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The Black Hole Clustering (BHC) algorithm is a density-based partitional clustering method inspired by the Density-based Spatial Clustering of Applications with Noise (DBSCAN). It does not require the number of clusters nor the computation of the pair-wise distance matrix between the data points, making it faster than DBSCAN. Also, it only needs one parameter that is intuitively easier to set than the epsilon parameter of DBSCAN. However, BHC needs the allocation of the so-called black holes that have to be linearly independent, making the algorithm in its current version suitable only for two or three-dimensional data sets. In this paper, we propose a generalized version of the black hole clustering algorithm (GBHC) by introducing a novel black hole allocation procedure for higher-dimensional data spaces. Furthermore, the proposed method is data-independent, so we have to run it once to obtain the black hole positions for all finite-dimensional metric spaces. We performed extensive computational experiments to compare GBHC with DBSCAN. The results show that both algorithms obtain comparable clustering solutions. GBHC, however, outperforms DBSCAN in computational complexity and explainability. • We propose a novel method to place the black holes for high-dimensional data sets. • This method is called Generalized Black Hole Clustering and it is data-independent. • We run the new method once to get black hole positions in all finite metric spaces. • We compare the GBHC and DBSCAN algorithms using several validation measures. [ABSTRACT FROM AUTHOR]

• Three-way concept stability and its properties. • Algorithm for the computation of three-way concept stability. • A case study on natural language generation scenario. Three-way concept analysis (3WCA) has been an emerging and important methodology for knowledge discovery and data analysis. Particularly, 3WCA can efficiently characterize the information of "jointly possessed" and "jointly not possessed" compared to the classical formal concept only can describe common attributes owned by objects. This property, typical of 3WCA has a huge potential in the field of Natural Language Generation (NLG). However, the construction of a three-way concept lattice is proved as an NP-complete problem and even harder than the construction of conventional concept lattice. This could negatively affect the use of 3WCA for NLG in real contexts. Hence, it is necessary to prune the three-way concept lattice and extract more interesting three-way concepts for knowledge acquisition. To this end, this paper defines the stability of a three-way concept and analyzes the relevant properties. An efficient computational algorithm for calculating the stability of three-way concepts is developed and evaluated by an experiment. In addition, a case study on NLG is conducted for demonstrating the applicability of the proposed technique. [ABSTRACT FROM AUTHOR]

• A novel Particle swarm optimization based algorithm (PSO-GES), is introduced. • A guided exploration strategy in order to generate high-quality rules, is proposed. • A new fitness funtion for obtain the fitness value in a shorter runtime, is introduced. • PSO-GES uses a summary matrix with a smaller number of rows than the original database. • PSO-GES mines a set of better quality rules than the association rules mining algorithms compared. Association rule mining is one of the most important and active research areas in data mining. In the literature, several association rule miners have been proposed; among them, those based on particle swarm optimization (PSO) have reported the best results. However, these algorithms tend to prematurely fall into local solutions, avoiding a wide exploration that could produce even better results. In this paper, an algorithm based on PSO, called PSO-GES, for mining association rules using a Guided Exploration Strategy is introduced. Our experiments, over real-world transactional databases, show that our proposed algorithm mines better quality association rules than the most recent PSO-based algorithms for mining association rules of the state of the art. [ABSTRACT FROM AUTHOR]

• An algorithm for multi-core frequent itemsets mining in data streams is presented. • It is proposed a processing scheme which allows to process data streams transmitted at different rates. • The Gearman framework is used to implement the proposed multi-core processing algorithm. • Hashing and lexicographic order of received items are used for frequent itemsets mining in data streams. Data streams are modern data sources that are gaining attention as a consequence of their many practical applications (they can be found in data transmission, eCommerce, and intrusion detection system among others). Nevertheless, the efforts to obtain insights from data streams are limited due to their massive information volume and the time needed to process them. In this paper, a new approach for Frequent Itemsets Mining on data streams based on prefix trees which takes advantage of multi-core systems is proposed. This approach uses the Gearman framework as the interface for multi-core processing, and it allows to exploit their scalability efficiently. Experimental results show that the proposed method obtains the same patterns compared with similar approaches reported in the state-of-the-art and outperforms them concerning the processing time required. Also, it is proved that the proposed method is insensitive to variations in the support threshold value, and its efficiency depends on the size of the transactions and not on the size of the alphabet, which is a significant issue in other Frequent Itemsets Mining algorithms. [ABSTRACT FROM AUTHOR]

