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EN
A new method of preparation of nanocrystalline zinc aluminate (ZnAl2O4) powder is described in this paper. Different organic acids are used as template material and nitric acid as an oxidant. Single phase ZnAl2O4 spinel can be formed at a much lower temperature through this route which gives nanocrystalline powder with uniform particle size and morphology. The powders are characterized by thermo gravimetric analysis (TGA), X-ray diffraction analysis (XRD), Fourier transform infrared spectroscopy (FT-IR), BET surface area analysis and field emission scanning electron microscopy (FE-SEM). The average crystallite size of the single phase material was of 20 to 30 nm and the surface area was found to be 21 to 27 m2g-1.
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Content available remote Unsupervised and Supervised Learning Approaches Together for Microarray Analysis
EN
In this article, a novel concept is introduced by using both unsupervised and supervised learning. For unsupervised learning, the problem of fuzzy clustering in microarray data as a multiobjective optimization is used, which simultaneously optimizes two internal fuzzy cluster validity indices to yield a set of Pareto-optimal clustering solutions. In this regards, a new multiobjective differential evolution based fuzzy clustering technique has been proposed. Subsequently, for supervised learning, a fuzzy majority voting scheme along with support vector machine is used to integrate the clustering information from all the solutions in the resultant Pareto-optimal set. The performances of the proposed clustering techniques have been demonstrated on five publicly available benchmark microarray data sets. A detail comparison has been carried out with multiobjective genetic algorithm based fuzzy clustering, multiobjective differential evolution based fuzzy clustering, single objective versions of differential evolution and genetic algorithm based fuzzy clustering as well as well known fuzzy c-means algorithm. While using support vector machine, comparative studies of the use of four different kernel functions are also reported. Statistical significance test has been done to establish the statistical superiority of the proposed multiobjective clustering approach. Finally, biological significance test has been carried out using a web based gene annotation tool to show that the proposed integrated technique is able to produce biologically relevant clusters of coexpressed genes.
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Content available remote Some Symmetry Based Classifiers
EN
In this paper, a novel point symmetry based pattern classifier (PSC) is proposed. A recently developed point symmetry based distance is utilized to determine the amount of point symmetry of a particular test pattern with respect to a class prototype. Kd-tree based nearest neighbor search is used for reducing the complexity of point symmetry distance computation. The proposed point symmetry based classifier is well-suited for classifying data sets having point symmetric classes, irrespective of any convexity, overlap or size. In order to classify data sets having line symmetry property, a line symmetry based classifier (LSC) along the lines of PSC is thereafter proposed in this paper. To measure the total amount of line symmetry of a particular point in a class, a new definition of line symmetry based distance is also provided. Proposed LSC preserves the advantages of PSC. The performance of PSC and LSC are demonstrated in classifying fourteen artificial and real-life data sets of varying complexities. For the purpose of comparison, k-NN classifier and the well-known support vector machine (SVM) based classifiers are executed on the data sets used here for the experiments. Statistical analysis, ANOVA, is also performed to compare the performance of these classification techniques.
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Content available remote Semi-GAPS: A Semi-supervised Clustering Method Using Point Symmetry
EN
In this paper, an evolutionary technique for the semi-supervised clustering is proposed. The proposed technique uses a point symmetry based distance measure. Semi-supervised classification uses aspects of both unsupervised and supervised learning to improve upon the performance of traditional classification methods. In this paper the existing point symmetry based genetic clustering technique, GAPS-clustering, is extended in two different ways to handle the semi-supervised classification problem. The proposed semi-GAPS clustering algorithmis able to detect any type of clusters irrespective of shape, size and convexity as long as they possess the point symmetry property. Kd-tree based nearest neighbor search is used to reduce the complexity of finding the closest symmetric point. Adaptive mutation and crossover probabilities are used. Experimental results demonstrate practical performance benefits of the methodology in detecting classes having symmetrical shapes in case of semi-supervised clustering.
5
EN
In this paper, the automatic segmentation of multispectral magnetic resonance image of the brain is posed as a clustering problem in the intensity space. Thereafter an automatic clustering technique is proposed to solve this problem. The proposed real-coded variable string length genetic clustering technique (MCVGAPS clustering) is able to evolve the number of clusters present in the data set automatically. Each cluster is divided into several small hyperspherical subclusters and the centers of all these small sub-clusters are encoded in a string to represent the whole clustering. For assigning points to different clusters, these local sub-clusters are considered individually. For the purpose of objective function evaluation, these sub-clusters are merged appropriately to form a variable number of global clusters. A recently developed point symmetry distance based cluster validity index, Sym-index, is optimized to automatically evolve the appropriate number of clusters present in an MR brain image. The proposed method is applied on several simulated T1-weighted, T2- weighted and proton density normal and MS lesion magnetic resonance brain images. Superiority of the proposed method over Fuzzy C-means, Expectation Maximization clustering algorithms are demonstrated quantitatively. The automatic segmentation obtained by multiseed based multiobjective clustering technique (MCVGAPS) is also compared with the available ground truth information.
