arXiv subjects

Ranjan Maitra

Publications and source records attributed to Ranjan Maitra.

35 records · Page 2Linked to original sources

arXiv2021

Fast model-based clustering of partial records

Partially recorded data are frequently encountered in many applications and usually clustered by first removing incomplete cases or features with missing values, or by imputing missing values, followed by application of a clustering algorithm to the resulting altered dataset. Here, we develop clustering methodology through a model-based approach using the marginal density for the observed values, assuming a finite mixture model of multivariate $t$ distributions. We compare our approximate algorithm to the corresponding full expectation-maximization (EM) approach that considers the missing values in the incomplete data set and makes a missing at random (MAR) assumption, as well as case deletion and imputation methods. Since only the observed values are utilized, our approach is computationally more efficient than imputation or full EM. Simulation studies demonstrate that our approach has favorable recovery of the true cluster partition compared to case deletion and imputation under various missingness mechanisms, and is at least competitive with the full EM approach, even when MAR assumptions are violated. Our methodology is demonstrated on a problem of clustering gamma-ray bursts and is implemented at https://github.com/emilygoren/MixtClust.

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arXiv2021

An Efficient $k$-modes Algorithm for Clustering Categorical Datasets

Mining clusters from data is an important endeavor in many applications. The $k$-means method is a popular, efficient, and distribution-free approach for clustering numerical-valued data, but does not apply for categorical-valued observations. The $k$-modes method addresses this lacuna by replacing the Euclidean with the Hamming distance and the means with the modes in the $k$-means objective function. We provide a novel, computationally efficient implementation of $k$-modes, called OTQT. We prove that OTQT finds updates to improve the objective function that are undetectable to existing $k$-modes algorithms. Although slightly slower per iteration due to algorithmic complexity, OTQT is always more accurate per iteration and almost always faster (and only barely slower on some datasets) to the final optimum. Thus, we recommend OTQT as the preferred, default algorithm for $k$-modes optimization.

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arXiv2021

Fracture Mechanics-Based Quantitative Matching of Forensic Evidence Fragments

Fractured metal fragments with rough and irregular surfaces are often found at crime scenes. Current forensic practice visually inspects the complex jagged trajectory of fractured surfaces to recognize a ``match'' using comparative microscopy and physical pattern analysis. We developed a novel computational framework, utilizing the basic concepts of fracture mechanics and statistical analysis to provide quantitative match analysis for match probability and error rates. The framework employs the statistics of fracture surfaces to become non-self-affine with unique roughness characteristics at relevant microscopic length scale, dictated by the intrinsic material resistance to fracture and its microstructure. At such a scale, which was found to be greater than two grain-size or micro-feature-size, we establish that the material intrinsic properties, microstructure, and exposure history to external forces on an evidence fragment have the premise of uniqueness, which quantitatively describes the microscopic features on the fracture surface for forensic comparisons. The methodology utilizes 3D spectral analysis of overlapping topological images of the fracture surface and classifies specimens with very high accuracy using statistical learning. Cross correlations of image-pairs in two frequency ranges are used to develop matrix variate statistical models for the distributions among matching and non-matching pairs of images, and provides a decision rule for identifying matches and determining error rates. A set of thirty eight different fracture surfaces of steel articles were correctly classified. The framework lays the foundations for forensic applications with quantitative statistical comparison across a broad range of fractured materials with diverse textures and mechanical properties.

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arXiv2020

Kernel-estimated Nonparametric Overlap-Based Syncytial Clustering

Commonly-used clustering algorithms usually find ellipsoidal, spherical or other regular-structured clusters, but are more challenged when the underlying groups lack formal structure or definition. Syncytial clustering is the name that we introduce for methods that merge groups obtained from standard clustering algorithms in order to reveal complex group structure in the data. Here, we develop a distribution-free fully-automated syncytial clustering algorithm that can be used with $k$-means and other algorithms. Our approach estimates the cumulative distribution function of the normed residuals from an appropriately fit $k$-groups model and calculates the estimated nonparametric overlap between each pair of clusters. Groups with high pairwise overlap are merged as long as the estimated generalized overlap decreases. Our methodology is always a top performer in identifying groups with regular and irregular structures in several datasets and can be applied to datasets with scatter or incomplete records. The approach is also used to identify the distinct kinds of gamma ray bursts in the Burst and Transient Source Experiment 4Br catalog and the distinct kinds of activation in a functional Magnetic Resonance Imaging study.

