Combined target factor analysis and Bayesian soft-classification of interference-contaminated samples: Forensic Fire Debris Analysis

Forensic Science International 222 (2012) 373–386

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Forensic Science International journal homepage: www.elsevier.com/locate/forsciint

Combined target factor analysis and Bayesian soft-classification of interference-contaminated samples: Forensic Fire Debris Analysis Mary R. Williams, Michael E. Sigman *, Jennifer Lewis, Kelly McHugh Pitan National Center for Forensic Science and Department of Chemistry, University of Central Florida, P.O. Box 162367, Orlando, FL 32816, USA

A R T I C L E I N F O

A B S T R A C T

Article history: Received 27 December 2011 Received in revised form 27 July 2012 Accepted 30 July 2012 Available online 21 August 2012

A Bayesian soft classification method combined with target factor analysis (TFA) is described and tested for the analysis of fire debris data. The method relies on analysis of the average mass spectrum across the chromatographic profile (i.e., the total ion spectrum, TIS) from multiple samples taken from a single fire scene. A library of TIS from reference ignitable liquids with assigned ASTM classification is used as the target factors in TFA. The class-conditional distributions of correlations between the target and predicted factors for each ASTM class are represented by kernel functions and analyzed by Bayesian decision theory. The soft classification approach assists in assessing the probability that ignitable liquid residue from a specific ASTM E1618 class, is present in a set of samples from a single fire scene, even in the presence of unspecified background contributions from pyrolysis products. The method is demonstrated with sample data sets and then tested on laboratory-scale burn data and large-scale field test burns. The overall performance achieved in laboratory and field test of the method is approximately 80% correct classification of fire debris samples. ß 2012 Elsevier Ireland Ltd. All rights reserved.

Keywords: Fire debris Factor analysis Bayesian decision theory Pattern classification Chemometrics

1. Introduction The determination of ignitable liquid residues in the presence of significant background interferences, typically arising from combustion and pyrolysis of building materials, is a challenge to the fire debris analyst and constitutes an important problem in the investigation of a possible arson. Most of the ignitable liquids commonly encountered in forensic casework are commercial products that may contain a large number of chemical constituents, i.e., gasoline. Some of the pyrolysis products formed in a structure fire may also be components of the ignitable liquid. When the contribution from the ignitable liquid is small relative to the pyrolysis contribution, and there is a coincidental matching of multiple components, even identifying the presence of an ignitable liquid can be a complicated forensic problem. On the other hand, when minor amounts of interferences are present, the challenge becomes one of identifying the possible origin of extraneous peaks in gas chromatography–mass spectrometry (GC–MS) data. In the United States, common practice requires that the ignitable liquid pattern of the total ion chromatogram be readily discernible by visual pattern recognition following the American Standard Testing and Materials (ASTM) E1618 Standard Test Method [1]. The problem is not one of identifying a specific ignitable liquid, i.e.

* Corresponding author. Tel.: +1 407 823 6469; fax: +1 407 823 3162. E-mail address: [email protected] (M.E. Sigman). 0379-0738/$ – see front matter ß 2012 Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.forsciint.2012.07.021

a specific brand of gasoline, but rather, it is a classification problem. In addition, contemporary methods of fire debris analysis do not assign error rates or correct classification probabilities, issues which are addressed in this work. The ignitable liquid residue signal must be sufficient to assign it to one of the seven classes of ignitable liquid defined in ASTM E1618, or the miscellaneous category defined in this same standard. The ASTM classes include gasoline (Gas), petroleum distillates (PD), isoparaffinic products (ISO), aromatic products (AR), naphthenic paraffinic products (NP), normal alkane products (NA) and oxygenated solvents (OXY). The classes may be subdivided based on carbon range as light (C4–C9), medium (C8–C13) and heavy (C8–C20+). For example, the PD class is frequently subdivided as light, medium and heavy petroleum distillates, designated as LPD, MPD and HPD, respectively. Miscellaneous solvents are best described as a ‘‘category’’ under ASTM E1618, since they do not possess defining class characteristics. The classification problem is further complicated for liquids in the oxygenate class, which may consist of oxygenated compounds in a mixture that would otherwise fall under a different ASTM E1618 classification. This paper directly addresses classification of ignitable liquid residue under ASTM E1618; however, the methodology is general and applicable to other classification standards. Classification schemes that are applicable across multiple organizations cannot be based upon highly variable parameters [2]. For example, chromatographic retention times often vary from laboratory to laboratory, and without the use of retention indices,

