Smarajit Bose

Multilayer statistical classifiers

A number of methods based on nonparametric regression have been developed in the last few years which are capable of approximating highly nonlinear class boundaries in classification problems. Bose (Comput. Statist. Data Anal. 22 (1996) 505) used additive splines for estimating the conditional class probabilities, and showed that the resulting method classification using splines (CUS) can achieve reasonably low misclassification error rates in many problems.This paper presents a powerful modification of CUS which we call the method of successive projections. This method can be used for any nonparametric regression based classification method but has been illustrated in this paper using mainly CUS, for simplicity and computational considerations. It seems to reduce the misclassification error rate of CUS in complex problems.

Generalized quadratic discriminant analysis

In linear discriminant analysis, the assumption of equality of the dispersion matrices of different classes leads to a classification rule based on minimum Mahalanobis distance from the class centres. However, without this assumption, the resulting quadratic discriminant classifier involves, in addition to the Mahalanobis distances, the ratio of the determinants of the dispersion matrices as a factor. In fact, it has been observed that, for discriminating between populations with underlying elliptically symmetric distributions, such classifiers also incorporate similar factors, apart from the Mahalanobis distances.In this paper, a nonparametric classification technique which generalizes discriminant analysis has been proposed. The method of cross-validation is used to make the technique adaptive to a given dataset. An extensive simulation study is presented to illustrate the potential of the method. Finally, through implementation on a number of real-life data sets, it has been demonstrated that the proposed generalized quadratic discriminant analysis (GQDA) compares very favourably with other nonparametric methods, and is computationally cost-effective. HighlightsA nonparametric classification technique has been proposed.It generalizes Fisher?s discriminant analysis.Cross-validation is used to make the technique adaptive to given data.Found empirically to compare very favourably with other nonparametric methods.Computationally cost-effective.

Modeling Bimodal Discrete Data Using Conway-Maxwell-Poisson Mixture Models

Bimodal truncated count distributions are frequently observed in aggregate survey data and in user ratings when respondents are mixed in their opinion. They also arise in censored count data, where the highest category might create an additional mode. Modeling bimodal behavior in discrete data is useful for various purposes, from comparing shapes of different samples (or survey questions) to predicting future ratings by new raters. The Poisson distribution is the most common distribution for fitting count data and can be modified to achieve mixtures of truncated Poisson distributions. However, it is suitable only for modeling equidispersed distributions and is limited in its ability to capture bimodality. The Conway–Maxwell–Poisson (CMP) distribution is a two-parameter generalization of the Poisson distribution that allows for over- and underdispersion. In this work, we propose a mixture of CMPs for capturing a wide range of truncated discrete data, which can exhibit unimodal and bimodal behavior. We present methods for estimating the parameters of a mixture of two CMP distributions using an EM approach. Our approach introduces a special two-step optimization within the M step to estimate multiple parameters. We examine computational and theoretical issues. The methods are illustrated for modeling ordered rating data as well as truncated count data, using simulated and real examples.

Backfitting Neural Networks

SummaryRegression and classification problems can be viewed as special cases of the problem of function estimation. It is rather well known that a two-layer perceptron with sigmoidal transformation functions can approximate any continuous function on the compact subsets ofRP if there are sufficient number of hidden nodes. In this paper, we present an algorithm for fitting perceptron models, which is quite different from the usual backpropagation or Levenberg-Marquardt algorithm. This new algorithm based on backfitting ensures a better convergence than backpropagation. We have also used resampling techniques to select an ideal number of hidden nodes automatically using the training data itself. This resampling technique helps to avoid the problem of overfitting that one faces for the usual perceptron learning algorithms without any model selection scheme. Case studies and simulation results are presented to illustrate the performance of this proposed algorithm.

