Piecewise Linear Discriminant Analysis Research Articles

Gamma-ray anomaly detector for airborne surveys based on a machine learning methodology

Machine learning methods were used to develop an automated classification model for detecting gamma-ray spectra with anomalous (i.e., non-background) signatures collected during airborne surveys. Spectra were preprocessed with an altitude-based normalization procedure, followed by application of a digital filter to remove baseline and noise effects. Segments of the preprocessed spectra were then used as input patterns to piecewise linear discriminant analysis (PLDA). For use in building the classification model, a training set was constructed based on two data classes: (1) spectra containing various radioisotope signatures and (2) background spectra. Through the use of a piecewise linear discriminant based on seven separating boundaries, a general-purpose spectral anomaly detector was developed for use in the automated screening of large spectral datasets collected during airborne surveys. The intended application of the methodology is to aid first responders in locating lost or stolen radioactive sources or in managing other incidents in which radioactive material is released into the environment. In developing and testing the methodology, laboratory spectra, spectra collected during airborne surveys, and mathematically synthesized spectra were used. When applied to 17 airborne surveys in which known radioisotope sources were present, the anomaly detector was able to locate each source with high confidence. While false detections were observed at a rate of 3.7%, many of these were in the vicinity of the known source location but the radioisotope signature could not be visually observed in the spectrum. For false detections away from the source locations, elevated signatures from naturally occurring background components were typically observed.

Nocturnal Hypoglycemic Alarm Based on Near-Infrared Spectroscopy: In Vivo Studies with a Rat Animal Model.

A noninvasive method for detecting episodes of nocturnal hypoglycemia is demonstrated with in vivo measurements made with a rat animal model. Employing spectra collected from the near-infrared combination region of 4000-5000 cm-1, piecewise linear discriminant analysis (PLDA) is used to classify spectra into alarm and nonalarm data classes on the basis of whether or not they correspond to glucose concentrations below a user-defined hypoglycemic threshold. A reference spectrum and corresponding glucose concentration are acquired at the start of the monitoring period, and spectra are then collected continuously and converted to absorbance units relative to the initial reference spectrum. The resulting differential spectra correspond to differential glucose concentrations that reflect the differences in concentration between each spectrum and the reference. Given an alarm threshold (e.g., 3.0 mM), a database of calibration differential spectra can be partitioned into two groups containing spectra above and below the threshold. A classification model is then computed with PLDA. The resulting model can be applied to the differential spectra collected during the monitoring period in order to identify spectra whose corresponding glucose concentrations lie in the hypoglycemic range. In this work, the alarm algorithm was tested in two single-day studies performed with anesthetized rats. Glucose concentrations spanned the range of 1.6 to 13.5 mM (29 to 244 mg/dL). For both rats, the alarm algorithm performed well. On average, 87.5% of alarm events were correctly detected, and the occurrence of false alarms was 7.2%. False alarms were restricted to times when the glucose concentrations were very close to the alarm threshold rather than at random times, thus demonstrating the potential of the approach for practical use.

Nocturnal hypoglycemic alarm based on near-infrared spectroscopy: In vitro simulation studies

An alarm algorithm for detecting episodes of nocturnal hypoglycemia is demonstrated in simulation studies that incorporate the use of a tissue phantom. Based on transmission spectra collected in the near-infrared combination region of 4000–5000 cm−1, pattern recognition methods are used to classify spectra into alarm and non-alarm data classes on the basis of whether or not they signify a glucose excursion below a user-defined hypoglycemic alarm threshold. A reference spectrum and corresponding glucose concentration are acquired at the start of the monitoring period, and absorbance values of subsequent spectra are computed relative to this reference. The resulting differential spectra reflect differential glucose concentrations that correspond to the differences in concentration between each spectrum and the reference. Given the alarm threshold, a database of calibration differential spectra are partitioned into those above and below the threshold. Piecewise linear discriminant analysis is then used to compute a classification model that can be applied to differential spectra collected during the monitoring period in order to identify spectra that signal glucose concentrations in the hypoglycemic range. This alarm algorithm is demonstrated in two multiple-day dynamic studies that incorporate a tissue phantom composed of films of keratin and collagen that approximate the thicknesses of the corresponding proteins found in human tissue.