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peak alignment software tools, or transforming the data to remove the temporal dependence, chromatographic profiles do not form the basis for a rugged classification scheme. Covariance mapping has been demonstrated as a time-independent method for comparing GC–MS data from complex mixtures, and for searching a database to find a nearest match [3]. Covariance mapping has also been demonstrated to provide a method for discriminating between fresh gasoline samples at a known level of statistical significance [4]. Covariance mapping [5–8], and coincidence measurements [9], have also been applied to time-of-flight mass spectrometry to resolve correlated events. Calculating the covariance matrix for very large datasets is computational-resource and memory intensive. An alternative method based on a total ion spectrum (previously termed summed-ion spectrum) was shown to provide database search results similar to covariance mapping, and require fewer computational resources [10]. The total ion spectrum is an average mass spectrum measured over the chromatographic profile, and has been shown in an interlaboratory test of neat ignitable liquids to give 85% classification into the primary ASTM classes. The total ion spectrum (TIS) from complex ignitable liquids is coupled with a multivariate statistical technique and Bayesian decision theory to form the classification method described in this work. Multivariate statistical techniques have previously been applied to the classification and identification of ignitable liquids. The combined use of PCA and linear discriminant analysis (LDA) has been applied to a set of gasoline samples for the purpose of discriminating between samples [11–13]. The combined PCA/LDA method correctly classified 96% of the fresh gasoline samples and 51% of the evaporated gasoline samples. Comparison between gasoline from Australia and New Zealand by PCA/LDA correctly classified 79.2% of the Australian gasoline. These studies used reference liquid gasoline samples rather than fire debris samples. Principal components analysis (PCA) and soft independent modeling of class analogy (SIMCA) were tested for the classification of a set of 51 ignitable liquids chosen from five ASTM classes [14]. The methods were applied to the analysis of fresh ignitable liquids, evaporated liquids and liquids recovered after addition to burned and unburned matrix (i.e., wood, carpet). In those experiments the gasoline did not undergo weathering from the high temperatures of the fire. High correct classification rates were reported for SIMCA in these tests. In related work, PCA was combined with Pearson product moment correlation (PPMC) in an attempt to ‘‘associate’’ ignitable liquid residues to neat ignitable liquids in the presence of matrix interferences [15]. The study was limited to 12 ignitable liquids, two from each of six ASTM classes, and demonstrated the difficulties of showing quantifiable ‘‘associations’’ between neat ignitable liquids and ignitable liquid residues extracted from burned nylon carpet substrate. A comparison of gas chromatography–mass spectrometry (GC–MS) and gas chromatography–differential mobility spectrometry (GC– DMS) has been reported for the analysis of fire debris using projected difference resolution [16]. Two-way data analysis gave lower prediction errors than analysis of the one-way (chromatographic or integrated MS) data. Samples examined in the research were limited to seven ignitable liquids from different ASTM classes. The samples were examined as neat liquids, as residue extracted from unburned carpeting, and as simulated fire debris samples by recovering spikes from previously burned nylon and polyester carpets. The authors pointed out that the abundant fragment ions in the integrated MS spectra (equivalent to the TIS) provided enough information to classify different ignitable liquids, in agreement with previous reports [10]. The difficulties classifying chromatographic data caused by retention time drift and peak alignment, were also identified by the authors [16]. Notably, the integrated MS spectra performed nearly as well as the two-way

