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1

Towards Obtaining Upper Bound on Sensitivity Computation Process for Cluster Validity Measures

Mishra S., Mondal S., Saha S.

Fundamenta Informaticae

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2018

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Vol. 163, nr 4

351--374

EN

Cluster validity indices are proposed in the literature to measure the goodness of a clustering result. The validity measure provides a value which shows how good or bad the obtained clustering result is, as compared to the actual clustering result. However, the validity measures are not arbitrarily generated. A validity measure should satisfy some of the important properties. However, there are cases when in-spite of satisfying these properties, a validity measure is not able to differentiate the two clustering results correctly. In this regard, sensitivity as a property of validity measure is introduced to capture the differences between the two clustering results. However, sensitivity computation is a computationally expensive task as it requires to explore all the possible combinations of clustering results which are very large in number and these are growing exponentially. So, it is required to compute the sensitivity efficiently. As the possible combinations of clustering results grow exponentially, so it is required to first obtain an upper bound on this possible number of combinations which will be sufficient to compute the value of the sensitivity. In this paper, we obtain an upper bound on the number of possible combinations of clustering results. For this purpose, a generic approach which is suitable for various validity measures and a specific approach which is applicable for two validity measures are proposed. It is also shown that this upper bound is sufficient to compute the sensitivity of various validity measures. This upper bound is very less as compared to the total number of possible combinations of clustering results.

2

Impact of Inhomogeneity on SH-type Wave Propagation in an Initially Stressed Composite Structure

Saha S., Chattopadhyay A., Singh A. K.

Acta Geophysica

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2018

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Vol. 66, no. 1

1--19

EN

The present analysis has been made on the influence of distinct form of inhomogeneity in a composite structure comprised of double superficial layers lying over a half-space, on the phase velocity of SH-type wave propagating through it. Propagation of SH-type wave in the said structure has been examined in four distinct cases of inhomogeneity viz. when inhomogeneity in double superficial layer is due to exponential variation in density only (Case I); when inhomogeneity in double superficial layers is due to exponential variation in rigidity only (Case II); when inhomogeneity in double superficial layer is due to exponential variation in rigidity, density and initial stress (Case III) and when inhomogeneity in double superficial layer is due to linear variation in rigidity, density and initial stress (Case IV). Closed-form expression of dispersion relation has been accomplished for all four aforementioned cases through extensive application of Debye asymptotic analysis. Deduced dispersion relations for all the cases are found in well-agreement to the classical Love-wave equation. Numerical computation has been carried out to graphically demonstrate the effect of inhomogeneity parameters, initial stress parameters as well as width ratio associated with double superficial layers in the composite structure for each of the four aforesaid cases on dispersion curve. Meticulous examination of distinct cases of inhomogeneity and initial stress in context of considered problem has been carried out with detailed analysis in a comparative approach.

3

Algorithm Based New Tone Reservation Method for Mitigating PAPR in OFDM Systems

Saha S., Chakrabarty S., Bhattacharjee S., Sil S.

International Journal of Electronics and Telecommunications

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2017

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Vol. 63, No. 3

293--298

EN

There are abundant methods to mitigate PAPR in OFDM signals among which algorithm based tone reservation is of great popularity owing to its low complexity as well as decent BER. Here we have put forward a new distinct algorithm based Tone Reservation technique which is not only less complex and calculates its own threshold as well as PRT signal (unlike other algorithms requiring predetermined threshold and PRT) but also aptly modifies the data by bit by bit comparison with a modified copy of itself (algorithm modified) thus scaling the peaks as and providing a decent BER and good PAPR reduction.

4

A comparative study between two systems with and without awareness in controlling HIV/AIDS

Saha S., Roy P. K.

International Journal of Applied Mathematics and Computer Science

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2017

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Vol. 27, no. 2

337--350

EN

It has always been a priority for all nations to reduce new HIV infections by implementing a comprehensive HIV prevention programme at a sufficient scale. Recently, the ‘HIV counselling & testing’ (HCT) campaign is gaining public attention, where HIV patients are identified through screening and immediately sent under a course of antiretroviral treatment (ART), neglecting the time extent they have been infected. In this article, we study a nonlinear mathematical model for the transmission dynamics of HIV/AIDS system receiving drug treatment along with effective awareness programs through media. Here, we consider two different circumstances: when treatment is only effective and when both treatment and awareness are included. The model is analyzed qualitatively using the stability theory of differential equations. The global stabilities of the equilibria under certain conditions are determined in terms of the model reproduction number. The effects of changes in some key epidemiological parameters are investigated. Projections are made to predict the long term dynamics of the disease. The epidemiological implications of such projections on public health planning and management are discussed. These studies show that the aware populations were less vulnerable to HIV infection than the unaware population.

5

Optimal selection of dental implant for different bone conditions based on the mechanical response

Roy S., Das M., Chakraborty P., Biswas J. K., Chatterjee S., Khutia N., Saha S., Roychowdhury A.

