J. Derek Tucker

Generative models for functional data using phase and amplitude separation

Constructing generative models for functional observations is an important task in statistical functional analysis. In general, functional data contains both phase (or x or horizontal) and amplitude (or y or vertical) variability. Traditional methods often ignore the phase variability and focus solely on the amplitude variation, using cross-sectional techniques such as fPCA for dimensional reduction and data modeling. Ignoring phase variability leads to a loss of structure in the data and inefficiency in data models. This paper presents an approach that relies on separating the phase ( x -axis) and amplitude ( y -axis), then modeling these components using joint distributions. This separation, in turn, is performed using a technique called elastic shape analysis of curves that involves a new mathematical representation of functional data. Then, using individual fPCAs, one each for phase and amplitude components, it imposes joint probability models on principal coefficients of these components while respecting the nonlinear geometry of the phase representation space. These ideas are demonstrated using random sampling, for models estimated from simulated and real datasets, and show their superiority over models that ignore phase-amplitude separation. Furthermore, the generative models are applied to classification of functional data and achieve high performance in applications involving SONAR signals of underwater objects, handwritten signatures, and periodic body movements recorded by smart phones.

Underwater target detection from multi-platform sonar imagery using multi-channel coherence analysis

This paper introduces a new target detection method for multiple disparate sonar platforms. The detection method is based upon multi-channel coherence analysis (MCA) framework which allows one to optimally decompose the multichannel data to analyze their linear dependence or coherence. This decomposition then allows one to extract MCA features which can be used to discriminate between two hypotheses, one corresponding to the presence of a target and one without, through the use of the log-likelihood ratio. Test results of the proposed detection system were applied to a data set of underwater side-scan sonar imagery provided by the Naval Surface Warfare Center (NSWC), Panama City. This database contains data from 4 disparate sonar systems, namely one high frequency (HF) sonar and three broadband (BB) sonars coregistered over the same area on the sea floor. Test results illustrate the effectiveness of the proposed multi-platform detection system in terms of probability of detection, false alarm rate, and receiver operating characteristic (ROC) curves.

Analysis of proteomics data: Phase amplitude separation using an extended Fisher-Rao metric

Abstract: We consider the problem of alignment and classification of proteomics data, that is described in Koch et al. [4], using the Extended FisherRao (EFR) framework introduced in [6]. We demonstrate this framework by separating amplitude and phase components of functional data from patients having therapeutic treatments for Acute Myeloid Leukemia (AML). Then, using individual functional principal component analysis, for both the phase and amplitude components [8], we obtain bases for principal subspaces and model the data by imposing probability models on principal coefficients. Lastly, using the distances calculated from individual components, we demonstrate a successful discrimination between responders and non-responders to treatment for AML.

Generalized likelihood ratio test for finite mixture model of K-distributed random variables

In this paper a new detection method for sonar imagery is developed for K-distributed background clutter using a finite mixture model (FMM) of K-distributions. The method for estimation of the parameters of the FMM and a generalized log-likelihood ratio test is derived. The detector is compared to the corresponding counterparts derived for the standard K-, Gaussian, and Rayleigh distributions. Test results of the proposed method on a data set of synthetic aperture sonar (SAS) images is also presented. This database contains images with synthetically generated targets of different shapes inserted into real SAS background imagery. Results illustrating the effectiveness of theFMMK-distributed detector are presented in terms of probability of detection, false alarm rates, and receiver operating characteristic (ROC) curves for various bottom clutter conditions.

Target detection from dual disparate sonar platforms using canonical correlations

In this paper a new coherence-based feature extraction method for sonar imagery generated from two disparate sonar systems is developed. Canonical correlation analysis (CCA) is employed to identify coherent information from co-registered regions of interest (ROIs) that contain target activities, while at the same time extract useful coherent features from both images. The extracted features can be used for simultaneous detection and classification of target and non-target objects in the sonar images. In this study, a side-scan sonar that provides high resolution images with good target definition and a broadband sonar that generates low resolution images, but with reduced background clutter. The optimum Neyman-Pearson detector will be presented and then extended to the dual sensor platform scenarios. Test results of the proposed methods on a dual sonar imagery data set provided by the Naval Surface Warfare Center (NSWC) Panama City, FL will be presented. This database contains co-registered pair of images over the same target field with varying degree of detection difficulty and bottom clutter. The effectiveness of CCA as the optimum detection tool is demonstrated in terms of probability of detection and false alarm rate.