data for the neat and burned samples, but appeared to perform less well for the samples recovered from spiked carpets without burning. Unsupervised self-organizing feature maps (SOFM) have recently been used to link evaporated lighter fluids to their unevaporated ‘‘parent’’ samples for a set of 15 different liquids [17]. In the SOFM study, a set of 51 components common to all liquids used in the study were included in the model. Successful classification by lighter fluid brand required the use of hierarchical cluster analysis coupled with SOFM, whereas SOFM alone was reported to be more robust in identifying visual similarities and differences in the chromatographic data. The multivariate methods that have previously been applied to the classification of ignitable liquid residue in fire debris are not specifically designed to identify the ignitable liquid pattern in the presence of significant interfering background contributions. The problem is further complicated by the large number of possible interferences. This paper demonstrates a method that facilitates classification of ignitable liquid residue from fire debris into the ASTM E1618 classes in the presence of background interference, without knowledge of the spectral signature of the interference. The method relies on combined use of target factor analysis [18], and Bayesian decision theory [2]. The method calculates a Bayesian posterior probability for each ASTM class, which may either be used for a minimum-error-rate class assignment, or as a softclassifier to aid the analyst in data interpretation under the ASTM E1618 standard method. Data from laboratory-scale and largescale burns are analyzed, posterior probabilities for class assignment are calculated and an assessment of correct classification rates is given. The method is generally applicable to classification problems other than the forensic science example presented here. 2. Materials and methods Target factor analysis, described below, requires a library of test data (spectra), with each entry assigned to a given class. In this work, we use data from the Ignitable Liquid Reference Collection (ILRC), created and maintained by the National Center for Forensic Science (NCFS) in collaboration with the Technical Working Group for Fire and Explosions (TWGFEX). The ILRC contains GC–MS data for over 500 commercial ignitable liquids that have been assigned to the ASTM E1618 classes by TWGFEX forensic fire debris analysts. Spectra in the ILRC library originated from 20 mL of a reference ignitable liquid diluted with 1 mL of carbon disulfide and analyzed by GC–MS as described below. Similarly, GC–MS data for substrate pyrolysis products have been taken from the NCFS/TWGFEX Substrate Database. Spectra in the Substrate library originated from materials heated to produce pyrolysis and combustion products. These combustion and pyrolysis products were adsorbed onto activated carbon and then desorbed with carbon disulfide for GC–MS analysis, as described below. Laboratory-burn test samples were created by depositing ignitable liquids onto substrate materials prior to heating. Substrate materials were purchased from local home improvement and furniture stores. These materials were cut to approximately 6 cm2 in size. The heated samples were produced by a modified destructive distillation method based on a procedure developed by the State of Florida Bureau of Forensic Fire and Explosives Analysis. The material samples were placed up-side down in an un-lined metal quart-size paint can (Best Containers, Eagle, ID) and a lid with nine 1 mm diameter holes was laid loosely onto the can. Heat was applied to the bottom of the can by a propane torch held at a distance of 4 cm from the bottom. Once smoke appeared from the holes in the can lid, heating was continued for an additional 2 min. After 2 min, the heat was removed and the perforated lid was replaced with a solid lid to retain vapors within the headspace as the can returned to room temperature. The resulting combustion and pyrolysis products along with any ignitable liquid residue were adsorbed onto activated carbon (described below) and then desorbed with carbon disulfide for GC–MS analysis. The target factor data analysis method requires that multiple samples, each potentially containing differing contributions from an ignitable liquid and substrates, be analyzed as a composite dataset. Typically 6–12 samples were prepared from each ignitable liquid by varying the volume of ignitable liquid (25–2000 mL) or using different substrates in each can with a constant volume of ignitable liquid. Specific sample details are given in Table 2. The volatile components were extracted from each sample of fire debris and the data concatenated into a single data matrix for analysis, as described below. The large-scale burns were conducted in 2.4 m  2.4 m  6.1 m Konex shipping containers that had been built-out on the inside with sheetrock walls and ceiling, and flooring (plywood subfloor with carpet and padding, vinyl or wood laminate). The containers were furnished with a chair, sofa, bed and tables purchased from

