arXiv subjects

Sabyasachi Mukhopadhyay

Publications and source records attributed to Sabyasachi Mukhopadhyay.

26 records · Page 2Linked to original sources

arXiv2013

Wavelet and Fast Fourier Transform based analysis of Solar Image

Both of Wavelet and Fast Fourier Transform are strong signal processing tools in the field of Data Analysis. In this paper fast fourier transform (FFT) and Wavelet Transform are employed to observe some important features of Solar image (December, 2004). We have tried to find out the periodicity and coherence of different sections of the solar image. We plotted the distribution of energy in solar surface by analyzing the solar image with scalograms and 3D-coefficient plots.

cs.CV↗

arXiv2013

Wavelet Transform-Based Analysis of QRS complex in ECG Signals

In the present paper we have reported a wavelet based time-frequency multiresolution analysis of an ECG signal. The ECG (electrocardiogram), which records hearts electrical activity, is able to provide with useful information about the type of Cardiac disorders suffered by the patient depending upon the deviations from normal ECG signal pattern. We have plotted the coefficients of continuous wavelet transform using Morlet wavelet. We used different ECG signal available at MIT-BIH database and performed a comparative study. We demonstrated that the coefficient at a particular scale represents the presence of QRS signal very efficiently irrespective of the type or intensity of noise, presence of unusually high amplitude of peaks other than QRS peaks and Base line drift errors. We believe that the current studies can enlighten the path towards development of very lucid and time efficient algorithms for identifying and representing the QRS complexes that can be done with normal computers and processors.

cs.CE↗

arXiv2013

Clustering Categorical Time Series into Unknown Number of Clusters: A Perfect Simulation based Approach

Pamminger and Fruwirth-Schnatter (2010) considered a Bayesian approach to model-based clustering of categorical time series assuming a fixed number of clusters. But the popular methods for selecting the number of clusters, for example, the Bayes Information Criterion (BIC), turned out to have severe problems in the categorical time series context. In this paper, we circumvent the difficulties of choosing the number of clusters by adopting the Bayesian semiparametric mixture model approach introduced by Bhattacharya (2008), who assume that the number of clusters is a random quantity, but is bounded above by a (possibly large) number of clusters. We adopt the perfect simulation approach of Mukhopadhyay and Bhattacharya (2012) for posterior simulation for completely solving the problems of convergence of the underlying Markov chain Monte Carlo (MCMC) approach. Importantly, within our main perfect simulation algorithm, there arose the necessity to simulate perfectly from the joint distribution of a set of continuous random variables with log-concave full conditional densities. We propose and develop a novel and efficient perfect simulation methodology for joint distributions with log-concave full conditionals. This perfect sampling methodology is of independent interest as well since in a very large and important class of Bayesian applications the full conditionals turn out to be log-concave. We will consider application of our model and methodology to the Austrian wage mobility data, also analysed by Pamminger and Fruwirth-Schnatter (2010), and adopting the methods developed in Mukhopadhyay et al. (2011), Mukhopadhyay et al. (2012), will obtain the posterior modes of clusterings and also the desired highest posterior distribution credible regions of the posterior distribution of clusterings.

stat.ME↗

arXiv2013

Application of Vertex coloring in a particular triangular closed path structure and in Krafts inequality

A good deal of research has been done and published on coloring of the vertices of graphs for several years while studying of the excellent work of those maestros, we get inspire to work on the vertex coloring of graphs in case of a particular triangular closed path structure what we achieve from the front view of a pyramidal structure. From here we achieve a repetitive nature of vertex coloring in case of odd and even number of horizontal lines within this triangular structure. In order to apply this repetitive nature of vertex coloring in case of a binary tree, we get a success in Krafts Inequality. Actually our work mainly deals with a particular triangular closed path vertex coloring and repetition of the vertex coloring nature in case of the Krafts inequality in the field of Information Theory and Coding.

