This survey provides a description of algorithms to reorder visual matrices of tabular data and adjacency matrix of networks. The goal of this survey is to provide a comprehensive list of reordering algorithms published in different fields such as statistics, bioinformatics, or graph theory. While several of these algorithms are described in publications and others are available in software libraries and programs, there is little awareness of what is done across all fields. Our survey aims at describing these reordering algorithms in a unified manner to enable a wide audience to understand their differences and subtleties. We organize this corpus in a consistent manner, independently of the application or research field. We also provide practical guidance on how to select appropriate algorithms depending on the structure and size of the matrix to reorder, and point to implementations when available.

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Matrix reordering methods for table and network visualization

For swarm intelligence algorithms, each individual in the swarm represents a solution in the search space, and it also can be seen as a data sample from the search space. Based on the analyses of these data, more effective algorithms and search strategies could be proposed. Brain storm optimization (BSO) algorithm is a new and promising swarm intelligence algorithm, which simulates the human brainstorming process. Through the convergent operation and divergent operation, individuals in BSO are grouped and diverged in the search space/objective space. In this paper, the history development, and the state-of-the-art of the BSO algorithm are reviewed. In addition, the convergent operation and divergent operation in the BSO algorithm are also discussed from the data analysis perspective. Every individual in the BSO algorithm is not only a solution to the problem to be optimized, but also a data point to reveal the landscape of the problem. Swarm intelligence and data mining techniques can be combined to produce benefits above and beyond what either method could achieve alone.

Brain storm optimization algorithm: a review

We propose an image classification and retrieval technique using PCNN and K-NN.We optimized the PCNN parameters using genetic algorithm.We implemented a prototype to validate our proposed technique.The results are represented and measured with precision, recall and accuracy.The proposed technique proved its efficiency in classifying and retrieving images with comparison to other techniques. Content-Based Image Retrieval (CBIR) has become a powerful tool that is used in many image applications and search engines. Thus, many techniques and approaches for CBIR were developed in literature. The CBIR approach works on the visual features of the image rather than a descriptive text. Therefore, it provides more effective and efficient retrieval. On the other hand, PCNN has proved its efficiency as an image processing tool for various tasks such as image segmentation and recognition, feature extraction, edge and object detection. This article introduces a technique for content-based image classification and retrieval using PCNN. The proposed technique uses an optimized Pulse-Coupled Neural Network (PCNN) to extract the visual features of the image in a form of a numeric vector called image signature. An optimization mechanism was applied to the PCNN parameters in order to improve the signature quality. Thus improving the classification and retrieval results. Additionally, it employs the K-Nearest Neighbor (K-NN) algorithm for classification and matching. By applying classification before retrieval, the number of images in the search space is optimized to include one category instead of multiple categories. Moreover, we developed a CBIR prototype to validate our technique. The results show that our technique can retrieve and classify images efficiently. Furthermore, we evaluated our prototype against one of the widely used techniques and it was proven that the proposed technique can enhance the search results and improve the accuracy by 3.5%.

Image classification and retrieval using optimized Pulse-Coupled Neural Network

The development, implementation, variant, and future directions of a new swarm intelligence algorithm, brain storm optimization (BSO) algorithm, are comprehensively surveyed. Brain storm optimization algorithm is a new and promising swarm intelligence algorithm, which simulates the human brainstorming process. Through the convergent operation and divergent operation, individuals in BSO are grouped and diverged in the search space/objective space. To the best of our knowledge, there are 75 papers, 8 theses, and 5 patents in total on the development and application of the BSO algorithm. Every individual in the BSO algorithm is not only a solution to the problem to be optimized, but also a data point to reveal the landscape of the problem. Based on the developments of brain storm optimization algorithms, different kinds of optimization problems and real-world applications could be solved.

A comprehensive survey of brain storm optimization algorithms

We investigate the use of bandwidth and wavefront reduction algorithms to determine a static BDD variable ordering. The aim is to reduce the size of BDDs arising in symbolic reachability. Previous work showed that minimizing the weighted event span of the variable dependency graph yields small BDDs. The bandwidth and wavefront of symmetric matrices are well studied metrics, used in sparse matrix solvers, and many bandwidth and wavefront reduction algorithms are readily available in libraries like Boost and ViennaCL.

