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Imbalanced classification is related to those problems that have an uneven distribution among classes. In addition to the former, when instances are located into the overlapped areas, the correct modeling of the problem becomes harder. Current solutions for both issues are often focused on the binary case study, as multi-class datasets require an additional effort to be addressed. In this research, we overcome these problems by carrying out a combination between feature and instance selections. Feature selection will allow simplifying the overlapping areas easing the generation of rules to distinguish among the classes. Selection of instances from all classes will address the imbalance itself by finding the most appropriate class distribution for the learning task, as well as possibly removing noise and difficult borderline examples. For the sake of obtaining an optimal joint set of features and instances, we embedded the searching for both parameters in a Multi-Objective Evolutionary Algorithm, using the C4.5 decision tree as baseline classifier in this wrapper approach. The multi-objective scheme allows taking a double advantage: the search space becomes broader, and we may provide a set of different solutions in order to build an ensemble of classifiers. This proposal has been contrasted versus several state-of-the-art solutions on imbalanced classification showing excellent results in both binary and multi-class problems.

Two aspects of fractal networks are considered: the community structure and the class structure, where classes of nodes appear as a consequence of a local symmetry of nodes. The analyzed systems are the networks constructed for two selected symmetric fractals: the Sierpinski triangle and the Koch curve. Communities are searched for by means of a set of differential equations. Overlapping nodes which belong to two different communities are identified by adding some noise to the initial connectivity matrix. Then, a node can be characterized by a spectrum of probabilities of belonging to different communities. Our main goal is that the overlapping nodes with the same spectra belong to the same class.

Recommendation systems (RSs) are tools for interacting with large and complex information spaces. They provide a personalized view of such spaces, prioritizing items likely to be of interest to the user. The main objective of RSs is to tool up users with desired items that meet their preferences. A major problem in RSs is called: “cold-start”; it is a potential problem called so in computer-based information systems which comprises a degree of automated data modeling. Particularly, it concerns the issue in which the system cannot draw any inferences nor have it yet gathered sufficient information about users or items. Since RSs performance is substantially limited by cold-start users and cold-start items problems; this research study takes the route for a major aim to attenuate users’ cold-start problem. Still in the process of researching, sundry studies have been conducted to tackle this issue by using clustering techniques to group users according to their social relations, their ratings or both. However, a clustering technique disregards a variety of users’ tastes. In this case, the researcher has adopted the overlapping technique as a tool to deal with the clustering technique’s defects. The advantage of the overlapping technique excels over others by allowing users to belong to multi-clusters at the same time according to their behavior in the social network and ratings feedback. On that account, a novel overlapping method is presented and applied. This latter is executed by using the partitioning around medoids (PAM) algorithm to implement the clustering, which is achieved by means of exploiting social relations and confidence values. After acquiring users’ clusters, the average distances are computed in each cluster. Thereafter, a content comparison is made regarding the distances between every user and the computed distances of the clusters. If the comparison result is less than or equal to the average distance of a cluster, a new user is added to this cluster. The singular value decomposition plus (SVD$++$) method is then applied to every cluster to compute predictions values. The outcome is calculated by computing the average of mean absolute error (MAE) and root mean square error (RMSE) for every cluster. The model is tested by two real world datasets: Ciao and FilmTrust. Ultimately, findings have exhibited a great deal of insights on how the proposed model outperformed a number of the state-of-the-art studies in terms of prediction accuracy.

In this paper we study a general separation property for subsystems G, whose attractor K_G is a sub-self-similar set. This is a generalization of the Lau-Ngai weak separation property for the bounded distortion case. For subsystems with positive Hausdorff measure in its similarity dimension, we characterize the subsets of K_G with positive measure where the separation property may fail. We exhibit two examples of fractal sets, one not satisfying the weak separation property and whose existence was questioned by Zerner, the other having positive Hausdorff measure in its dimension and with the separation property failing on a subset of positive measure.

Sliced inverse regression (SIR) is a pioneer tool for supervised dimension reduction. It identifies the effective dimension reduction space, the subspace of significant factors with intrinsic lower dimensionality. In this paper, we propose to refine the SIR algorithm through an overlapping slicing scheme. The new algorithm, called overlapping SIR (OSIR), is able to estimate the effective dimension reduction space and determine the number of effective factors more accurately. We show that such overlapping procedure has the potential to identify the information contained in the derivatives of the inverse regression curve, which helps to explain the superiority of OSIR. We also prove that OSIR algorithm is $\sqrt{n}$-consistent and verify its effectiveness by simulations and real applications.

We propose and implement a method to obtain all duplicated sequences (repeats) from a chromosome or whole genome. Unlike existing approaches our method makes it possible to simultaneously identify and classify repeats into super, local, and non-nested local maximal repeats. Computation verification demonstrates that maximal repeats for a genome of several gigabases can be identified in a reasonable time, enabling us to identified these maximal repeats for any sequenced genome. The algorithm used for the identification relies on enhanced suffix array data structure to achieve practical space and time efficiency, to identify and classify the maximal repeats, and to perform further post-processing on the identified duplicated sequences. The simplicity and effectiveness of the implementation makes the method readily extendible to more sophisticated computations. Maxmers can be exhaustively accounted for in few minutes for genome sequences of dozen megabases in length and in less than a day or two for genome sequences of few gigabases in length. One application of duplicated sequence identification is to the study of duplicated sequence length distributions, which our found to exhibit for large lengths a persistent power-law behavior. Variation of estimated exponents of this power law are studied among different species and successive assembly release versions of the same species. This makes the characterization of the power-law regime of sequenced genomes via maximal repeats identification and classification, an important task for the derivation of models that would help us to elucidate sequence duplication and genome evolution.

In this study, we discuss overlapping possibilities of Sparse Matrix-Vector multiplication (SpMV) in cases where we have multiple RHS-vectors and where the whole sparse matrix data may or may not fit into the memory of the discrete GPU, at once, by using OpenACC. With GPUs, one can take advantage of their relatively high memory bandwidths. However, data needs to be transferred over the relatively slow PCIe bus. We implement communication-hiding to increase performance.

In the case of three degrees of freedom and modeling 2,097,152 nodes, we observe a just above 40% performance increase by applying communication-hiding in our routine. This underlines the importance of applying such techniques in simulations, when it is suitable with the algorithmic structure of the problem in relation to the underlying computer architecture.

Some kinds of the self-similar sets with overlapping structures are studied by introducing the graph-directed constructions satisfying the open set condition that coincide with these sets. In this way, the dimensions and the measures are obtained.