cs.DM↗

arXiv2012

Perfect Simulation for Mixtures with Known and Unknown Number of components

We propose and develop a novel and effective perfect sampling methodology for simulating from posteriors corresponding to mixtures with either known (fixed) or unknown number of components. For the latter we consider the Dirichlet process-based mixture model developed by these authors, and show that our ideas are applicable to conjugate, and importantly, to non-conjugate cases. As to be expected, and, as we show, perfect sampling for mixtures with known number of components can be achieved with much less effort with a simplified version of our general methodology, whether or not conjugate or non-conjugate priors are used. While no special assumption is necessary in the conjugate set-up for our theory to work, we require the assumption of bounded parameter space in the non-conjugate set-up. However, we argue, with appropriate analytical, simulation, and real data studies as support, that such boundedness assumption is not unrealistic and is not an impediment in practice. Not only do we validate our ideas theoretically and with simulation studies, but we also consider application of our proposal to three real data sets used by several authors in the past in connection with mixture models. The results we achieved in each of our experiments with either simulation study or real data application, are quite encouraging.

stat.CO↗

arXiv2011

On Bayesian "central clustering": Application to landscape classification of Western Ghats

Landscape classification of the well-known biodiversity hotspot, Western Ghats (mountains), on the west coast of India, is an important part of a world-wide program of monitoring biodiversity. To this end, a massive vegetation data set, consisting of 51,834 4-variate observations has been clustered into different landscapes by Nagendra and Gadgil [Current Sci. 75 (1998) 264--271]. But a study of such importance may be affected by nonuniqueness of cluster analysis and the lack of methods for quantifying uncertainty of the clusterings obtained. Motivated by this applied problem of much scientific importance, we propose a new methodology for obtaining the global, as well as the local modes of the posterior distribution of clustering, along with the desired credible and "highest posterior density" regions in a nonparametric Bayesian framework. To meet the need of an appropriate metric for computing the distance between any two clusterings, we adopt and provide a much simpler, but accurate modification of the metric proposed in [In Felicitation Volume in Honour of Prof. B. K. Kale (2009) MacMillan]. A very fast and efficient Bayesian methodology, based on [Sankhyā Ser. B 70 (2008) 133--155], has been utilized to solve the computational problems associated with the massive data and to obtain samples from the posterior distribution of clustering on which our proposed methods of summarization are illustrated.

stat.AP↗

arXiv2011

Characteristic noise features in light transmission across membrane protein undergoing photocycle

We demonstrate a technique based on noise measurements which can be utilized to study dynamical processes in protein assembly. Direct visualization of dynamics in membrane protein system such as bacteriorhodopsin (bR) upon photostimulation are quite challenging. bR represents a model system where the stimulus-triggered structural dynamics and biological functions are directly correlated. Our method utilizes a pump-probe near field microscopy method in the transmission mode and involves analyzing the transmittance fluctuations from a finite size of molecular assembly. Probability density distributions indicating the effects of finite size and statistical correlations appear as a characteristic frequency distribution in the noise spectra of bR whose origin can be traced to photocycle kinetics. Valuable insight into the molecular processes were obtained from the noise studies of bR and its mutant D96N as a function of external parameters such as temperature, humidity or presence of an additional pump source.

physics.chem-ph↗

arXiv2009

Fast Bayesian Semiparametric Curve-Fitting and Clustering in Massive Data With Application to Cosmology

Recent technological advances have led to a flood of new data on cosmology rich in information about the formation and evolution of the universe, e.g., the data collected in Sloan Digital Sky Survey (SDSS) for more than 200 million objects. The analyses of such data demand cutting edge statistical technologies. Here, we have used the concept of mixture model within Bayesian semiparametric methodology to fit the regression curve with the bivariate data for the apparent magnitude and redshift for Quasars in SDSS (2007) catalogue. Associated with the mixture modeling is a highly efficient curve-fitting procedure, which is central to the application considered in this paper. Moreover, we adopt a new method for analysing the posterior distribution of clusterings, also generated as a by-product of our methodology. The results of our analysis of the cosmological data clearly indicate the existence of four change points on the regression curve andposssibiltiy of clustering of quasars specially at high redshift. This sheds new light not only on the issue of evolution, existence of acceleration or decceleration and environment around quasars at high redshift but also help us to estimate thecosmological parameters related to acceleration or decceleration.

astro-ph.CO↗