Characteristic of partition-circuit matroid through approximation number

Rough set theory is a useful tool to deal with uncertain, granular and incomplete knowledge in information systems. And it is based on equivalence relations or partitions. Matroid theory is a structure that generalizes linear independence in vector spaces, and has a variety of applications in many fields. In this paper, we propose a new type of matroids, namely, partition-circuit matroids, which are induced by partitions. Firstly, a partition satisfies circuit axioms in matroid theory, then it can induce a matroid which is called a partition-circuit matroid. A partition and an equivalence relation on the same universe are one-to-one corresponding, then some characteristics of partition-circuit matroids are studied through rough sets. Secondly, similar to the upper approximation number which is proposed by Wang and Zhu, we define the lower approximation number. Some characteristics of partition-circuit matroids and the dual matroids of them are investigated through the lower approximation number and the upper approximation number.Comment: 12 page

An Application on Text Classification Based on Granular Computing

Machine learning is the key to text classification, a granular computing approach to machine learning is applied to learning classification rules by considering the two basic issues: concept formation and concept relationships identification. In this paper, we concentrate on the selection of a single granule in each step to construct a granule network. A classification rule induction method is proposed

Protein Local Tertiary Structure Prediction by Super Granule Support Vector Machines with Chou-Fasman Parameter

Prediction of a protein's tertiary structure from its sequence information alone is considered a major task in modern computational biology.  In order to closer the gap between protein sequences to its tertiary structures, we discuss the correlation between protein sequence and local tertiary structure information in this paper.  The strategy we used in this work is predict small portions (local) of protein tertiary structure with high confidence from conserved protein sequences, which are called “protein sequence motifs”. 799 protein sequence motifs that transcend protein family boundaries were obtained from our previous work.  The prediction accuracy generated from the best group of protein sequence motifs always keep higher than 90% while more than 8% of the independent testing data segments are predicted. Since the most meaningful result published in latest publication is merely 70.02% accuracy under the coverage of 4.45%, the research results achieved in this paper are obviously outperformed. Besides, we also set up a stricter evaluation to our prediction to further understand the relation between protein sequence motifs and tertiary structure predictions.  The results suggest that the hidden sequence-to-structure relationship can be uncovered using the Super Granule SVM Model with the Chou-Fasman Parameter.  With the high local tertiary structure prediction accuracy provided in this article, the hidden relation between protein primary sequences and their 3D structure are uncovered considerably

Uncertainty quantification of granular computing‑neural network model for prediction of pollutant longitudinal dispersion coefficient in aquatic streams

Discharge of pollution loads into natural water systems remains a global challenge that threatens water and food supply, as well as endangering ecosystem services. Natural rehabilitation of contaminated streams is mainly influenced by the longitudinal dispersion coefficient, or the rate of longitudinal dispersion (Dx), a key parameter with large spatiotemporal fluctuations that characterizes pollution transport. The large uncertainty in estimation of Dx in streams limits the water quality assessment in natural streams and design of water quality enhancement strategies. This study develops an artificial intelligence-based predictive model, coupling granular computing and neural network models (GrC-ANN) to provide robust estimation of Dx and its uncertainty for a range of flow-geometric conditions with high spatiotemporal variability. Uncertainty analysis of Dx estimated from the proposed GrC-ANN model was performed by alteration of the training data used to tune the model. Modified bootstrap method was employed to generate different training patterns through resampling from a global database of tracer experiments in streams with 503 datapoints. Comparison between the Dx values estimated by GrC-ANN to those determined from tracer measurements shows the appropriateness and robustness of the proposed method in determining the rate of longitudinal dispersion. The GrC-ANN model with the narrowest bandwidth of estimated uncertainty (bandwidth-factor = 0.56) that brackets the highest percentage of true Dx data (i.e., 100%) is the best model to compute Dx in streams. Considering the significant inherent uncertainty reported in the previous Dx models, the GrC-ANN model developed in this study is shown to have a robust performance for evaluating pollutant mixing (Dx) in turbulent environmental flow systems

Fuzzy-Granular Based Data Mining for Effective Decision Support in Biomedical Applications