Abstract: Feature selection methods have been extensively applied in machine learning tasks, such as computer vision, pattern recognition, and data mining. These methods aim to identify a subset of the original features with high discriminating power. Among them, the feature selection technique for unsupervised tasks is more attractive since the cost to obtain the labels of the data and/or the information between classes is often high. On the other hand, the low-dimensional manifold of the “same” class data is usually revealed by considering the local invariance of the data structure, it may not be adequate to deal with unsupervised tasks where the class information is completely absent. In this paper, a novel feature selection method, called Minimum–maximum local structure information Laplacian Score (MMLS), is proposed to minimize the within-locality information (i.e., preserving the manifold structure of the “same” class data) and to maximize the between-locality information (i.e., maximizing the information between the manifold structures of the “different” class data) at the same time. The effectiveness of the proposed algorithm is demonstrated with experiments on classification and clustering. [Copyright &y& Elsevier]

Abstract: Similarity is the core problem of clustering. Clustering algorithms that are based on a certain, fixed type of similarity are not sufficient to explore complicated structures. In this paper, a constructing method for multiple similarity is proposed to deal with complicated structures of data sets. Multiple similarity derives from the local modification of the initial similarity, based on the feedback information of elementary clusters. Combined with the proposed algorithm, the repeated modifications of local similarity measurement generate a hierarchical clustering result. Some synthetic and real data sets are employed to exhibit the superiority of the new clustering algorithm. [Copyright &y& Elsevier]

Abstract: The present paper considers the problem of partitioning a dataset into a known number of clusters using the sum of squared errors criterion (SSE). A new clustering method, called DE-KM, which combines differential evolution algorithm (DE) with the well known K-means procedure is described. In the method, the K-means algorithm is used to fine-tune each candidate solution obtained by mutation and crossover operators of DE. Additionally, a reordering procedure which allows the evolutionary algorithm to tackle the redundant representation problem is proposed. The performance of the DE-KM clustering method is compared to the performance of differential evolution, global K-means method, genetic K-means algorithm and two variants of the K-means algorithm. The experimental results show that if the number of clusters K is sufficiently large, DE-KM obtains solutions with lower SSE values than the other five algorithms. [Copyright &y& Elsevier]

Abstract: Principal component analysis (PCA) is widely used in recently proposed manifold learning algorithms to provide approximate local tangent spaces. However, such approximations provided by PCA may be inaccurate when local neighborhoods of the data manifold do not lie in or close to a linear subspace. Furthermore, the approximated tangent spaces can not fit the change in data distribution density. In this paper, a new method is proposed for providing faithful approximations to the local tangent spaces of a data manifold, which is proved to be more accurate than PCA. With this new method, an improved local tangent space alignment (ILTSA) algorithm is developed, which can efficiently recover the geometric structure of data manifolds even in the case when data are sparse or non-uniformly distributed. Experimental results are presented to illustrate the better performance of ILTSA on both synthetic data and image data. [ABSTRACT FROM AUTHOR]

Abstract: It is desirable to find unusual data objects by Ramaswamy et al.’s distance-based outlier definition, because only a metric distance function between two objects is required. This definition does not need any neighborhood distance threshold required by many existing algorithms based on the definition of Knorr and Ng. Bay and Schwabacher proposed an efficient algorithm ORCA, which can give near linear time performance, for this task. To further reduce the running time, we propose in this paper two algorithms RC and RS using the following two techniques, respectively: (i) faster cutoff update, and (ii) space utilization after pruning. We tested RC, RS, and RCS (a hybrid approach combining both RC and RS) on several large and high-dimensional real data sets with millions of objects. The experiments show that the speed of RCS is as fast as 1.4–2.3 times that of ORCA, and the improvement of RCS is relatively insensitive to the increase in the data size. [Copyright &y& Elsevier]

Abstract: Rough set theory is one of the effective methods to feature selection, which can preserve the meaning of the features. The essence of rough set approach to feature selection is to find a subset of the original features. Since finding a minimal subset of the features is a NP-hard problem, it is necessary to investigate effective and efficient heuristic algorithms. Ant colony optimization (ACO) has been successfully applied to many difficult combinatorial problems like quadratic assignment, traveling salesman, scheduling, etc. It is particularly attractive for feature selection since there is no heuristic information that can guide search to the optimal minimal subset every time. However, ants can discover the best feature combinations as they traverse the graph. In this paper, we propose a new rough set approach to feature selection based on ACO, which adopts mutual information based feature significance as heuristic information. A novel feature selection algorithm is also given. Jensen and Shen proposed a ACO-based feature selection approach which starts from a random feature. Our approach starts from the feature core, which changes the complete graph to a smaller one. To verify the efficiency of our algorithm, experiments are carried out on some standard UCI datasets. The results demonstrate that our algorithm can provide efficient solution to find a minimal subset of the features. [Copyright &y& Elsevier]