M.R. Williams et al. / Forensic Science International 222 (2012) 373–386 commercial vendors. Additional clothing, papers and plastic items were added to increase the fuel load for the burns. Each container had a 1.2 m  1.2 m ‘‘window’’ flap in the rear, cut on three sides, to allow partial control of the amount of air provided to the fire. The fire was initiated by pouring 500 mL of an ignitable liquid on a trail leading from the front to the back of the container and placing a torch on one end of the pour trail. The large-scale burns were allowed to proceed for different periods of time, typically 5–15 min, during which time, the containers reached temperatures as high as 870 8C and the containers typically achieved a condition known as ‘‘flashover’’. Flashover is defined as ‘‘[a] transition phase in the development of a contained fire in which surfaces explosed to thermal radiation reach ignition temperature more or less simultaneously and fire spreads rapidly throughout the space’’ [19]. These burns consumed sufficient quantities of the ignitable liquid and produced pyrolysis products, giving samples resembling those obtained from structural fires encountered by forensic laboratories. After extinguishment and subsequent cool down of the container, fire debris samples were collected in various places throughout the container and deposited into individual one gallon metal paint cans. Any volatile compounds from the liquid residues and pyrolysis and combustion products were adsorbed onto activated carbon, as described in the following paragraph and subsequently desorbed with carbon disulfide for GC–MS analysis. The ignitable liquid residue along with pyrolysis and combustion products from the laboratory-scale and large-scale burns were collected by passive headspace adsorption onto activated carbon following the ASTM E1412-07 standard method [20]. A 10 mm  22 mm activated carbon strip (Albrayco Technologies, Inc., Cromwell, CT) was suspended into the headspace of the can by a paperclip and unwaxed dental floss. The sealed can was heated for 16–18 h at 66 8C. Once cooled to room temperature, the activated carbon strip was removed from the can and cut in half lengthwise. One half was archived and the other was deposited into a vial with 1 ml of low benzene carbon disulfide (Fisher Scientific) for GC–MS analysis. Gas chromatography–mass spectrometry analysis was performed utilizing an auto-sampler on an Agilent 6890 gas chromatograph interfaced to a 5973 mass spectrometer. One microliter of the CS2-diluted ignitable liquid was injected into a 250 8C injection port. The compounds were separated by a 100% dimethylpolysiloxane (HP-1) capillary column with a film thickness of 0.50 mm, a nominal diameter of 200 mm, and 25 m length. Helium gas was maintained at a constant flow rate of 0.8 mL/min with an average velocity of 36 cm/s. The injection was split in a 50:1 ratio. The initial oven temperature of 50 8C was held for 3 min, followed by a temperature ramp of 10 8C/min to a final temperature of 280 8C, which was held for 4 min. The mass spectrometer transfer line temperature was 280 8C with a source temperature of 230 8C and a quadrupole temperature of 150 8C. Mass spectra were scanned between 30 and 350 mass to charge ratio at an acquisition rate of 2.29 scans/s. The detector was turned on at 2.00 min after solvent elution. 2.1. Data treatment The target factor analysis method described in the following section requires the analysis of a set of multiple spectra taken from a single fire, or from a set of laboratory test burns as described above. In this study, typically 6–15 total ion spectra from individual GC–MS data sets were concatenated into a single matrix for analysis. The GC–MS data from each sample was exported as a comma-separated values file and the total ion spectrum (from 30 to 200 m/z) for each sample was calculated by summing each mass channel over the chromatographic profile and normalizing the data such that the intensities across the entire m/z range summed to one. Each row of the data matrix corresponded to a sample and each column corresponded to a variable (i.e., m/z ratio). The library spectra from the ILRC were prepared the same way and compiled for target factor analysis. 2.2. Target factor analysis (TFA) A set of spectra, each composed of multiple contributing factors, may be analyzed by target factor analysis (TFA), wherein the dimensionality of the data is first reduced by abstract factor analysis to identify a limited set of latent variables that represent a significant portion of the variance in the data, Eq. (1). The data matrix, [D], is expressed as the product of a scores matrix [Rz] and a loadings matrix [Cz], containing a limited number of eigenvectors that comprise the principle factors. The scores and loadings matrix containing only the principal factors are denoted by z in Eq. (1). The matrix [E] contains the error which accounts for the portion of [D] that is not reproduced by the product [Rz][Cz]. Determination of the number of latent variables to retain may be accomplished by various methods, including the determination of rank by median absolute deviation (DRMAD) used in this work [21]. h ih i ½D ¼ Rz C z þ ½E

(1)