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arXiv2020

Estimating Basis Functions in Massive Fields under the Spatial Mixed Effects Model

Spatial prediction is commonly achieved under the assumption of a Gaussian random field (GRF) by obtaining maximum likelihood estimates of parameters, and then using the kriging equations to arrive at predicted values. For massive datasets, fixed rank kriging using the Expectation-Maximization (EM) algorithm for estimation has been proposed as an alternative to the usual but computationally prohibitive kriging method. The method reduces computation cost of estimation by redefining the spatial process as a linear combination of basis functions and spatial random effects. A disadvantage of this method is that it imposes constraints on the relationship between the observed locations and the knots. We develop an alternative method that utilizes the Spatial Mixed Effects (SME) model, but allows for additional flexibility by estimating the range of the spatial dependence between the observations and the knots via an Alternating Expectation Conditional Maximization (AECM) algorithm. Experiments show that our methodology improves estimation without sacrificing prediction accuracy while also minimizing the additional computational burden of extra parameter estimation. The methodology is applied to a temperature data set archived by the United States National Climate Data Center, with improved results over previous methodology.

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arXiv2019

A Matrix--free Likelihood Method for Exploratory Factor Analysis of High-dimensional Gaussian Data

This paper proposes a novel profile likelihood method for estimating the covariance parameters in exploratory factor analysis of high-dimensional Gaussian datasets with fewer observations than number of variables. An implicitly restarted Lanczos algorithm and a limited-memory quasi-Newton method are implemented to develop a matrix-free framework for likelihood maximization. Simulation results show that our method is substantially faster than the expectation-maximization solution without sacrificing accuracy. Our method is applied to fit factor models on data from suicide attempters, suicide ideators and a control group.

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arXiv2019

Classification with the matrix-variate-$t$ distribution

Matrix-variate distributions can intuitively model the dependence structure of matrix-valued observations that arise in applications with multivariate time series, spatio-temporal or repeated measures. This paper develops an Expectation-Maximization algorithm for discriminant analysis and classification with matrix-variate $t$-distributions. The methodology shows promise on simulated datasets or when applied to the forensic matching of fractured surfaces or the classification of functional Magnetic Resonance, satellite or hand gestures images.

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arXiv2019

FAST Adaptive Smoothing and Thresholding for Improved Activation Detection in Low-Signal fMRI

Functional Magnetic Resonance Imaging is a noninvasive tool for studying cerebral function. Many factors challenge activation detection, especially in low-signal scenarios that arise in the performance of high-level cognitive tasks. We provide a fully automated fast adaptive smoothing and thresholding (FAST) algorithm that uses smoothing and extreme value theory on correlated statistical parametric maps for thresholding. Performance on experiments spanning a range of low-signal settings is very encouraging. The methodology also performs well in a study to identify the cerebral regions that perceive only-auditory-reliable or only-visual-reliable speech stimuli.

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arXiv2019

TiK-means: $K$-means clustering for skewed groups

The $K$-means algorithm is extended to allow for partitioning of skewed groups. Our algorithm is called TiK-Means and contributes a $K$-means type algorithm that assigns observations to groups while estimating their skewness-transformation parameters. The resulting groups and transformation reveal general-structured clusters that can be explained by inverting the estimated transformation. Further, a modification of the jump statistic chooses the number of groups. Our algorithm is evaluated on simulated and real-life datasets and then applied to a long-standing astronomical dispute regarding the distinct kinds of gamma ray bursts.

