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1

The global influence of local symmetry on entropy of the Universe

Majka M., Gajewski M., Hasan M. K., Majka T. M.

Journal of Education and Technical Sciences

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2016

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Vol. 3, nr 1

5--7

EN

Space and matter were created in the Big Bang. Since Big Bang, the Universe has been expanding continually by increasing its entropy. The fundamental forces broke their symmetries, making impossible to unify them together. Nevertheless, the symmetry of the Universe has not changed and interestingly will never. By analysing global and local symmetry, this paper will present a hypothesis on the future shape and energy expansion of the Universe. A new theory of point symmetry of the Universe will also be introduced.

2

Some Symmetry Based Classifiers

Saha S., Bandyopadhyay S.

Fundamenta Informaticae

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2009

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Vol. 90, nr 1-2

107-123

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.

3

A new multiobjective simulated annealing based fuzzy clustering technique: application to automatic pixel classification in remote sensing imagery

Saha S., Bandyopadhyay S.

Foundations of Computing and Decision Sciences

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2009

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Vol. 34, No. 3

209-229

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.