Multi-objective clustering ensemble for gene expression data analysis

In this paper, we present an algorithm for cluster analysis that integrates aspects from cluster ensemble and multi-objective clustering. The algorithm is based on a Pareto-based multi-objective genetic algorithm, with a special crossover operator, which uses clustering validation measures as objective functions. The algorithm proposed can deal with data sets presenting different types of clusters, without the need of expertise in cluster analysis. its result is a concise set of partitions representing alternative trade-offs among the objective functions. We compare the results obtained with our algorithm, in the context of gene expression data sets, to those achieved with multi-objective Clustering with automatic K-determination (MOCK). the algorithm most closely related to ours. (C) 2009 Elsevier B.V. All rights reserved.

On comparing two sequences of numbers and its applications to clustering analysis

A conceptual problem that appears in different contexts of clustering analysis is that of measuring the degree of compatibility between two sequences of numbers. This problem is usually addressed by means of numerical indexes referred to as sequence correlation indexes. This paper elaborates on why some specific sequence correlation indexes may not be good choices depending on the application scenario in hand. A variant of the Product-Moment correlation coefficient and a weighted formulation for the Goodman-Kruskal and Kendall`s indexes are derived that may be more appropriate for some particular application scenarios. The proposed and existing indexes are analyzed from different perspectives, such as their sensitivity to the ranks and magnitudes of the sequences under evaluation, among other relevant aspects of the problem. The results help suggesting scenarios within the context of clustering analysis that are possibly more appropriate for the application of each index. (C) 2008 Elsevier Inc. All rights reserved.

On the efficiency of evolutionary fuzzy clustering

This paper tackles the problem of showing that evolutionary algorithms for fuzzy clustering can be more efficient than systematic (i.e. repetitive) approaches when the number of clusters in a data set is unknown. To do so, a fuzzy version of an Evolutionary Algorithm for Clustering (EAC) is introduced. A fuzzy cluster validity criterion and a fuzzy local search algorithm are used instead of their hard counterparts employed by EAC. Theoretical complexity analyses for both the systematic and evolutionary algorithms under interest are provided. Examples with computational experiments and statistical analyses are also presented.

Quality indices for (practical) clustering evaluation

Clustering quality or validation indices allow the evaluation of the quality of clustering in order to support the selection of a specific partition or clustering structure in its natural unsupervised environment, where the real solution is unknown or not available. In this paper, we investigate the use of quality indices mostly based on the concepts of clusters` compactness and separation, for the evaluation of clustering results (partitions in particular). This work intends to offer a general perspective regarding the appropriate use of quality indices for the purpose of clustering evaluation. After presenting some commonly used indices, as well as indices recently proposed in the literature, key issues regarding the practical use of quality indices are addressed. A general methodological approach is presented which considers the identification of appropriate indices thresholds. This general approach is compared with the simple use of quality indices for evaluating a clustering solution.

The constrained compartmentalized knapsack problem: mathematical models and solution methods

The constrained compartmentalized knapsack problem can be seen as an extension of the constrained knapsack problem. However, the items are grouped into different classes so that the overall knapsack has to be divided into compartments, and each compartment is loaded with items from the same class. Moreover, building a compartment incurs a fixed cost and a fixed loss of the capacity in the original knapsack, and the compartments are lower and upper bounded. The objective is to maximize the total value of the items loaded in the overall knapsack minus the cost of the compartments. This problem has been formulated as an integer non-linear program, and in this paper, we reformulate the non-linear model as an integer linear master problem with a large number of variables. Some heuristics based on the solution of the restricted master problem are investigated. A new and more compact integer linear model is also presented, which can be solved by a branch-and-bound commercial solver that found most of the optimal solutions for the constrained compartmentalized knapsack problem. On the other hand, heuristics provide good solutions with low computational effort. (C) 2011 Elsevier BM. All rights reserved.

Partial spectral projected gradient method with active-set strategy for linearly constrained optimization

A method for linearly constrained optimization which modifies and generalizes recent box-constraint optimization algorithms is introduced. The new algorithm is based on a relaxed form of Spectral Projected Gradient iterations. Intercalated with these projected steps, internal iterations restricted to faces of the polytope are performed, which enhance the efficiency of the algorithm. Convergence proofs are given and numerical experiments are included and commented. Software supporting this paper is available through the Tango Project web page: http://www.ime.usp.br/similar to egbirgin/tango/.

