sets, and to study on their applications each other.

Granularity and Entropy of Intuitionistic Fuzzy Information and Their Applications

A granular structure of intuitionistic fuzzy (IF) information presents simultaneously the similarity and diversity of samples. However, this structural representation has rarely displayed its technical capability in data mining and information processing due to the lack of suitable constructive methods and semantic interpretation for IF information with regard to real data. To pursue better performance of the IF-based technique in real-world data mining, in this article, we examine information granularity, information entropy of IF granular structures, and their applications to data reduction of IF information systems. First, several types of partial-order relations at different hierarchical levels are defined to reveal the granularity of IF granular structures. Second, the granularity invariance between different IF granular structures is characterized by using relational mappings. Third, Shannon's entropies are generalized to IF entropies and their relationships with the partial-order relations are addressed. Based on the theoretical analysis above, the significance of intuitionistic attributes using the information measures is then introduced and the information-preserving algorithm for data reduction of IF information systems is constructed. Finally, by inducing substantial IF relations from public datasets that take both the similarity/diversity between the samples from the same/different classes into account, a collection of numerical experiments is conducted to confirm the performance of the proposed technique.

An Efficient Alert Aggregation Method Based on Conditional Rough Entropy and Knowledge Granularity

With the emergence of network security issues, various security devices that generate a large number of logs and alerts are widely used. This paper proposes an alert aggregation scheme that is based on conditional rough entropy and knowledge granularity to solve the problem of repetitive and redundant alert information in network security devices. Firstly, we use conditional rough entropy and knowledge granularity to determine the attribute weights. This method can determine the different important attributes and their weights for different types of attacks. We can calculate the similarity value of two alerts by weighting based on the results of attribute weighting. Subsequently, the sliding time window method is used to aggregate the alerts whose similarity value is larger than a threshold, which is set to reduce the redundant alerts. Finally, the proposed scheme is applied to the CIC-IDS 2018 dataset and the DARPA 98 dataset. The experimental results show that this method can effectively reduce the redundant alerts and improve the efficiency of data processing, thus providing accurate and concise data for the next stage of alert fusion and analysis.

Multi-Granulation Picture Hesitant Fuzzy Rough Sets

We lay the theoretical foundations of a novel model, termed picture hesitant fuzzy rough sets, based on picture hesitant fuzzy relations. We also combine this notion with the ideas of multi-granulation rough sets. As a consequence, a new multi-granulation rough set model on two universes, termed a multi-granulation picture hesitant fuzzy rough set, is developed. When the universes coincide or play a symmetric role, the concept assumes the standard format. In this context, we put forward two new classes of multi-granulation picture hesitant fuzzy rough sets, namely, the optimistic and pessimistic multi-granulation picture hesitant fuzzy rough sets. Further, we also investigate the relationships among these two concepts and picture hesitant fuzzy rough sets.

Clustering Homogeneous Granular Data: Formation and Evaluation

In this paper, we develop a comprehensive conceptual and algorithmic framework to cope with a problem of clustering homogeneous information granules. While there have been several approaches to coping with granular (viz. non-numeric) data, the origin of granular data themselves considered there is somewhat unclear and, as a consequence, the results of clustering start lacking some full-fledged interpretation. In this paper, we offer a holistic view at clustering information granules and an evaluation of the results of clustering. We start with a process of forming information granules with the use of the principle of justifiable granularity (PJG). With this regard, we discuss a number of parameters used in this development of information granules as well as quantify the quality of the granules produced in this manner. In the sequel, Fuzzy C -Means is applied to cluster the derived information granules, which are represented in a parametric manner and associated with weights resulting from the usage of the PJG. The quality of clustering results is evaluated through the use of the reconstruction criterion (quantifying the concept of information granulation and degranulation). A suite of experiments using synthetic and publicly available datasets is reported to quantify the performance of the proposed approach and highlight its key features.

Lower Approximation Reduction Based on Discernibility Information Tree in Inconsistent Ordered Decision Information Systems

Attribute reduction is an important topic in the research of rough set theory, and it has been widely used in many aspects. Reduction based on an identifiable matrix is a common method, but a lot of space is occupied by repetitive and redundant identifiable attribute sets. Therefore, a new method for attribute reduction is proposed, which compresses and stores the identifiable attribute set by a discernibility information tree. In this paper, the discernibility information tree based on a lower approximation identifiable matrix is constructed in an inconsistent decision information system under dominance relations. Then, combining the lower approximation function with the discernibility information tree, a complete algorithm of lower approximation reduction based on the discernibility information tree is established. Finally, the rationality and correctness of this method are verified by an example.