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arXiv2019

Efficient Bandwidth Estimation in Two-dimensional Filtered Backprojection Reconstruction

A generalized cross-validation approach to estimate the reconstruction filter bandwidth in two-dimensional Filtered Backprojection is presented. The method writes the reconstruction equation in equivalent backprojected filtering form, derives results on eigendecomposition of symmetric two-dimensional circulant matrices and applies them to make bandwidth estimation a computationally efficient operation within the context of standard backprojected filtering reconstruction. Performance evaluations on a wide range of simulated emission tomography experiments give promising results. The superior performance holds at both low and high total expected counts, pointing to the method's applicability even in weaker signal-noise situations. The approach also applies to the more general class of elliptically symmetric filters, with reconstruction performance often better than even that obtained with the true optimal radially symmetric filter.

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arXiv2018

An efficient $k$-means-type algorithm for clustering datasets with incomplete records

The $k$-means algorithm is arguably the most popular nonparametric clustering method but cannot generally be applied to datasets with incomplete records. The usual practice then is to either impute missing values under an assumed missing-completely-at-random mechanism or to ignore the incomplete records, and apply the algorithm on the resulting dataset. We develop an efficient version of the $k$-means algorithm that allows for clustering in the presence of incomplete records. Our extension is called $k_m$-means and reduces to the $k$-means algorithm when all records are complete. We also provide initialization strategies for our algorithm and methods to estimate the number of groups in the dataset. Illustrations and simulations demonstrate the efficacy of our approach in a variety of settings and patterns of missing data. Our methods are also applied to the analysis of activation images obtained from a functional Magnetic Resonance Imaging experiment.

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arXiv2018

Multivariate $t$-Mixtures-Model-based Cluster Analysis of BATSE Catalog Establishes Importance of All Observed Parameters, Confirms Five Distinct Ellipsoidal Sub-populations of Gamma Ray Bursts

Determining the kinds of gamma-ray bursts (GRBs) has been of interest to astronomers for many years. We analyzed 1599 GRBs from the Burst and Transient Source Experiment (BATSE) 4Br catalogue using $t$-mixtures-model-based clustering on all nine observed parameters ($T_{50}$, $T_{90}$, $F_1$, $F_2$, $F_3$, $F_4$, $P_{64}$, $P_{256}$, $P_{1024}$) and found evidence of five types of GRBs. Our results further refine the findings of Chattopadhyay and Maitra (2017) by providing groups that are more distinct. Using the Mukherjee et al. (1998) classification scheme, also used by Chattopadhyay and Maitra (2017), of duration, total fluence ($F_t = F_1 + F_2 + F_3 + F_4$)) and spectrum (using Hardness Ratio $H_{321} = F_3/(F_1 + F_2)$) our five groups are classified as long-intermediate-intermediate, short-faint-intermediate, short-faint-soft, long-bright-hard, and long-intermediate-hard. We also classify 374 GRBs in the BATSE catalogue that have incomplete information in some of the observed variables (mainly the four time integrated fluences $F_1$, $F_2$, $F_3$ and $F_4$) to the five groups obtained, using the 1599 GRBs having complete information in all the observed variables. Our classification scheme puts 138 GRBs in the first group, 52 GRBs in the second group, 33 GRBs in the third group, 127 GRBs in the fourth group and 24 GRBs in the fifth group.

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arXiv2018

Reduced Basis Kriging for Big Spatial Fields

In spatial statistics, a common method for prediction over a Gaussian random field (GRF) is maximum likelihood estimation combined with kriging. For massive data sets, kriging is computationally intensive, both in terms of CPU time and memory, and so fixed rank kriging has been proposed as a solution. The method however still involves operations on large matrices, so we develop an alteration to this method by utilizing the approximations made in fixed rank kriging combined with restricted maximum likelihood estimation and sparse matrix methodology. Experiments show that our methodology can provide additional gains in computational efficiency over fixed-rank kriging without loss of accuracy in prediction. The methodology is applied to climate data archived by the United States National Climate Data Center, with very good results.