In this paper, we transform the dependency matrix to a symmetric matrix and apply various bandwidth and wavefront reduction algorithms, measuring their influence on the weighted event span. We show that Sloan's algorithm, executed on the total graph of the dependency matrix, yields a variable order with minimal event span. We demonstrate this on a large benchmark of Petri nets, Dve, Promela, B, and mcrl2 models. As a result, good static variable orders can now be determined in milliseconds by using standard sparse matrix solvers.

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Bandwidth and Wavefront Reduction for Static Variable Ordering in Symbolic Reachability Analysis

The bandwidth, average bandwidth, envelope, prole and antibandwidth of the matrices have been the subjects of study for at least 45 years. These problems have generated considerable interest over the years because of them practical relevance in ar- eas like: solving the system of equations, nite element methods, circuit design, hypertext layout, chemical kinetics, numerical geo- physics etc. In this paper a brief description of these problems are made in terms of their denitions, followed by a comparative study of them, using both approaches: matrix geometry and graph theory. Time evolution of the corresponding algorithms as well as a short description of them are made. The work also contains concrete real applications for which a large part of presented al- gorithms were developed.

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The Bandwidths of a Matrix. A Survey of Algorithms

This paper proposes a metaheuristic inspired from human brainstorming combined with concepts from graph theory for solving system of equations. The proposed method is able to find solutions of a given system of equations, even in cases where traditional methods fail. In the cases where no exact solution exists, an approximate solution is good and it can be obtained by the proposed method. Directions for future research are also provided.

A New Approach for Solving Equations Systems Inspired from Brainstorming

This paper proposes a memetic algorithm (MA) to solve linear systems of equations, by transforming the linear system of equations into an optimization problem. Such exploitation of knowledge obtained in a local search/optimization allows the evolutionary programming implementation to produce very good results at a relatively low computational cost. The proposed MA is able to determine solutions of a given linear system of equations, even in cases where traditional methods fail ( determinant null, ill-conditioned systems, subdeterminate systems, supradeterminate systems, system doesn’t satisfy the convergence conditions etc). In situations when a linear system of equations has multiple solutions, in proposed approach, the task is to find as many solutions as possible, inside of a given interval. In cases where no accurate solution for a linear system of equations exists, an approximate solution can be acceptable and it can be obtained by the proposed method.

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Solving Linear Systems of Equations using a Memetic Algorithm

The paper presents experimental results on parallel variants of some classical methods for solving systems of equations. The following four methods are studied: Newton method, Chebyshev method, Gradient method with Fridman control sequence, a method of conjugate gradient type. The main conclusion is that the precondition of the sparse systems (both linear and nonlinear) improves in a great extent the performance of the parallel algorithms.

http://www.computer.org/csdl/proceedings/synasc/2012/4934/00/4934a103.pdf

Experimental Study on Parallel Methods for Solving Systems of Equations

Distance measures is very important in some clustering and machine learning techniques. At present there are many such measures for determining the dissimilarity between the featurevectors, but it is very important to make a choice that depends on the problem to be solved. This paper proposes a simple but robust distance measure called Reference Distance Weighted, for calculating distance between feature-vectors with real values. The basic attribute that distinguishes it from other measures is that the distance is measured from one of the feature-vector, considered as a reference system, to other feature-vectors. In fact this reference vector belongs to a class of a classification system. A second distinctive attribute is that its value does not depend on the orders of magnitude of the different characteristics of vectors. In addition, through a parameter called factor of relevance, each feature receives a weight in terms of its influence, because different features have different influence on dissimilarity estimation depending on the final problem to be solved. An extension of the proposed distance allows working with hybrid vectors, ie real and logical values. Future research directions are also provided.

/pdf/a-new-dissimilarity-measure-between-feature-vectors-zntspnhhq2.pdf

Liviu Octavian Mafteiu-Scai

Papers

The Bandwidths of a Matrix. A Survey of Algorithms

A New Approach for Solving Equations Systems Inspired from Brainstorming

Solving Linear Systems of Equations using a Memetic Algorithm

Experimental Study on Parallel Methods for Solving Systems of Equations

A New Dissimilarity Measure between Feature-Vectors