Granular clustering of de novo protein models

Motivation

Modern algorithms for de novo prediction of protein structures typically output multiple full-length models (decoys) rather than a single solution. Subsequent clustering of such decoys is used both to gauge the success of the modelling and to decide on the most native-like conformation. At the same time, partial protein models are sufficient for some applications such as crystallographic phasing by molecular replacement (MR) in particular, provided these models represent a certain part of the target structure with reasonable accuracy.

Results

Here we propose a novel clustering algorithm that natively operates in the space of partial models through an approach known as granular clustering (GC). The algorithm is based on growing local similarities found in a pool of initial decoys. We demonstrate that the resulting clusters of partial models provide a substantially more accurate structural detail on the target protein than those obtained upon a global alignment of decoys. As the result, the partial models output by our GC algorithm are also much more effective towards the MR procedure, compared to the models produced by existing software.

Availability and Implementation

The source code is freely available at https://github.com/biocryst/gc

Contact

sergei.strelkov@kuleuven.be

Suplementary Information

Supplementary data are available at Bioinformatics online.

GrCS: Granular Computing-Based Crowd Segmentation

Crowd segmentation is important in serving as the basis for a wide range of crowd analysis tasks such as density estimation and behavior understanding. However, due to interocclusions, perspective distortion, clutter background, and random crowd distribution, localizing crowd segments is technically a very challenging task. This paper proposes a novel crowd segmentation framework-based on granular computing (GrCS) to enable the problem of crowd segmentation to be conceptualized at different levels of granularity, and to map problems into computationally tractable subproblems. It shows that by exploiting the correlation among pixel granules, we are able to aggregate structurally similar pixels into meaningful atomic structure granules. This is useful in outlining natural boundaries between crowd and background (i.e., noncrowd) regions. From the structure granules, we infer the crowd and background regions by granular information classification. GrCS is scene-independent and can be applied effectively to crowd scenes with a variety of physical layout and crowdedness. Extensive experiments have been conducted on hundreds of real and synthetic crowd scenes. The results demonstrate that by exploiting the correlation among granules, we can outline the natural boundaries of structurally similar crowd and background regions necessary for crowd segmentation.

Granular Computing Approach to Two-Way Learning Based on Formal Concept Analysis in Fuzzy Datasets

The main task of granular computing (GrC) is about representing, constructing, and processing information granules. Information granules are formalized in many different approaches. Different formal approaches emphasize the same fundamental facet in different ways. In this paper, we propose a novel GrC method of machine learning by using formal concept description of information granules. Based on information granules, the model and mechanism of two-way learning system is constructed in fuzzy datasets. It is addressed about how to train arbitrary fuzzy information granules to become necessary, sufficient, and necessary and sufficient fuzzy information granules. Moreover, an algorithm of the presented approach is established, and the complexity of the algorithm is analyzed carefully. Finally, to interpret and help understand the theories and algorithm, a real-life case study is considered and experimental evaluation is performed by five datasets from the University of California-Irvine, which is valuable for applying these theories to deal with practical issues.

Concept learning via granular computing: A cognitive viewpoint

Concepts are the most fundamental units of cognition in philosophy and how to learn concepts from various aspects in the real world is the main concern within the domain of conceptual knowledge presentation and processing. In order to improve efficiency and flexibility of concept learning, in this paper we discuss concept learning via granular computing from the point of view of cognitive computing. More precisely, cognitive mechanism of forming concepts is analyzed based on the principles from philosophy and cognitive psychology, including how to model concept-forming cognitive operators, define cognitive concepts and establish cognitive concept structure. Granular computing is then combined with the cognitive concept structure to improve efficiency of concept learning. Furthermore, we put forward a cognitive computing system which is the initial environment to learn composite concepts and can integrate past experiences into itself for enhancing flexibility of concept learning. Also, we investigate cognitive processes whose aims are to deal with the problem of learning one exact or two approximate cognitive concepts from a given object set, attribute set or pair of object and attribute sets.