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arXiv2017

Merging $K$-means with hierarchical clustering for identifying general-shaped groups

Clustering partitions a dataset such that observations placed together in a group are similar but different from those in other groups. Hierarchical and $K$-means clustering are two approaches but have different strengths and weaknesses. For instance, hierarchical clustering identifies groups in a tree-like structure but suffers from computational complexity in large datasets while $K$-means clustering is efficient but designed to identify homogeneous spherically-shaped clusters. We present a hybrid non-parametric clustering approach that amalgamates the two methods to identify general-shaped clusters and that can be applied to larger datasets. Specifically, we first partition the dataset into spherical groups using $K$-means. We next merge these groups using hierarchical methods with a data-driven distance measure as a stopping criterion. Our proposal has the potential to reveal groups with general shapes and structure in a dataset. We demonstrate good performance on several simulated and real datasets.

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arXiv2017

Gaussian-Mixture-Model-based Cluster Analysis Finds Five Kinds of Gamma Ray Bursts in the BATSE Catalog

Clustering methods are an important tool to enumerate and describe the different coherent kinds of Gamma Ray Bursts (GRBs). But their performance can be affected by a number of factors such as the choice of clustering algorithm and inherent associated assumptions, the inclusion of variables in clustering, nature of initialization methods used or the iterative algorithm or the criterion used to judge the optimal number of groups supported by the data. We analyzed GRBs from the BATSE 4Br catalog using $k$-means and Gaussian Mixture Models-based clustering methods and found that after accounting for all the above factors, all six variables -- different subsets of which have been used in the literature -- and that are, namely, the flux duration variables ($T_{50}$, $T_{90}$), the peak flux ($P_{256}$) measured in 256-millisecond bins, the total fluence ($F_t$) and the spectral hardness ratios ($H_{32}$ and $H_{321}$) contain information on clustering. Further, our analysis found evidence of five different kinds of GRBs and that these groups have different kinds of dispersions in terms of shape, size and orientation. In terms of duration, fluence and spectrum, the five types of GRBs were characterized as intermediate/faint/intermediate, long/intermediate/soft, intermediate/intermediate/intermediate, short/faint/hard and long/bright/intermediate.

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arXiv2017

A Statistical Framework for Improved Automatic Flaw Detection in Nondestructive Evaluation Images

Nondestructive evaluation (NDE) techniques are widely used to detect flaws in critical components of systems like aircraft engines, nuclear power plants and oil pipelines in order to prevent catastrophic events. Many modern NDE systems generate image data. In some applications an experienced inspector performs the tedious task of visually examining every image to provide accurate conclusions about the existence of flaws. This approach is labor-intensive and can cause misses due to operator ennui. Automated evaluation methods seek to eliminate human-factors variability and improve throughput. Simple methods based on peak amplitude in an image are sometimes employed and a trained-operator-controlled refinement that uses a dynamic threshold based on signal-to-noise ratio (SNR) has also been implemented. We develop an automated and optimized detection procedure that mimics these operations. The primary goal of our methodology is to reduce the number of images requiring expert visual evaluation by filtering out images that are overwhelmingly definitive on the existence or absence of a flaw. We use an appropriate model for the observed values of the SNR-detection criterion to estimate the probability of detection. Our methodology outperforms current methods in terms of its ability to detect flaws.

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arXiv2011

A nonstationary nonparametric Bayesian approach to dynamically modeling effective connectivity in functional magnetic resonance imaging experiments

Effective connectivity analysis provides an understanding of the functional organization of the brain by studying how activated regions influence one other. We propose a nonparametric Bayesian approach to model effective connectivity assuming a dynamic nonstationary neuronal system. Our approach uses the Dirichlet process to specify an appropriate (most plausible according to our prior beliefs) dynamic model as the "expectation" of a set of plausible models upon which we assign a probability distribution. This addresses model uncertainty associated with dynamic effective connectivity. We derive a Gibbs sampling approach to sample from the joint (and marginal) posterior distributions of the unknowns. Results on simulation experiments demonstrate our model to be flexible and a better candidate in many situations. We also used our approach to analyzing functional Magnetic Resonance Imaging (fMRI) data on a Stroop task: our analysis provided new insight into the mechanism by which an individual brain distinguishes and learns about shapes of objects.

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