Clustering and diffusion in a symplectic map lattice with non-local coupling

We study a symplectic chain with a non-local form of coupling by means of a standard map lattice where the interaction strength decreases with the lattice distance as a power-law, in Such a way that one can pass continuously from a local (nearest-neighbor) to a global (mean-field) type of coupling. We investigate the formation of map clusters, or spatially coherent structures generated by the system dynamics. Such clusters are found to be related to stickiness of chaotic phase-space trajectories near periodic island remnants, and also to the behavior of the diffusion coefficient. An approximate two-dimensional map is derived to explain some of the features of this connection. (C) 2008 Elsevier Ltd. All rights reserved.

Synthesis and analgesic profile of conformationally constrained N-acylhydrazone analogues: Discovery of novel N-arylideneamino quinazolin-4(3H)-one compounds derived from natural safrole

In this work we reported the synthesis and evaluation of the analgesic, anti-inflammatory, and platelet anti-aggregating properties of new 3-(arylideneamino)-2-methyl-6,7-methylenedioxy-quinazolin-4 (3H)-one derivatives (3a-j), designed as conformationally constrained analogues of analgesic 1,3- benzodioxolyl-N- acylhydrazones (1) previously developed at LASSBio. Target compounds were synthesized in very good yields exploiting abundant Brazilian natural product safrole (2) as starting material. The pharmacological assays lead us to identify compounds LASSBio-1240 (3b) and LASSBio-1272 (3d) as new analgesic prototypes, presenting an antinociceptive pro. le more potent and effective than dipyrone and indomethacin used, respectively, as standards in AcOH-induced abdominal constrictions assay and in the formalin test. These results confirmed the success in the exploitation of conformation restriction strategy for identification of novel cyclic N-acylhydrazone analogues with optimized analgesic profile (C) 2009 Elsevier Ltd. All rights reserved.

Continuous GRASP with a local active-set method for bound-constrained global optimization

Global optimization seeks a minimum or maximum of a multimodal function over a discrete or continuous domain. In this paper, we propose a hybrid heuristic-based on the CGRASP and GENCAN methods-for finding approximate solutions for continuous global optimization problems subject to box constraints. Experimental results illustrate the relative effectiveness of CGRASP-GENCAN on a set of benchmark multimodal test functions.

Global minimization using an Augmented Lagrangian method with variable lower-level constraints

A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the epsilon(k)-global minimization of the Augmented Lagrangian with simple constraints, where epsilon(k) -> epsilon. Global convergence to an epsilon-global minimizer of the original problem is proved. The subproblems are solved using the alpha BB method. Numerical experiments are presented.

Second-order negative-curvature methods for box-constrained and general constrained optimization

A Nonlinear Programming algorithm that converges to second-order stationary points is introduced in this paper. The main tool is a second-order negative-curvature method for box-constrained minimization of a certain class of functions that do not possess continuous second derivatives. This method is used to define an Augmented Lagrangian algorithm of PHR (Powell-Hestenes-Rockafellar) type. Convergence proofs under weak constraint qualifications are given. Numerical examples showing that the new method converges to second-order stationary points in situations in which first-order methods fail are exhibited.

Outer Trust-Region Method for Constrained Optimization

Given an algorithm A for solving some mathematical problem based on the iterative solution of simpler subproblems, an outer trust-region (OTR) modification of A is the result of adding a trust-region constraint to each subproblem. The trust-region size is adaptively updated according to the behavior of crucial variables. The new subproblems should not be more complex than the original ones, and the convergence properties of the OTR algorithm should be the same as those of Algorithm A. In the present work, the OTR approach is exploited in connection with the ""greediness phenomenon"" of nonlinear programming. Convergence results for an OTR version of an augmented Lagrangian method for nonconvex constrained optimization are proved, and numerical experiments are presented.

Clustering Lab value working with medical data

Data mining is a relatively new field of research that its objective is to acquire knowledge from large amounts of data. In medical and health care areas, due to regulations and due to the availability of computers, a large amount of data is becoming available [27]. On the one hand, practitioners are expected to use all this data in their work but, at the same time, such a large amount of data cannot be processed by humans in a short time to make diagnosis, prognosis and treatment schedules. A major objective of this thesis is to evaluate data mining tools in medical and health care applications to develop a tool that can help make rather accurate decisions. In this thesis, the goal is finding a pattern among patients who got pneumonia by clustering of lab data values which have been recorded every day. By this pattern we can generalize it to the patients who did not have been diagnosed by this disease whose lab values shows the same trend as pneumonia patients does. There are 10 tables which have been extracted from a big data base of a hospital in Jena for my work .In ICU (intensive care unit), COPRA system which is a patient management system has been used. All the tables and data stored in German Language database.