From principal curves to granular principal curves

Principal curves arising as an essential construct in dimensionality reduction and data analysis have recently attracted much attention from theoretical as well as practical perspective. In many real-world situations, however, the efficiency of existing principal curves algorithms is often arguable, in particular when dealing with massive data owing to the associated high computational complexity. A certain drawback of these constructs stems from the fact that in several applications principal curves cannot fully capture some essential problem-oriented facets of the data dealing with width, aspect ratio, width change, etc. Information granulation is a powerful tool supporting processing and interpreting massive data. In this paper, invoking the underlying ideas of information granulation, we propose a granular principal curves approach, regarded as an extension of principal curves algorithms, to improve efficiency and achieve a sound accuracy-efficiency tradeoff. First, large amounts of numerical data are granulated into C intervals-information granules developed with the use of fuzzy C-means clustering and the two criteria of information granulation, which significantly reduce the amount of data to be processed at the later phase of the overall design. Granular principal curves are then constructed by determining the upper and the lower bounds of the interval data. Finally, we develop an objective function using the criteria of information confidence and specificity to evaluate the granular output formed by the principal curves. We also optimize the granular principal curves by adjusting the level of information granularity (the number of clusters), which is realized with the aid of the particle swarm optimization. A number of numeric studies completed for synthetic and real-world datasets provide a useful quantifiable insight into the effectiveness of the proposed algorithm.

Granular computing: perspectives and challenges

Granular computing, as a new and rapidly growing paradigm of information processing, has attracted many researchers and practitioners. Granular computing is an umbrella term to cover any theories, methodologies, techniques, and tools that make use of information granules in complex problem solving. The aim of this paper is to review foundations and schools of research and to elaborate on current developments in granular computing research. We first review some basic notions of granular computing. Classification and descriptions of various schools of research in granular computing are given. We also present and identify some research directions in granular computing.

Statistical discovery of site inter-dependencies in sub-molecular hierarchical protein structuring

BACKGROUND

Much progress has been made in understanding the 3D structure of proteins using methods such as NMR and X-ray crystallography. The resulting 3D structures are extremely informative, but do not always reveal which sites and residues within the structure are of special importance. Recently, there are indications that multiple-residue, sub-domain structural relationships within the larger 3D consensus structure of a protein can be inferred from the analysis of the multiple sequence alignment data of a protein family. These intra-dependent clusters of associated sites are used to indicate hierarchical inter-residue relationships within the 3D structure. To reveal the patterns of associations among individual amino acids or sub-domain components within the structure, we apply a k-modes attribute (aligned site) clustering algorithm to the ubiquitin and transthyretin families in order to discover associations among groups of sites within the multiple sequence alignment. We then observe what these associations imply within the 3D structure of these two protein families.

RESULTS

The k-modes site clustering algorithm we developed maximizes the intra-group interdependencies based on a normalized mutual information measure. The clusters formed correspond to sub-structural components or binding and interface locations. Applying this data-directed method to the ubiquitin and transthyretin protein family multiple sequence alignments as a test bed, we located numerous interesting associations of interdependent sites. These clusters were then arranged into cluster tree diagrams which revealed four structural sub-domains within the single domain structure of ubiquitin and a single large sub-domain within transthyretin associated with the interface among transthyretin monomers. In addition, several clusters of mutually interdependent sites were discovered for each protein family, each of which appear to play an important role in the molecular structure and/or function.

CONCLUSIONS

Our results demonstrate that the method we present here using a k-modes site clustering algorithm based on interdependency evaluation among sites obtained from a sequence alignment of homologous proteins can provide significant insights into the complex, hierarchical inter-residue structural relationships within the 3D structure of a protein family.

A granular reflex fuzzy min-max neural network for classification

Granular data classification and clustering is an upcoming and important issue in the field of pattern recognition. Conventionally, computing is thought to be manipulation of numbers or symbols. However, human recognition capabilities are based on ability to process nonnumeric clumps of information (information granules) in addition to individual numeric values. This paper proposes a granular neural network (GNN) called granular reflex fuzzy min-max neural network (GrRFMN) which can learn and classify granular data. GrRFMN uses hyperbox fuzzy set to represent granular data. Its architecture consists of a reflex mechanism inspired from human brain to handle class overlaps. The network can be trained online using granular or point data. The neuron activation functions in GrRFMN are designed to tackle data of different granularity (size). This paper also addresses an issue to granulate the training data and learn from it. It is observed that such a preprocessing of data can improve performance of a classifier. Experimental results on real data sets show that the proposed GrRFMN can classify granules of different granularity more correctly. Results are compared with general fuzzy min-max neural network (GFMN) proposed by Gabrys and Bargiela and with some classical methods.