The eigenvectors comprising [Cz] are ortho-normal and do not represent real (i.e., physically meaningful) spectra that contribute to [D]. The latent variables may contain contributions from the background pyrolysis components as well as contributions from the ignitable liquid residue. Oblique target factor rotations are used to identify spectra that are physically meaningful. The vector transformation is expressed mathematically as in Eq. (2), where [T] is the transformation matrix that

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brings about the oblique rotations and the error contribution, [E] has been dropped from Eq. (2). h i h i ½D ¼ Rz ½T ½T 1 C z

(2)

h iT 0 Tl ¼ C l C z

(3)

h 0

C l ¼ Tl C z

i

(4) 1

Identifying the entire transformation matrix [T] (or [T] ) in Eq. (2) is not necessary, since individual transformation vectors can be found one at a time. The 0 transformation vector Tl corresponding to the lth row transformation vector of 1 [T] can be found by Eq. (3), where C l is the test vector. The predicted vector C l is obtained by Eq. (4) and represents the least-squares prediction that best matches the test vector [18]. The test vectors in the case described here, come from a library of spectra. In Malinowski’s classic text [18], rotation of the scores factors, [Rz] was discussed; however, Eqs. (3) and (4) are easily derived from the same principles. The test vector C l and predicted vector C l will show a high degree of similarity (i.e., Pearson product moment correlation approaching 1, minimal distance metric, similarity approaching 1) if the test vector is a real factor that contributes to the data set. In this work, the Pearson product moment correlation coefficient, r, is used to judge the similarity of the test and predicted vectors. The property of target factor analysis that allows the search for one transformation vector at a time can then be utilized to identify factors that contribute to a data set and are representative of specific classes of analytes, even in the presence of interferences. 2.3. Assigning class membership Bayesian decision theory may be applied to a multiclass classification problem using Eq. (5). In Eq. (5), P(vijr) it posterior probability, p(rjvi) is the class-conditional probability, and P(vi) is prior probability that an object to be classified will belong to class vi [2]. Each class is characterized by one or more parameters; however, the discussion here will be limited to a single parameter, r. In this work, prior probabilities for all classes are set equal, so they cancel out of Eq. (5), and the classconditional probabilities will be approximated by kernel functions, as discussed below. The posterior probability that an object in question is a member of a given classis typically calculated at a prescribed value of the parameter(s), designated here as r. Assigning membership to the class with the largest posterior probability will produce a minimum-error-rate classification process with an associated risk equal to 1  P(vijrcalc) [2]. Alternatively, the poster probabilities may be utilized to estimate the degree of class membership, resulting in a Bayesian soft-classifier [22]. The soft-classifier approach may be preferable in fire debris analysis since the results allow the analyst to assess the probabilities and associated risks of assigning an ignitable liquid residue into an ASTM class. pðrjvi ÞPðvi Þ Pðvi jrÞ ¼ P i pðrjvi ÞPðvi Þ

(5)

In classification problems, it is common for each class to correspond to characteristic distribution of a parameter (i.e., r) or set of parameters, and the range of parameter values characterizing the class does not change. For the method under discussion here, the class-conditional probabilities, p(rjvi), are based on the distributions of Pearson correlations between test and predicted spectra for each class, and the correlations for each class change with every set of TFA results. It is necessary to calculate a set of class-conditional distributions, p(rjvi), following every TFA analysis. The kernel approximation, Eq. (6), expresses the classconditional probability as a superposition of Gaussian functions centered at the ni correlation values for each class vi [2]. The value hi is an adjustable bandwidth which may be calculated by Eq. (7), where Ai is an adaptive estimate of the spread in the correlations for class vi [23]. In Eq. (8), si is the sample standard deviation of the correlations corresponding to class vi, Ri is the inter-quartile range of the correlations for class vi, and min indicates that the minimum of the two values (si and Ri/1.34) is assigned to Ai. Eqs. (7) and (8) are reported to give a mean integrated squared error within 10% of the optimum for t-distributions, log-normal distributions with skewness up to 1.8 and for multimodal distributions [23]. pðrjvi Þ ¼

