Categorical data analysis using multiobjective differential evolution based fuzzy clustering

Clustering is a widely used technique in data mining application for discovering patterns in underlying data. Most traditional clustering algorithms are limited in handling datasets that contain categorical attributes. Howerver, datasets with categorical types of attributes are common in real life data mining problem. For these data sets, no inherent distance measure, like the Euclidean distance, would work to compute the distance between two catgorical objects. In this article, we have described differential evolution, genetic algorithm and simulated annealing based fuzzy clustering. The performance of the proposed algorithms have been compared with that of different well known categorical data clustering algorithms and demonstrated for a variety of artificial and real life categorical data sets. Statistical significance test has been performed to establish the superiority of the proposed algorithms.

Information utilization based modified Differential evolution algorithm (IUMDE) is an improved version of DE algorithm. In IUMDE, Mutation and Selection operation of basic Differential Evolution (DE) algorithm are modified. In proposed IUMDE initially modified mutation operation provides a selection criterion of base vector before performing the basic DE mutation operation. Further the modified selection operation utilizes the neglected trial vector and hence helps to improve the performance of DE algorithm. In this paper IUMDE algorithm is employed on 6 constrained benchmark optimization problems, selected from the literature. The numerical results expose that the IUMDE algorithm perform more accurately and significantly better than other algorithms with these constrained optimization problems.

Particle Swarm Optimization or Differential Evolution—A comparison

Some Thoughts About Data Type, Distribution, and Statistical Significance

The berth allocation problem (BAP) is an important and challenging problem in the maritime transportation industry. BAP can be defined as the problem of assigning a berth position and service time to a given set of vessels while ensuring that all BAP constraints are respected. The goal is to minimize the total waiting time of all vessels. In this paper, we propose a differential evolution (DE) algorithm for the BAP. DE is a nature-inspired meta-heuristic that has been shown to be an effective method to addresses continuous optimization problems. It involves a population of solutions that undergo the process of selection and variation. In DE, the mutation operator is considered the main variation operator responsible for generating new solutions. Several mutation operators have been proposed and they have shown that different operators are more suitable for different problem instances and even different stages in the search process. In this paper, we propose an enhanced DE that utilizes several mutation operators and employs game theory to control the selection of mutation operators during the search process. The BAP benchmark instances that have been used by other researchers are used to assess the performance of the proposed algorithm. Our experimental results reveal that the proposed DE can obtain competitive results with less computational time compared to existing algorithms for all tested problem instances.

Differential evolution (DE) is a powerful evolutionary algorithms, widely applied in different fields of science and engineering for solving the problem of optimization. Since image encryption has been viewed as an interesting research topic by many experts and innumerable methods to encrypt images have emerged, currently, the focus is on obtaining optimized images. The paper presents a novel image encryption scheme that uses intertwining logistic map (ILM), DNA encoding and DE optimization. The proposed approach is based on three phases: permutation involving ILM, diffusion engaging DNA and optimization using DE. Parameters like entropy, key sensitivity, secret key space, unified average change in intensity (UACI), correlation coefficient —vertical, horizontal and diagonal, and number of pixel change rate have been evaluated to test the efficiency of the proposed method. The paper also compares this performance with that of the genetic algorithms (GA), used previously for optimization. The significance of this approach is enhancing entropy, the essential characteristic of randomness, resisting against numerous statistical and differential attacks and generating good experimental results. The main contribution of this paper is to present the efficiency of DE in image optimization and exhibit how DE is better than GA.

Carpooling is an effective transport model that can significantly reduce transportation costs. The problem to match passengers with drivers is a difficult problem due to complex constraints to be satisfied in the solution processes. The goals of this paper are to propose a model and a solution methodology that is seamlessly integrated with existing geographic information system to determine drivers/passengers for ride sharing. In this paper, we formulate a car pooling problem and propose a solution algorithm for it based on a meta-heuristic approach. Differential evolution (DE) is a competitive evolutionary algorithm widely utilized in the science and engineering fields. The simple and straightforward evolving mechanisms of DE endow it with the powerful capability to solve optimization problems. To achieve the goal, we first formulate the carpooling optimization problem as an integer programming problem. We then develop variants of DE algorithm for it. We also conduct experiments to illustrate and compare effectiveness of the proposed DE algorithms.