Simulated Radiance Profiles for Automating the Interpretation of Airborne Passive Multi-Spectral Infrared Images

Methodology is developed for simulating the radiance profiles acquired from airborne passive multispectral infrared imaging measurements of ground sources of volatile organic compounds (VOCs). The simulation model allows the superposition of pure-component laboratory spectra of VOCs onto spectral backgrounds that simulate those acquired during field measurements conducted with a downward-looking infrared line scanner mounted on an aircraft flying at an altitude of 2000-3000 ft (approximately 600-900 m). Wavelength selectivity in the line scanner is accomplished through the use of a multichannel Hg:Cd:Te detector with up to 16 integrated optical filters. These filters allow the detection of absorption and emission signatures of VOCs superimposed on the upwelling infrared background radiance within the instrumental field of view (FOV). By combining simulated radiance profiles containing analyte signatures with field-collected background signatures, supervised pattern recognition methods can be employed to train automated classifiers for use in detecting the signatures of VOCs during field measurements. The targeted application for this methodology is the use of the imaging system to detect releases of VOCs during emergency response scenarios. In the work described here, the simulation model is combined with piecewise linear discriminant analysis to build automated classifiers for detecting ethanol and methanol. Field data collected during controlled releases of ethanol, as well as during a methanol release from an industrial facility, are used to evaluate the methodology.

Remote Detection of Volatile Organic Compounds by Passive Multispectral Infrared Imaging Measurements

Automated pattern recognition methodology is described for the detection of signatures of volatile organic compounds from passive multispectral infrared imaging data collected from an aircraft platform. Data are acquired in an across-track scanning mode with a downward-looking line scanner based on 8 to 16 spectral channels in the 8-14 and 3-5 microm spectral ranges. Two controlled release experiments are performed in which plumes of ethanol are generated and detected from aircraft overflights at altitudes of 2200 to 2800 ft (671 to 853 m). In addition, a methanol release from a chemical manufacturing facility is monitored. Automated classifiers are developed by application of piecewise linear discriminant analysis to the calibrated, registered, and preprocessed radiance data acquired by the line scanner. Preprocessing steps evaluated include contrast enhancement, temperature-emissivity separation, feature selection, and feature extraction/noise reduction by the minimum noise fraction (MNF) transform. Successful classifiers are developed for both compounds and are tested with data not used in the classifier development. Separation of temperature and emissivity by use of the alpha residual calculation is found to reduce false positive detections to a negligible level, and the MNF transform is shown to enhance detection sensitivity.

Mathematical programming models for piecewise-linear discriminant analysis

Mathematical programming (MP) discriminant analysis models are widely used to generate linear discriminant functions that can be adopted as classification models. Nonlinear classification models may have better classification performance than linear classifiers, but although MP methods can be used to generate nonlinear discriminant functions, functions of specified form must be evaluated separately. Piecewise-linear functions can approximate nonlinear functions, and two new MP methods for generating piecewise-linear discriminant functions are developed in this paper. The first method uses maximization of classification accuracy (MCA) as the objective, while the second uses an approach based on minimization of the sum of deviations (MSD). The use of these new MP models is illustrated in an application to a test problem and the results are compared with those from standard MCA and MSD models.

Robust classifier for the automated detection of ammonia in heated plumes by passive fourier transform infrared spectrometry.