" # ni 1X 1 1 2 pffiffiffiffiffiffiffi exp ðr  r Þ j ni j¼1 hi 2p 2h2i 1=5

(6)

hi ¼ 0:9Ai ni

(7)

  R Ai ¼ min si ; i 1:34

(8)

When the posterior probability is calculated from Eq. (5), it is based on the relative probabilities at a specified correlation, r. The posterior probabilities based on Eq. (5) can vary significantly over a small range of r, especially if the classconditional probabilities have small variances, and there is no theoretical reason for choosing one r over another, with the possible exception of r = 1, where the test and predicted spectra are perfectly correlated. On the other hand, it would seem

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reasonable to assess classification by identifying the class with the highest probability of showing correlations between the test and predicted spectra that exceeds a specified lower limit, rLL. This probability is given by the integrated area under p(rjvi) for correlations exceeding rLL. Although r is theoretically bound to the interval [1,1], for classes giving high correlations between the test and predicted spectra, p(rjvi) may not go to zero at the boundary r = 1 due to a finite bandwidth hi in Eqs. (6) and (7). Consequently the integrated area over the interval [1,1] may be less than one. The boundary problem is addressed in this work by indirectly calculating the integrated area for r > rLL by the expression 1  Ii[1,rLL], where Ii[1,rLL] is the integrated are a under p(rjvi) between limits 1 and rLL, and is easily calculated by numerical integration. The posterior probability is now calculated by Eq. (9). ð1  Ii ½1; r LL ÞPðvi Þ Pðvi j½rLL ; 1Þ ¼ P i ð1  I i ½1; r LL ÞPðvi Þ

(9)

3. Results and discussion

Table 1 Simulation sample details. ID

Sample description

Ignitable liquids A1 BP regular unleaded gasoline, 25% weathered A2 Sunnyside odorless paint thinner A3 Ace premium quality charcoal lighter Pyrolyzed substrates S1 Carpet padding S2 Clear white oak laminate Olefin nylon blend carpet S3 S4 Roofing shingles S5 Yellow pine S6 PET polyester carpet and padding S7 Street smart boots S8 Vinyl floor S9 Polyurethane foam mattress S10 Cardboard box

TIS figure ASTM class Fig. 1a Fig. 1b Fig. 1c

Gas ISO MPD

Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig.

Sub Sub Sub Sub Sub Sub Sub Sub Sub Sub

2a 2b 2c 2d 2e 3a 3b 3c 3d 3e

3.1. Simulation studies The TFA method was tested on simulated data sets composed of representative total ion spectra from the ASTM classes Gas, ISO and MPD. The spectra are shown in Fig. 1a–c and ignitable liquid details are given in Table 1. The ignitable liquid total ion spectra were mixed in known quantities with pyrolysis products from up to 10 common building materials. The total ion spectra from pyrolysis products of substrates 1–5 are shown in Fig. 2, and the spectra for substrates 6–10 are shown in Fig. 3, sample details are given in Table 1. Comparison of the spectra in Figs. 1–3 show that the substrate pyrolysis spectra are, in general, more complex than the ignitable liquid spectra, with the exception of the vinyl flooring pyrolysis products (Fig. 3c). The library of target factors for the simulation studies was comprised of the total ion spectra from samples of the ASTM classes Gas (23 samples), ISO (33 samples) and MPD (93 samples). The total ion spectra for the ignitable liquids used in the simulation and those in the target factor library were normalized so that the intensities sum to one. Each spectrum in the spectral sets used for TFA analysis was prepared by mixing one or two ignitable liquids from Table 1 with a single substrate pyrolysis sample from Table 1 and 5% random noise. The sum of the fractional contributions from the ignitable liquid(s), substrate and noise summed to one. Each