Differential Evolution (DE) has become an advanced, robust, and proficient alternative technique for clustering on account of their population-based stochastic and heuristic search manners. Balancing better the exploitation and exploration power of the DE algorithm is important because this ability influences the performance of the algorithm. Besides, keeping superior solutions for the initial population raises the probability of finding better solutions and the rate of convergence. In this paper, an enhanced DE algorithm is introduced for clustering to offer better cluster solutions with faster convergence. The proposed algorithm performs a modified mutation strategy to improve the DE’s search behavior and exploits Quasi-Opposition-based Learning (QBL) to choose fitter initial solutions. This mutation strategy that uses the best solution as a target solution and applies three differentials contributes to avoiding local optima trap and slow convergence. The QBL based initialization method also contributes to increasing the quality of the clustering results and convergence rate. The experimental analysis was conducted on seven real datasets from the UCI repository to evaluate the performance of the proposed clustering algorithm. The obtained results showed that the proposed algorithm achieves more compact clusters and stable solutions than the competing conventional DE variants. Moreover, the performance of the proposed algorithm was compared with the existing state of the art clustering techniques based on DE. The corresponding results also pointed out that the proposed algorithm is comparable to other DE based clustering approaches in terms of the value of the objective functions. Therefore, the proposed algorithm can be regarded as an efficient clustering tool.

In this chapter, a new multi-objective blended particle swarm optimization (MOBPSO) technique is proposed for the selection of significant and informative genes from the cancer datasets. As the basic optimization algorithm suffers from the local trapping, a blended Laplacian operator is integrated with it to overcome the drawback. The concept is also implemented for differential evolution, artificial bee colony, genetic algorithm and subsequently multi-objective blended differential evolution (MOBDE), multi-objective blended artificial bee colony (MOBABC) and multi-objective blended genetic algorithm (MOBGA) are proposed to extract the relevant genes from the cancer datasets. Proposed methodology utilizes two objective functions to sort out the genes which are differentially expressed from class to class as well as provides good results for the classification of disease. Experimental result reveals that the proposed methodology very efficiently selects differential and biologically relevant genes which are effective for the classification of disease which in turn offers more useful information about the gene–disease association.

Differential evolution (DE) is a well-known evolutionary algorithm which has been successfully applied in many scientific and engineering fields. In most DE algorithms, the base and difference vectors for mutation are randomly selected from the current population. That is, the useful population information cannot be fully exploited to guide the search of DE through mutation. Furthermore, the selection of parents in mutation has been verified to be critical for the DE performance. Therefore, to alleviate this drawback and improve the performance of DE, a novel DE algorithm with a directional mutation based on cellular topology is proposed in this study. This proposed algorithm is named as Cellular Direction Information based DE (DE-CDI). In DE-CDI, the cellular topology is employed first to define a neighborhood for each individual of population and then the direction information based on the neighborhood is incorporated into the mutation operator. In this way, DE-CDI not only utilizes the neighborhood information to exploit the regions of better individuals and accelerate convergence, but also introduces the direction information to guide the search to the promising area. To evaluate the performance of the proposed method, DE-CDI is applied to the original DE algorithms, as well as several advanced DE variants. Experimental results demonstrate the high performance of DE-CDI for most DE algorithms studied.

Differential evolution (DE) is one of the most successful evolutionary algorithms (EAs) for global numerical optimization. Like other EAs, maintaining population diversity is important for DE to escape from local optima and locate a near-global optimum. Using a multi-population algorithm is a representative method to avoid early loss of population diversity. In this paper, we propose a multi-population DE algorithm (MPDE) which manipulates multiple sub-populations. Different sub-populations in MPDE exchange information via a novel mutation operation instead of migration used in most multi-population EAs. The mutation operation is helpful to balance the fast convergence and population diversity of the proposed algorithm. Moreover, the performance of MPDE is further improved by an adaptive parameter control scheme designed based on the multi-population approach. Each sub-population in MPDE evolves with its own set of control parameters, and a learning strategy is used to adaptively adjust the parameter values. A set of benchmark functions is used to test the proposed MPDE algorithm. The experimental results show that MPDE performs better than, or at least comparably, to the classical single population DE with fixed parameter values and three existing state-of-the-art DE variants.