An automated classification algorithm is implemented for the detection of ammonia vapor in heated plumes by passive Fourier transform infrared (FT-IR) spectrometry. This classification methodology allows the real-time detection of chemical signatures in gaseous effluents such as those generated from industrial processes. The characteristics of real-time implementation and excellent robustness are achieved by an analysis strategy based on the application of band-pass digital filters to short segments of the interferogram data collected by the FT-IR spectrometer, followed by the use of piecewise linear discriminant analysis to obtain a yes/no classification regarding the presence of the analyte signature in the filtered data. The optimal classifier developed through this work is based on only 110 interferogram points and employs a single band-pass filter centered at 945 cm(-)(1) with a pass-band full width at half-maximum of 93 cm(-)(1). The average stop-band attenuation of the optimal filter is 42.1 dB. The robustness of the algorithm is tested by exposing it to chemical releases of sulfur hexafluoride, ethanol, methanol, sulfur dioxide, and hydrogen chloride that were not included in the development of the classifier. Excellent classification performance is demonstrated, with missed ammonia detections occurring at a rate of approximately 1%. The occurrence of false detections is less than 0.1% for SF(6) and less than 0.02% for the other interferences tested.

Automated Detection of Chemical Vapors by Pattern Recognition Analysis of Passive Multispectral Infrared Remote Sensing Imaging Data

Pattern recognition methods are developed for the automated interpretation of passive multispectral imaging data collected from an airborne platform. Through the use of an infrared line scanner equipped with 14 spectral bandpass filters, passive infrared images are collected of an ammonia plant within a nitrogen fertilizer facility. Piecewise linear discriminant analysis is used to implement an automated algorithm for the detection of scene pixels that correspond to chemical vapor signatures. A separate classifier is used to detect the presence of hot carbon dioxide (CO2) within the images. In the assembly of training and prediction data for the development of both classifiers, the K-means clustering algorithm is used together with knowledge of the site to assign pixels to the plume/nonplume and CO2/non-CO2 categories. The effects of temperature variation within the imaged scene are removed from the data through the use of an algorithm for separating the contributions of temperature and emissivity to the Planck equation. Averaged across four data runs containing a total of 3.5 million pixels, the resulting discriminants are observed to detect approximately 91% of the plume pixels while achieving a false detection rate of less than 0.01%. The corresponding performance criteria for the CO2 classifier are a successful detection of approximately 94% of the pixels with a CO2 signature and a false detection rate of less than 0.7%. The robustness of the CO2 classifier is further enhanced through the adoption of a probability-based classification rule.

Calibration Transfer in the Automated Detection of Acetone by Passive Fourier Transform Infrared Spectrometry

The qualitative determination of acetone is performed by passive Fourier transform infrared (FT-IR) spectrometry with data spanning two spectrometers. Digital filtering and piecewise linear discriminant analysis techniques are optimized and applied directly to short interferogram segments to eliminate background and instrument variation and then perform pattern recognition. Once optimized, this methodology classifies remote sensing data into categories representing the presence or absence of the analyte in an automated fashion. The addition to the training set of small numbers of interferogram data from a second spectrometer is evaluated in the creation of qualitative models robust with respect to differences between the instruments. Results of these experiments show that classification percentages averaged across all tested interferogram segments are improved from 76.2 ± 6.4% to 95.1 ± 2.2% with the addition of as few as 10 background interferograms collected in the field with the secondary instrument. The results also demonstrate that a broader, more optimal range of segments in the interferogram can be utilized when these background data are added from the secondary instrument. It is also found possible to standardize the data from the secondary instrument with blackbody background interferograms collected in the laboratory.

Artificial neural networks for the automated detection of trichloroethylene by passive Fourier transform infrared spectrometry

Artificial neural networks are applied to the automated classification of trichloroethylene (TCE) signatures from passive Fourier transform infrared remote sensing interferogram data. Through the use of three data collection methods, a combination of laboratory and field data is acquired that allows the methodology to be evaluated under a variety of infrared background conditions and in the presence of potentially interfering compounds such as sulfur hexafluoride, methyl ethyl ketone, acetone, carbon tetrachloride, and ammonia. To maximize the computational efficiency of the network optimization, experimental design techniques are employed to develop a training protocol for the network that takes into account the relationships among five variables that are related either to the network architecture or to the training process. This protocol is implemented for the case of a back-propagation neural network (BNN) and is used to develop an optimized network for the detection of TCE. The classification performance of the network is assessed by comparing both TCE detection capabilities and false detection rates to similar classification results obtained with the technique of piecewise linear discriminant analysis (PLDA). When applied to prediction data withheld from the optimization of both the BNN and PLDA algorithms, the BNN method is observed to outperform PLDA overall, with TCE detection rates in excess of 99% and false detection rates less than 0.5%.