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Content available remote Mining the Largest Dense Vertexlet in a Weighted Scale-free Graph
EN
An important problem of knowledge discovery that has recently evolved in various reallife networks is identifying the largest set of vertices that are functionally associated. The topology of many real-life networks shows scale-freeness, where the vertices of the underlying graph follow a power-law degree distribution. Moreover, the graphs corresponding to most of the real-life networks are weighted in nature. In this article, the problem of finding the largest group or association of vertices that are dense (denoted as dense vertexlet) in a weighted scale-free graph is addressed. Density quantifies the degree of similarity within a group of vertices in a graph. The density of a vertexlet is defined in a novel way that ensures significant participation of all the vertices within the vertexlet. It is established that the problem is NP-complete in nature. An upper bound on the order of the largest dense vertexlet of a weighted graph, with respect to certain density threshold value, is also derived. Finally, an O(n2 log n) (n denotes the number of vertices in the graph) heuristic graph mining algorithm that produces an approximate solution for the problem is presented.
EN
An important approach for landcover classification in remote sensing images is by clustering the pixels in the spectral domain into several fuzzy partitions. In this article the problem of fuzzy partitioning the satellite images is posed as one of searching for some suitable number of cluster centers so that some measures of validity of the obtained partitions should be optimized. Thus the problem is posed as one of multiobjective optimization. A recently developed multiobjective simulated annealing based technique, AMOSA (archived multiobjective simulated annealing technique), is used to perform clustering, taking two validity measures as two objective functions. Center based encoding is used. The membership values of points to different clusters are computed based on the newly developed point symmetry based distance rather than the Euclidean distance. Two fuzzy cluster validity functions namely, Euclidean distance based well-known XB-index and the newly developed point symmetry based FSym-index are optimized simultaneously to automatically evolve the appropriate number of clusters present in an image. The proposed algorithm provides a set of final non-dominated solutions. A new method of selecting a single solution from this final Pareto optimal front is also developed subsequently. The effectiveness of this proposed clustering technique in comparison with the existing Fuzzy C-means clustering is shown for automatically classifying one artificially generated, three remote sensing satellite images of the parts of the cities of Kolkata and Mumbai.
EN
The problem of classifying an image into different homogeneous regions is viewed as the task of clustering the pixels in the intensity space. In particular, satellite images contain landcover types some of which cover significantly large areas, while some (e.g., bridges and roads) occupy relatively much smaller regions. Automatically detecting regions or clusters of such widely varying sizes presents a challenging task. In this paper, a newly developed real-coded variable string length genetic fuzzy clustering technique with a new point symmetry distance is used for this purpose. The proposed algorithm is capable of automatically determining the number of segments present in an image. Here assignment of pixels to different clusters is done based on the point symmetry based distance rather than the Euclidean distance. The cluster centers are encoded in the chromosomes, and a newly developed fuzzy point symmetry distance based cluster validity index, FSym-index, is used as a measure of the validity of the corresponding partition. This validity index is able to correctly indicate presence of clusters of different sizes and shapes as long as they are internally symmetrical. The space and time complexities of the proposed algorithm are also derived. The effectiveness of the proposed technique is first demonstrated in identifying two small objects from a large background from an artificially generated image and then in identifying different landcover regions in remote sensing imagery. Results are compared with those obtained using the well known fuzzy C-means algorithm both qualitatively and quantitatively.
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Content available remote An annealing-evolution technique for clustering
EN
An efficient partitional clustering technique, called Annealing-Evolution-clustering (ANEV-clustering), and its fuzzy version, that integrate the power of simulated annealing for obtaining minimum energy configuration, and the searching capability of evolutionary programming are proposed in this article. Two other evolutionary programming based clustering techniques are also developed where Gauss and Cauchy mutation strategies have been used. The clustering methodology is used to search for appropriate cluster centers in multi-dimensional feature space such that a similarity metric of the resulting clusters is optimized. In ,AN.EV-clustering, data points are redistributed among the clusters probabilistically in the mutation phase of the evolution process, so that points that are farther away from the cluster center have higher probabilities of migrating to other clusters than those which are closer to it. The superiority of the AN EV -clustering algorithm over the widely used fc-means algorithm, simulated annealing and conventional evolutionary programming based clustering algorithms is extensively demonstrated for artificial and real life data sets. For the fuzzy clustering algorithm, we have compared the results with the well known fuzzy c-means algorithm. The proposed crisp clustering method is also used for classifying the pixels of a satellite image of a part of the city of Kolkata.
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Content available remote Relation between VGA-classifier and MLP : determination of network architecture
EN
An analogy between a genetic algorithm based pattern classification scheme (where hyper-planes are used to approximate the class boundaries through searching) and multiplayer per-ceptron (MLP) based classifier is established. Based on this, a method for determining the MLP architecture automatically is described. It is shown that the architecture would need at-most two hidden layers, the neurons of which are responsible for generating hyperplanes and regions. The neurons in the second hidden and output layers perform the AND & OR func-tions respectively. The methodology also includes a post processing step which automatically removes any redundant neuron in the hidden/output layer. An extensive comparative study of the performance of the MLP, thus derived using the proposed method, with those of several other conventional MLP's is presented for different data sets.
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