This article reviews and compares different existing statistical tests utilized in significance analysis of gene expression from DNA microarray data. Microarray gene expression study facilitates the investigation of genes that are differentially expressed with respect to different classes of samples. Many gene expression studies also aim to find groups of genes that do something together, or to find out molecular similarities among a group of samples. In all respects, it is very important to know whether there is a difference between two sets of results, and whether that difference is likely to occur due to random variations of the datasets. Hence instead of simple data analysis, statistical tests are the proper way to check statistical relevance. Basically, the statistical significance test is compulsory for yielding an ordered list of relevant genes in terms of differential expression to the investigator. This article surveys a few important statistical tests which include both parametric and nonparametric tests and compares those statistical tests with respect to different performance metrics. The statistical tests have been applied on several artificial and real-life microarray gene expression datasets. Most of the time, real-life datasets contain noise and noisy data can have undesirable effect on the results of any data mining analysis. Therefore, performance analysis on noisy datasets for different statistical tests has also been performed to facilitate the comparative study. Furthermore, correlation analysis of the resultant genes from different statistical methods has been accomplished. Keywords: Analysis, correlation analysis, eigenvector, nonparametric tests, P-value, parametric tests, principal component, statistical tests.

Differential evolution (DE) is a population-based algorithm which has been widely-used in various science and engineering fields. Much recent attention has aimed to improve the DE global convergence by altering the control parameters CR and F. However, the structure and implementation of DEs has become increasingly more complicated. This paper investigated a more efficient and simple differential evolution algorithm based on an evolutional information matrix (EMDE). An evolutional information matrix which includes crossover and mutation amplitude information is proposed. Additionally, the EMDE algorithm uses a memory population generated by a previous population to control the population search direction. Experimental results based on 12 standard benchmarks indicate that the EMDE algorithm outperforms other comparable DE variants.

Clustering is an important data mining technique that groups similar data records. In this research, the problem of clustering categorical (or transactional) data is studied. An algorithm for clustering transactional data, called F-Tree (frequent tree), is proposed, and a new similarity measure function, called PWO (probability of the weights of overlapped items), is introduced. Then, a framework to detect the best similarity value for different datasets is developed. Based on the items' frequencies in transactions, the F-Tree algorithm first generates small but highly pure clusters. It then merges similar clusters using the PWO similarity measure function, which depends on the probability of weights of overlapped items. One advantage of PWO is that it outputs the percentage of similarity between items; this is a clearer and more accurate measure of similarity than other similarity measures. Our experimental evaluation on real categorical datasets such as (Mushrooms, KrVskp, Congressional Voting, Soybean-Large, Soybean-Small, Hepatitis, Zoo, Lenses, and Adult-Stretch) shows that: Firstly, F-Tree is effective in finding rare or interesting clusters, and produces clusters with higher purity than LargeItem, WCD and CLOPE. Secondly, PWO is more effective in measuring the similarity between categorical data than LargeItem and CLOPE. Thirdly, clustering using the similarity measure PWO with pre-defined number of clusters results in separate classes with a good purity of average 80% coverage of real classes. Fourthly, the overlap estimator perfectly estimates the value of the overlap threshold using a small sample of dataset of around 5%. Finally, it is seen that the process of merging pure and small clusters increases the purity of resulted clusters as well as reduces time of clustering better than the process of generating clusters directly from the dataset then refining clusters. Based on the items' frequencies in transactions, The F-Tree algorithm first generates small but highly pure clusters. It then merges similar clusters using the PWO similarity measure function, which depends on the probability of weights of overlapped items. One advantage of PWO is that it outputs the percentage of similarity between items; this is a clearer and more accurate measure of similarity than other similarity measures. Our experimental evaluation on real categorical datasets such as "Mushrooms, KrVskp, Congressional Voting, Soybean-Large, Soybean-Small, Hepatitis, Zoo, Lenses, and Adult-Stretch" shows that: Firstly, F-Tree is effective in finding rare or interesting clusters, and produces clusters with higher purity than LargeItem, WCD and CLOPE. Secondly, PWO is more effective in measuring the similarity between categorical data than LargeItem and CLOPE. Thirdly, Clustering using the similarity measure PWO with pre-defined number of clusters results in separate classes with a good purity of average 80% coverage of real classes. Fourthly, the overlap estimator perfectly estimates the value of the overlap threshold using a small sample of dataset of around 5 percent. Finally, It is seen that the process of merging pure and small clusters increases the purity of resulted clusters as well as reduces time of clustering better than the process of generating clusters directly from the dataset then refining clusters.

Differential evolution with dynamic combination based mutation operator and two-level parameter adaptation strategy