Calibration transfer algorithm for automated qualitative analysis by passive Fourier transform infrared spectrometry

The automated qualitative analysis of passive Fourier transform infrared (FT-IR) remote sensing data is made difficult by the presence in the data of background and instrument-specific variation. For data collected with a single instrument, variation in the data arises from changes in the infrared background radiance, changes in the atmospheric composition within the field-of-view of the spectrometer, and changes in the instrument response function arising from temperature variation in the spectrometer. When more than one spectrometer is used, the variation in detector responses and phase signatures between instruments serves to complicate further the task of implementing an automated processing algorithm for detecting the signature of a target compound. In this work, a combination of signal processing and pattern recognition methodology is applied directly to the interferogram data collected by the FT-IR spectrometer to implement an automated compound detection procedure that is independent of background and instrument-specific variation. The key to this algorithm is the use of highly attenuating digital filters to isolate in the interferogram the frequencies associated with an analyte absorption or emission band while suppressing information at other frequencies. For the test compounds, acetone and sulfur hexafluoride, it is demonstrated that when this digital filtering procedure is coupled with either piecewise linear discriminant analysis or a back-propagation neural network, an automated detection algorithm can be developed with data from a primary instrument and then subsequently used to predict the presence of analyte signatures in data collected with a secondary spectrometer. Correct classification rates in excess of 92% are obtained for both compounds when the algorithm is applied to data collected with the secondary instrument.

Automated Detection of Trichloroethylene by Fourier Transform Infrared Remote Sensing Measurements

Passive Fourier transform infrared (FT-IR) remote sensing measurements are used to implement the automated detection of trichloroethylene (TCE) vapor in the presence of a variety of infrared background signatures. Through the use of a combination of bandpass digital filtering and piecewise linear discriminant analysis, this detection procedure is applied directly to short segments of the interferogram data collected by the FT-IR spectrometer. Data employed in this work were collected during open-air/passive cell terrestrial and passive cell laboratory measurements. Infrared backgrounds employed included terrain, low-angle sky, and water backgrounds, in addition to laboratory blackbody measurements. Other potentially interfering chemical species present were carbon tetrachloride, acetone, methyl ethyl ketone, and sulfur hexafluoride (SF6). These data are used to assemble two data sets of differing complexity. Optimization studies are performed separately with each data set to study the influence of filter bandpass position, bandpass width, interferogram segment location, and segment size on the ability to detect TCE. The optimal parameters found consist of a Gaussian-shaped filter positioned at 939.5 cm-1, with a width at half-height of 123.4 cm-1. This filter is applied to interferogram points 111−220 (relative to the centerburst). When applied to a prediction set of 60 000 interferograms, the piecewise linear discriminant developed on the basis of these optimal parameters is found to detect TCE successfully in 96.2% of the cases in which it is present. The overall rate of false detections is 0.5%. The limit of detection of TCE is found to be 102 ppm-m at a temperature difference of 10.5 °C between the infrared background and the analyte. SF6 is observed to provide the greatest spectral interference among the compounds tested, producing a false detection rate of 8.6%. It is found that this false detection rate can be reduced to 1.5% through the development of a probability-based interpretation of the piecewise linear discriminant results. These results are observed to compare favorably with those obtained in a separate analysis of filtered single-beam spectra.

