Robust fuzzyclustering for object recognition and classification of relational data

Prototype based fuzzy clustering algorithms have unique ability to partition the data while detecting multiple clusters simultaneously. However since real data is often contaminated with noise, the clustering methods need to be made robust to be useful in practice. This dissertation focuses on robust detection of multiple clusters from noisy range images for object recognition. Dave\u27s noise clustering (NC) method has been shown to make prototype-based fuzzy clustering techniques robust. In this work, NC is generalized and the new NC membership is shown to be a product of fuzzy c-means (FCM) membership and robust M-estimator weight (or possibilistic membership). Thus the generalized NC approach is shown to have the partitioning ability of FCM and robustness of M-estimators. Since the NC (or FCM) algorithms are based on fixed-point iteration technique, they suffer from the problem of initializations. To overcome this problem, the sampling based robust LMS algorithm is considered by extending it to fuzzy c-LMS algorithm for detecting multiple clusters. The concept of repeated evidence has been incorporated to increase the speed of the new approach. The main problem with the LMS approach is the need for ordering the distance data. To eliminate this problem, a novel sampling based robust algorithm is proposed following the NC principle, called the NLS method, that directly searches for clusters in the maximum density region of the range data without requiring the specification of number of clusters. The NC concept is also introduced to several fuzzy methods for robust classification of relational data for pattern recognition. This is also extended to non-Euclidean relational data. The resulting algorithms are used for object recognition from range images as well as for identification of bottleneck parts while creating desegregated cells of machine/ components in cellular manufacturing and group technology (GT) applications

A Mean Field Approach to Empirical Bayes Estimation in High-dimensional Linear Regression

We study empirical Bayes estimation in high-dimensional linear regression. To facilitate computationally efficient estimation of the underlying prior, we adopt a variational empirical Bayes approach, introduced originally in Carbonetto and Stephens (2012) and Kim et al. (2022). We establish asymptotic consistency of the nonparametric maximum likelihood estimator (NPMLE) and its (computable) naive mean field variational surrogate under mild assumptions on the design and the prior. Assuming, in addition, that the naive mean field approximation has a dominant optimizer, we develop a computationally efficient approximation to the oracle posterior distribution, and establish its accuracy under the 1-Wasserstein metric. This enables computationally feasible Bayesian inference; e.g., construction of posterior credible intervals with an average coverage guarantee, Bayes optimal estimation for the regression coefficients, estimation of the proportion of non-nulls, etc. Our analysis covers both deterministic and random designs, and accommodates correlations among the features. To the best of our knowledge, this provides the first rigorous nonparametric empirical Bayes method in a high-dimensional regression setting without sparsity.Comment: 38 pages, 1 figure; Clarified some details in this draf

Cosmological evolution in a two-brane warped geometry model

We study an effective 4-dimensional scalar-tensor field theory, originated from an underlying brane-bulk warped geometry, to explore the scenario of inflation. It is shown that the inflaton potential naturally emerges from the radion energy-momentum tensor which in turn results into an inflationary model of the Universe on the visible brane that is consistent with the recent results from the Planck's experiment. The dynamics of modulus stabilization from the inflaton rolling condition is demonstrated. The implications of our results in the context of recent BICEP2 results are also discussed.Comment: 11 pages, Latex style, 4 eps figures and 1 tabl

Inventory Model with Ramp-type Demand and Price Discount on Back Order for Deteriorating Items under Partial Backlogging

Modeling of inventory problems provides a good insight to retailers and distributors to maintain stock of different items such as seasonal products, perishable goods and daily useable goods etc. The deterioration of all these items exists to a certain extent due to several reasons like mishandling, evaporation, decay, environmental conditions, transportation etc. It is found from the literature that previously many of the researchers have developed inventory model ignoring deterioration and drawn conclusion. In the absence of deterioration parameter, an inventory model cannot be completely realistic. In this paper, we have made an attempt to extend an inventory model with ramp-type demand and price discount on back order where deterioration was not taken into account. In our study, deterioration and constant holding cost are taken into consideration keeping all other parameters same. As a result, the inventory cost function is newly constructed in the presence of deterioration. The objective of this investigation is to obtain optimal cycle length, time of occurrence of shortages and corresponding inventory cost. This extended model is solved for minimum value of average inventory cost analytically. A theorem is framed to characterize the optimal solution. To validate the proposed model, a numerical example is taken and convexity of the cost function is verified. In order to study the effect of changes of different parameters of the inventory system on optimal cycle length, time of occurrence of shortages and average inventory cost, sensitivity analyses have been performed. Also, the numerical result and sensitivity analyses are graphically presented in the respective section of this paper to demonstrate the model. This study reveals that a better solution can be obtained in the presence of our newly introduced assumptions in the existing model

Cambios temporales en la diversidad de los cangrejos braquiuros a lo largo de un hábitat heterogéneo del manglar indio de Sundarban

The present study investigates the effect of different habitat attributes on brachyuran crab diversity in two different study sites in the Sundarban mangrove, India. The two sites differ in the level of anthropogenic intrusion and in the age of the mangrove forest. Seasonal changes in the environment and in brachyuran faunal abundance were recorded for three years. Species composition varied between the two habitats irrespective of season. The habitat heterogeneity and the recorded crab community was analysed by several univariate and multivariate statistical techniques. The newly replanted mangrove site showed lesser diversity than the natural one. Ocypodid crabs, mainly Uca rosea, dominated both study sites, whereas Uca triangularis was totally absent from the replanted site. Canonical correspondence analysis showed that the total acidity, total alkalinity, pH content of water, total dissolved solids, inorganic phosphate content of water, soil specific gravity, soil density and the physical constructions of the habitat play a crucial role in moderating the crab community structure. This study reveals that brachyuran crab diversity can be used as a potential indicator of the alterations of mangrove habitats.El presente estudio investiga el efecto de las diferentes características de hábitat sobre la diversidad de los cangrejos braquiuros en dos lugares diferentes del manglar Sundarban, India. Los dos sitios difieren en el nivel de intrusión antropogénica, así como en la edad del bosque de manglar. Se registraron cambios estacionales en el medio y en la abundancia de la fauna de braquiuros durante tres años. A pesar de las diferencias estacionales, la composición de especies difiere en los dos hábitats. Se analizó la heterogeneidad del hábitat y la comunidad de cangrejos mediante técnicas estadísticas univariantes y multivariantes. La zona de manglares replantada recientemente mostró menor diversidad que la zona natural. Los cangrejos ocipódidos, principalmente Uca rosea, dominaron en ambas zonas de estudio, mientras que Uca triangularis estuvo totalmente ausente en la zona replantada. El análisis de Correspondencia Canónica (CCA) mostró que la acidez total, la alcalinidad total, el contenido de pH del agua, los sólidos totales disueltos (TDS), el contenido de fosfato inorgánico del agua, el peso específico del suelo, la densidad del suelo, junto con las construcciones físicas del hábitat desempeñan un papel fundamental en la estructura de la comunidad de cangrejos. Este estudio revela que la diversidad de los cangrejos braquiuros puede ser utilizada como un potencial indicador de las alteraciones de los hábitats de manglares