Acta of Bioengineering and Biomechanics

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2017

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Vol. 19, no. 2

11--20

EN

Bone quality varies from one patient to another extensively; also, Young’s modulus may deviate up to 40% of normal bone quality, which results into alteration of bone stiffness immensely. The prime goal of this study is to design the optimum dental implant considering the mechanical response at bone implant interfaces for a patient with specific bone quality. Method. 3D model of mandible and natural molar tooth were prepared from CT scan data while, dental implants were modelled using different diameter, length and porosity and FE analysis was carried out. Based on the variation in bone density, five different bone qualities were considered. First, failure analysis of implants, under maximum biting force of 250N had been performed; next, the implants, those survived were selected for observing the mechanical response at bone implant interfaces under common chewing load of 120N. Result. Maximum Von Mises stress did not surpass the yield strength of the implant material (TiAl4V). However, factor of safety of 1.5 was considered and all but two dental implants survived the design stress or allowable stress. Under 120N load, distribution of Von Mises stress and strain at the bone-implant interface corresponding to the rest of the implants for five bone conditions were obtained and enlisted. Conclusion. Implants, exhibiting interface strain within 1500-3000 microstrain range show the best bone remodelling and osseointegration. So, implant models, having this range of interface strains were selected corresponding to the particular bone quality. A set of optimum dental implants for each of the bone qualities were predicted.

6

Tensor Framework and Combined Symmetry for Hypertext Mining

Saha S., Murthy C.A., Pal S.K.

Fundamenta Informaticae

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2009

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Vol. 97, nr 1/2

215-234

EN

We have made a case here for utilizing tensor framework for hypertext mining. Tensor is a generalization of vector and tensor framework discussed here is a generalization of vector space model which is widely used in the information retrieval and web mining literature. Most hypertext documents have an inherent internal tag structure and external link structure that render the desirable use of multidimensional representations such as those offered by tensor objects. We have focused on the advantages of Tensor Space Model, in which documents are represented using sixth-order tensors. We have exploited the local-structure and neighborhood recommendation encapsulated by the proposed representation. We have defined a similarity measure for tensor objects corresponding to hypertext documents, and evaluated the proposed measure for mining tasks. The superior performance of the proposed methodology for clustering and classification tasks of hypertext documents have been demonstrated here. The experiment using different types of similarity measure in the different components of hypertext documents provides the main advantage of the proposed model. It has been shown theoretically that, the computational complexity of an algorithm performing on tensor framework using tensor similarity measure as distance is at most the computational complexity of the same algorithmperforming on vector space model using vector similarity measure as distance.

7

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.

8

Semi-GAPS: A Semi-supervised Clustering Method Using Point Symmetry

Saha S., Bandyopadhyay S.

Fundamenta Informaticae

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2009

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Vol. 96, nr 1/2

195-209

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.

9

MR Brain Image Segmentation Using A Multi-seed Based Automatic Clustering Technique

Saha S., Bandyopadhyay S.

Fundamenta Informaticae

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2009

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Vol. 97, nr 1/2

199-214

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.

10

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.

11

Fuzzy Symmetry Based Real-Coded Genetic Clustering Technique for Automatic Pixel Classification in Remote Sensing Imagery

Saha S., Bandyopadhyay S.

Fundamenta Informaticae

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2008

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Vol. 84, nr 3-4

471-492

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.

12

Rough set Based Ensemble Classifier for Web Page Classification

Saha S., Murthy C.A., Pal S.K.

Fundamenta Informaticae

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2007

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Vol. 76, nr 1-2

171-187

EN

Combining the results of a number of individually trained classification systems to obtain a more accurate classifier is a widely used technique in pattern recognition. In this article, we have introduced a rough set based meta classifier to classify web pages. The proposed method consists of two parts. In the first part, the output of every individual classifier is considered for constructing a decision table. In the second part, rough set attribute reduction and rule generation processes are used on the decision table to construct a meta classifier. It has been shown that (1) the performance of the meta classifier is better than the performance of every constituent classifier and, (2) the meta classifier is optimal with respect to a quality measure defined in the article. Experimental studies show that the meta classifier improves accuracy of classification uniformly over some benchmark corpora and beats other ensemble approaches in accuracy by a decisive margin, thus demonstrating the theoretical results. Apart from this, it reduces the CPU load compared to other ensemble classification techniques by removing redundant classifiers from the combination.

13

Reflection and refraction of quasi-SV waves at the interface of the monoclinic media

Chattopadhyay A., Saha S.

Acta Geophysica Polonica

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1999

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Vol. 47, nr 3

307-322

EN

Reflection and refraction phenomena of quasi-SV waves at a plane interface of two monoclinic half-spaces have been discussed. It has been pointed out that due to incident quasi-SV wave in a monoclinic medium, the three types of waves exist: quasi-P (qP), quasi-SV (qSV) and quasi-SH (qSH). The reflection and refraction coefficients for qP, qSV and qSH waves have been computed. The effects due to the crystalline nature of the medium have been distinctly marked. The results are presented graphically and compared with the isotropic case.