Genetic algorithms for the optimization of piecewise linear discriminants

The application of genetic algorithms (GAs) to the optimization of piecewise linear discriminants is described. Piecewise linear discriminant analysis (PLDA) is a supervised pattern recognition technique employed in this work for the automated classification of Fourier transform infrared (FTIR) remote sensing data. PLDA employs multiple linear discriminants to approximate a nonlinear separating surface between data categories defined in a vector space. The key to the successful implementation of PLDA is the positioning of the individual discriminants that comprise the piecewise linear discriminant. For the remote sensing application, the discriminant optimization is challenging due to the large number of input variables required and the corresponding tendency for local optima to occur on the response surface of the optimization. In this work, three implementations of GAs are configured and evaluated: a binary-coded GA (GAB), a real-coded GA (GAR), and a Simplex-GA hybrid (SGA). GA configurations are developed by use of experimental design studies, and piecewise linear discriminants for acetone, methanol, and sulfur hexafluoride are optimized (trained). The training and prediction classification results indicate that GAs area viable approach for discriminant optimization. On average, the best piecewise linear discriminant optimized by a GA is observed to classify 11% more analyte-active patterns correctly in prediction than an unoptimized piecewise linear discriminant. Discriminant optimization problems not used in the experimental design study are employed to test the stability of the GA configurations. For these cases, the best piecewise linear discriminant optimized by SGA is shown to classify 19% more analyte-active patterns correctly in prediction than an unoptimized discriminant. These results also demonstrate that the two real number coded GAs (GAR and SGA) perform better than the GAB. Real number coded GAs are also observed to execute faster and are simpler to implement.

Comparison of optimization algorithms for piecewise linear discriminant analysis: application to Fourier transform infrared remote sensing measurements

Simplex optimization, simulated annealing, generalized simulated annealing, genetic algorithms, and a Simplex-genetic algorithm hybrid are compared for their ability to optimize piecewise linear discriminants. Nonparametric piecewise linear discriminant analysis (PLDA) is employed here to develop an automated detection scheme for Fourier transform infrared remote sensing interferogram data. Piecewise linear discriminants are computed and optimized for interferograms collected when sulfur hexafluoride, acetone, and methanol were present in the optical path of the spectrometer. The success of this methodology is based on the proper positioning of the discriminant. Discriminant optimization is a challenging problem due to the tendency for local optima to occur on the response surface and the large number of variables being optimized. Among the methods compared in the context of the remote sensing application, Simplex optimization is found to be the best method for discriminant optimization. Discriminants positioned using Simplex optimization are observed to consistently outperform discriminants positioned using algorithms based on simulated annealing and genetic algorithms. The justification for this result is based on three arguments. First, a good starting point for the optimization is available in the PLDA application and only a limited number of response function evaluations are possible due to the requirement of the remote sensing application. These features create an optimization problem that favors Simplex optimization. Second, the response surface is smooth near the starting point and becomes increasingly rugged as the optimal region is approached. Simplex could move quickly at first and then move from local optima through the use of a kick operator. Third, the variables being optimized are highly correlated with each other. The effect of a variable on the response function score is highly dependent on the current values of the other variables. Epistatic optimization problems such as this are very difficult for genetic algorithms but do not impact the performance of Simplex optimization.

Ridge regression techniques for the optimization of piecewise linear discriminants: application to Fourier transform infrared remote sensing measurements

An optimization procedure for piecewise linear discriminant analysis is described based on the application of ridge regression techniques. The method is based on the use of a matrix transformation that stabilizes data that exhibit a high degree of collinearity. Linear discriminants computed from collinear data exhibit imprecision in the estimation of the discriminant coefficients. The transform described here produces a perturbed data matrix in which the degree of collinearity has been decreased and which can be used in place of the original for subsequent discriminant calculations. The degree of stabilization provided by the transform is specified by the user in the form of a perturbation constant. The discriminant optimization procedure is demonstrated with an application in which an automated algorithm is implemented for the detection of SF 6 by Fourier transform infrared remote sensing measurements. A detailed study is described in which 96 data sets are investigated consisting of four different numbers of observations, four different dimensionalities, and six different levels of the perturbation constant. The results of this study indicate that the optimization procedure significantly improves the precision of discriminants computed with collinear data. The level of improvement is greatest in the case of greatest collinearity.