Robust discriminant analysis using weighted likelihood estimators

The procedures in traditional discriminant analysis suffer from serious lack of robustness under model misspecifications. Weighted likelihood estimators based on certain minimum divergence criteria have recently been shown (Markatou et al., 1998) to retain first order efficiency under the model while having attractive robustness properties away from it. In this paper, these estimators have been used to develop classifiers which are robust alternatives to Fishers discriminant analysis. Results of an extensive simulation study and some real data sets are presented to illustrate the usefulness of the proposed methods. *E-mail: ayanbasu@isical.ac.in †E-mail: smarajit@isical.ac.in

Gamma/hadron segregation for a ground based imaging atmospheric Cherenkov telescope using machine learning methods: Random Forest leads

A detailed case study of γ-hadron segregation for a ground based atmospheric Cherenkov telescope is presented. We have evaluated and compared various supervised machine learning methods such as the Random Forest method, Artificial Neural Network, Linear Discriminant method, Naive Bayes Classifiers, Support Vector Machines as well as the conventional dynamic supercut method by simulating triggering events with the Monte Carlo method and applied the results to a Cherenkov telescope. It is demonstrated that the Random Forest method is the most sensitive machine learning method for γ-hadron segregation.

SPEAKER IDENTIFICATION BY AGGREGATING GAUSSIAN MIXTURE MODELS (GMMs) BASED ON UNCORRELATED MFCC-DERIVED FEATURES

For solving speaker identification problems, the approach proposed by Reynolds [IEEE Signal Process. Lett.2 (1995) 46–48], using Gaussian Mixture Models (GMMs) based on Mel Frequency Cepstral Coefficients (MFCCs) as features, is one of the most effective available in the literature. The use of GMMs for modeling speaker identity is motivated by the interpretation that the Gaussian components represent some general speaker-dependent spectral shapes, and also by the capability of Gaussian mixtures to model arbitrary densities. In this work, we have initially illustrated, with the help of a new bilingual speech corpus, how the well-known principal component transformation, in conjunction with the principle of classifier combination can be used to enhance the performance of the MFCC-GMM speaker recognition systems significantly. Subsequently, we have emphatically and rigorously established the same using the benchmark speech corpus NTIMIT. A significant outcome of this work is that the proposed approach has the potential to enhance the performance of any speaker recognition system based on correlated features.

Minimum Distance Estimation of Milky Way Model Parameters and Related Inference

We propose a method to estimate the location of the Sun in the disk of the Milky Way using a method based on the Hellinger distance and construct confidence sets on our estimate of the unknown location using a bootstrap-based method. Assuming the Galactic disk to be two-dimensional, the sought solar location then reduces to the radial distance separating the Sun from the Galactic center and the angular separation of the Galactic center to Sun line, from a pre-fixed line on the disk. On astronomical scales, the unknown solar location is equivalent to the location of us earthlings who observe the velocities of a sample of stars in the neighborhood of the Sun. This unknown location is estimated by undertaking pairwise comparisons of the estimated density of the observed set of velocities of the sampled stars, with the density estimated using synthetic stellar velocity data sets generated at chosen locations in the Milky Way disk. The synthetic data sets are generated at a number of locations that we choose f...

Feature extraction for nonlinear classification

Following the idea of neural networks, multi-layer statistical classifier [3] was designed to capture interactions between measurement variables using nonlinear transformation of additive models. However, unlike neural nets, this statistical method can not readjust the initial features, and as a result it often leads to poor classification when those features are not adequate. This article presents an iterative algorithm based on backfitting which can modify these features dynamically. The resulting method can be viewed as an approach for estimating posterior class probabilities by projection pursuit regression, and the associated model can be interpreted as a generalized version of the neural network and other statistical models.

Sensitivity estimate of the MACE gamma ray telescope

The MACE (Major Atmospheric Cherenkov Experiment) is a 21 m diameter γ-ray telescope which is presently being installed at Hanle in Ladakh, India (32° 46′ 46″ N, 78° 58′ 35″ E) at an altitude of 4270 m a.s.l. Once operational, it will become the highest altitude very high energy (VHE) γ-ray telescope in the world based on Imaging Atmospheric Cherenkov Technique (IACT). In the present work, we discuss the sensitivity estimate of the MACE telescope by using a substantially large Monte Carlo simulation database at 5° zenith angle. The sensitivity of MACE telescope is estimated by carrying out the γ-hadron segregation using the Random Forest method. It is estimated that the MACE telescope will have an analysis energy threshold of 38 GeV for image intensities above 50 photoelectrons. The integral sensitivity for point like sources with Crab Nebula-like spectrum above 38 GeV is ∼2.7% of Crab Nebula flux at 5 σ statistical significance level in 50 h of observation.