Abstract: In real world situations, explanations for the same observations may be different depending on perceptions or contexts. They may change with time especially when concept drift occurs. This phenomenon incurs ambiguities. It is useful if an algorithm can learn to reflect ambiguities and select the best decision according to context or situation. Based on this viewpoint, we study the problem of deriving ambiguous decision trees from data streams to cope with concept drift. CVFDT (Concept-adapting Very Fast Decision Tree) is one of the most well-known streaming data mining methods that can learn decision trees incrementally. In this paper, we establish a method called ambiguous CVFDT (aCVFDT), which integrates ambiguities into CVFDT by exploring multiple options at each node whenever a node is to be split. When aCVFDT is used to make class predictions, it is guaranteed that the best and newest knowledge is used. When old concepts recur, aCVFDT can immediately relearn them by using the corresponding options recorded at each node. Furthermore, CVFDT does not automatically detect occurrences of concept drift and only scans trees periodically, whereas an automatic concept drift detecting mechanism is used in aCVFDT. In our experiments, hyperplane problem and two benchmark problems from the UCI KDD Archive, namely Network Intrusion and Forest CoverType, are used to validate the performance of aCVFDT. The experimental results show that aCVFDT obtains significantly improved results over traditional CVFDT. [Copyright &y& Elsevier]

Abstract: Catalog segmentation is an important issue in data mining in business from the microeconomic point of view. In catalog segmentation, an enterprise tries to develop k catalogs with r products that are sent to corresponding customers in order to maximize the overall number of catalog products purchased. In this paper, a novel model called catalog segmentation problem with double constraints (DCCSP) is presented. In this model, the interest constraint is minimized and the profit constraint is maximized so that the profit of products purchased by customers who have at least t interesting products in receiving catalogs is maximized. The complexity of the DCCSP is analyzed, and a DCCS algorithm to solve the optimization is proposed. The experimental results show that the proposed algorithm is efficient and can be used to solve the DCCSP effectively. [Copyright &y& Elsevier]

Univariate decision tree algorithms are widely used in data mining because (i) they are easy to learn (ii) when trained they can be expressed in rule based manner. In several applications mainly including data mining, the dataset to be learned is very large. In those cases it is highly desirable to construct univariate decision trees in reasonable time. This may be accomplished by parallelizing univariate decision tree algorithms. In this paper, we first present two different univariate decision tree algorithms C4.5 and univariate linear discriminant tree. We show how to parallelize these algorithms in three ways: (i) feature based; (ii) node based; (iii) data based manners. Experimental results show that performance of the parallelizations highly depend on the dataset and the node based parallelization demonstrate good speedups. [Copyright &y& Elsevier]

Abstract: While data mining algorithms are often designed to operate on centralized data, in practice data is often acquired and stored in a distributed manner. Centralization of such data before analysis may not be desirable, and often not possible due to a variety of real-life constraints such as security, privacy and communication costs. This paper presents a general framework for distributed clustering that takes into account privacy requirements. It is based on building probabilistic models of the data at each local site, whose parameters are then transmitted to a central location. We mathematically show that the best representative of all the local models is a certain “mean” model, and empirically show that this model can be approximated quite well by generating artificial samples from the local models using sampling techniques, and then fitting a global model of a chosen parametric form to these samples. We also propose a new measure that quantifies privacy based on information theoretic concepts, and show that decreasing privacy improves the quality of the global model and vice versa. Empirical results are provided on different kinds of data to highlight the generality of our framework. The results show that high quality global clusters can be achieved with little loss of privacy. [Copyright &y& Elsevier]

The original k-means clustering algorithm is designed to work primarily on numeric data sets. This prohibits the algorithm from being directly applied to categorical data clustering in many data mining applications. The k-modes algorithm [Z. Huang, Clustering large data sets with mixed numeric and categorical value, in: Proceedings of the First Pacific Asia Knowledge Discovery and Data Mining Conference. World Scientific, Singapore, 1997, pp. 21–34] extended the k-means paradigm to cluster categorical data by using a frequency-based method to update the cluster modes versus the k-means fashion of minimizing a numerically valued cost. However, as is the case with most data clustering algorithms, the algorithm requires a pre-setting or random selection of initial points (modes) of the clusters. The differences on the initial points often lead to considerable distinct cluster results. In this paper we present an experimental study on applying Bradley and Fayyad''s iterative initial-point refinement algorithm to the k-modes clustering to improve the accurate and repetitiveness of the clustering results [cf. P. Bradley, U. Fayyad, Refining initial points for k-mean clustering, in: Proceedings of the 15th International Conference on Machine Learning, Morgan Kaufmann, Los Altos, CA, 1998]. Experiments show that the k-modes clustering algorithm using refined initial points leads to higher precision results much more reliably than the random selection method without refinement, thus making the refinement process applicable to many data mining applications with categorical data. [Copyright &y& Elsevier]