Due to complexity of biomedical problems, adaptive and intelligent knowledge discovery and data mining systems are highly needed to help humans to understand the inherent mechanism of diseases. For biomedical classification problems, typically it is impossible to build a perfect classifier with 100% prediction accuracy. Hence a more realistic target is to build an effective Decision Support System (DSS). In this dissertation, a novel adaptive Fuzzy Association Rules (FARs) mining algorithm, named FARM-DS, is proposed to build such a DSS for binary classification problems in the biomedical domain. Empirical studies show that FARM-DS is competitive to state-of-the-art classifiers in terms of prediction accuracy. More importantly, FARs can provide strong decision support on disease diagnoses due to their easy interpretability. This dissertation also proposes a fuzzy-granular method to select informative and discriminative genes from huge microarray gene expression data. With fuzzy granulation, information loss in the process of gene selection is decreased. As a result, more informative genes for cancer classification are selected and more accurate classifiers can be modeled. Empirical studies show that the proposed method is more accurate than traditional algorithms for cancer classification. And hence we expect that genes being selected can be more helpful for further biological studies

Study of First Local Maximum of Confidence in Mining Sequential Patterns

Sequential data mining is increasingly important in many domains. WinMiner is a constraint-based algorithm to retrieve frequent episodes and association rules of high confidence and to search first local maximum (FLM) - rules. An algorithm for mining FLM rules from sequential dataset is implemented and is applied to several datasets of different origins. The experiments show that FLM rules are rare in randomly generated dataset and loosening the mining constraints leads to the increase of numbers of FLM rules. Correlations or dependencies among the constituent events introduced into the randomly generated dataset can dramatically increase numbers of FLM rules.Computer Science Departmen

Granular Support Vector Machines Based on Granular Computing, Soft Computing and Statistical Learning

With emergence of biomedical informatics, Web intelligence, and E-business, new challenges are coming for knowledge discovery and data mining modeling problems. In this dissertation work, a framework named Granular Support Vector Machines (GSVM) is proposed to systematically and formally combine statistical learning theory, granular computing theory and soft computing theory to address challenging predictive data modeling problems effectively and/or efficiently, with specific focus on binary classification problems. In general, GSVM works in 3 steps. Step 1 is granulation to build a sequence of information granules from the original dataset or from the original feature space. Step 2 is modeling Support Vector Machines (SVM) in some of these information granules when necessary. Finally, step 3 is aggregation to consolidate information in these granules at suitable abstract level. A good granulation method to find suitable granules is crucial for modeling a good GSVM. Under this framework, many different granulation algorithms including the GSVM-CMW (cumulative margin width) algorithm, the GSVM-AR (association rule mining) algorithm, a family of GSVM-RFE (recursive feature elimination) algorithms, the GSVM-DC (data cleaning) algorithm and the GSVM-RU (repetitive undersampling) algorithm are designed for binary classification problems with different characteristics. The empirical studies in biomedical domain and many other application domains demonstrate that the framework is promising. As a preliminary step, this dissertation work will be extended in the future to build a Granular Computing based Predictive Data Modeling framework (GrC-PDM) with which we can create hybrid adaptive intelligent data mining systems for high quality prediction

Innovative Algorithms and Evaluation Methods for Biological Motif Finding

Biological motifs are defined as overly recurring sub-patterns in biological systems. Sequence motifs and network motifs are the examples of biological motifs. Due to the wide range of applications, many algorithms and computational tools have been developed for efficient search for biological motifs. Therefore, there are more computationally derived motifs than experimentally validated motifs, and how to validate the biological significance of the ‘candidate motifs’ becomes an important question. Some of sequence motifs are verified by their structural similarities or their functional roles in DNA or protein sequences, and stored in databases. However, biological role of network motifs is still invalidated and currently no databases exist for this purpose. In this thesis, we focus not only on the computational efficiency but also on the biological meanings of the motifs. We provide an efficient way to incorporate biological information with clustering analysis methods: For example, a sparse nonnegative matrix factorization (SNMF) method is used with Chou-Fasman parameters for the protein motif finding. Biological network motifs are searched by various clustering algorithms with Gene ontology (GO) information. Experimental results show that the algorithms perform better than existing algorithms by producing a larger number of high-quality of biological motifs. In addition, we apply biological network motifs for the discovery of essential proteins. Essential proteins are defined as a minimum set of proteins which are vital for development to a fertile adult and in a cellular life in an organism. We design a new centrality algorithm with biological network motifs, named MCGO, and score proteins in a protein-protein interaction (PPI) network to find essential proteins. MCGO is also combined with other centrality measures to predict essential proteins using machine learning techniques. We have three contributions to the study of biological motifs through this thesis; 1) Clustering analysis is efficiently used in this work and biological information is easily integrated with the analysis; 2) We focus more on the biological meanings of motifs by adding biological knowledge in the algorithms and by suggesting biologically related evaluation methods. 3) Biological network motifs are successfully applied to a practical application of prediction of essential proteins