Multi-sonar target detection using multi-channel coherence analysis

The use of multiple disparate platforms in many remote sensing and surveillance applications allows one to exploit the coherent information shared among all sensory systems thereby potentially reducing the risk of making single-sensory biased detection and classification decisions. This paper introduces a target detection method based upon multi-channel coherence analysis (MCA) framework which optimally decomposes the multi-channel data to analyze their linear dependence or coherence. This decomposition then allows one to extract MCA features that can be used to implement a coherence-based detector. This detector is applied to a data set of underwater side-scan sonar imagery provided by the Naval Surface Warfare Center Panama City Division. This database contains data from 2 disparate sonar systems, namely one high frequency (HF) sonar and one broadband (BB) sonar coregistered over the same region on the sea floor. Test results illustrate the effectiveness of the proposed multi-platform detection system in terms of probability of detection, false alarm rate, and receiver operating characteristic (ROC) curves.

Neyman Pearson detection of K-distributed random variables

In this paper a new detection method for sonar imagery is developed in K-distributed background clutter. The equation for the log-likelihood is derived and compared to the corresponding counterparts derived for the Gaussian and Rayleigh assumptions. Test results of the proposed method on a data set of synthetic underwater sonar images is also presented. This database contains images with targets of different shapes inserted into backgrounds generated using a correlated K-distributed model. Results illustrating the effectiveness of the K-distributed detector are presented in terms of probability of detection, false alarm, and correct classification rates for various bottom clutter scenarios.

Statistical analysis and classification of acoustic color functions

In this paper we present a method for clustering and classification of acoustic color data based on statistical analysis of functions using square-root velocity functions (SVRF). The convenience of the SVRF is that it transforms the Fisher-Rao metric into the standard L2 metric. As a result, a formal distance can be calculated using geodesic paths. Moreover, this method allows optimal deformations between acoustic color data to be computed for any two targets allowing for robustness to measurement error. Using the SVRF formulation statistical models can then be constructed using principal component analysis to model the functional variation of acoustic color data. Empirical results demonstrate the utility of functional data analysis for improving performance results in pattern recognition using acoustic color data.

Analysis of signals under compositional noise with applications to SONAR data

We consider the problem of estimation and classification of signals in presence of compositional noise, where the traditional techniques do not provide either a consistent estimator for signals or a robust distance for classification. We use a recently introduced comprehensive framework that: (1) uses a distance-based objective function for data alignment leading to a consistent estimator of signals, (2) combines the classical data and smoothness terms for signal registration in a natural fashion, obviating the need for an arbitrary relative weight, and (3) leads to warping-invariant distances between signals for robust clustering and classification. We use this framework to introduce two pairwise distances that can be used for signal classification: (1) a y-distance which is the distance between the aligned signals and (2) an x-distance, that measures the amount of warping needed to align the signals. This problem is motivated by automatic target recognition in underwater acoustic data, where the task of clustering and classifying objects using acoustic spectrum is complicated by the uncertainties in aspect angles at data collections. Small changes in the aspect angles corrupt signals in a way that amounts to compositional noise. We demonstrate the use of this framework in classification of spectral signatures in acoustic data and highlight improvements in signal classification over current methods.

Compressive sensing for Gauss-Gauss detection

The recently introduced theory of compressed sensing (CS) enables the reconstruction of sparse signals from a small set of linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist rate samples. However, despite the intense focus on the reconstruction of signals, many signal processing problems do not require a full reconstruction of the signal and little attention has been paid to doing inference in the CS domain. In this paper we show the performance of CS for the problem of signal detection using Gauss-Gauss detection. We investigate how the J-divergence and Fisher Discriminant are affected when used in the CS domain. In particular, we demonstrate how to perform detection given the measurements without ever reconstructing the signals themselves and provide theoretical bounds on the performance. A numerical example is provided to demonstrate the effectiveness of CS under Gauss-Gauss detection.