spectral set for TFA analysis was comprised of 10 spectra. A spectral set contained multiple substrates and one or two ignitable liquids. The first tests examine the performance of the method applied to a six factor data set containing a relatively small contribution of a single ignitable liquid, Gas A1 and five substrates, S1–S5, from Table 1. Each spectrum in the data set was composed of A1 in the range of 1–15%, 5% random noise and one of the five substrates, accounting for the remainder (80–94%) of each composite spectrum. The fraction of A1 contribution was chosen randomly from a uniform distribution on the interval [0.01, 0.15]. In this example, the rank of the data would be six, corresponding to five substrates and one ignitable liquid. Fig. 4a–e shows five of the 10 spectra, corresponding to S1–S5 with 1–15% A1 contribution, and Fig. 4f shows the scree plot of the eigen values resulting from abstract factor analysis of the data. The number of principal factors is not entirely clear based on the scree plot; however, the DRMAD method correctly predicts six principal factors, corresponding to the rank of the data. The first six eigenvectors are shown in Fig. 5. Eigenvector 6 (Fig. 5f) contains the largest loadings on variables m/z 91 and 105, which are significant ions in the gasoline spectrum; however, the loadings on these variables are also

Fig. 1. Total ion spectra of ignitable liquids used in simulation studies: (a) Gas, (b) ISO, (c) MPD. See Table 1 for sample details.

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Fig. 2. Total ion spectra for pyrolysis products from substrates 1–5, labeled as (a)–(e) respectively. See Table 1 for sample detail.

Fig. 3. Total ion spectra for pyrolysis products from substrates 6–10, labeled as (a)–(e) respectively. See Table 1 for sample detail.

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Fig. 4. Five representative spectra corresponding to S1–S5 with 1–5% A1 contribution shown as (a)–(e) and (f) shows the screen plot for the abstract factor analysis.

Fig. 5. Eigenvectors (i.e., abstract factors) 1–6 from the factor analysis of six factor data set composed of 1–15% A1 and 90–94% S1–S5 (see Table 1).

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Fig. 6. (a) Regression (r = 0.621, n = 171) of a 90% evaporated Gas test spectrum against the predicted spectrum when retaining six eigenvectors, (b) regression (r = 0.930, n = 171) of a fresh Gas test spectrum against the predicted spectrum when retaining six eigenvectors.

significant in other principal eigenvectors. Fig. 6 demonstrates the range of regression results for gasoline test spectra in the library. Fig. 6a shows a regression (r = 0.621, n = 171) of a 90% evaporated Gas test spectrum against the predicted spectrum when retaining six eigenvectors and Fig. 6b shows the regression (r = 0.930, n = 171) for an un-evaporated gasoline test spectrum against the predicted spectrum when retaining six eigenvectors. Target transformation of spectra from the ISO and MPD classes generally gave poorer correlations between the test and predicted vectors. Class-conditional probability distributions calculated using Eqs. (6)–(8) (hGas = 0.035, hISO = 0.013 and hMPD = 0.007) and based on the correlation coefficients for each class are shown in Fig. 7. The graph in Fig. 7a reflects generally larger correlations for library spectra from the Gas class. When Eq. (9) is used to calculate p(vij[rLL,1]), the Gas, ISO and MPD probabilities of 0.89, 0 and 0.11 respectively at rLL = 0.9 are similar to the values of 1, 0, 0 as rLL approaches one. Notably from Fig. 7b, as rLL drops below 0.6, the value of p(vij[rLL,1]) for each class goes to 0.33, as anticipated. When the test was repeated with each spectrum containing A1 in the range of 1–5%, 5% random noise and one of the five substrates accounting for the remainder (90–94%), nearly identical results were obtained when retaining 6 principal factors, as indicated by DRMAD. Notably, a 1–5% contribution of ignitable liquid (i.e. 95% contribution from pyrolysis products) is not easily detected visually in a total ion chromatogram (TIC). This is demonstrated in Fig. 8, which depicts a TIC from: (a) gasoline, (b) asphalt roofing shingle pyrolysis products, and (c) 95% shingle pyrolysis and 5% gasoline. The asterisk (*) symbols in Fig. 8c indicate positions where there is a small, but noticeable, difference between the two TIC shown in Fig. 8b and c.

Fig. 7. (a) Kernel probability distribution functions calculated by Eqs. (6)–(8) (hGas = 0.035, hISO = 0.013 and hMPD = 0.007) from the distributions of r for Gas (solid line), MPD (long dash) and ISO (short dash), (b) posterior probability calculated by Eq. (9) as a function of rLL.

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Fig. 8. Total ion chromatograms are shown from: (a) gasoline, (b) asphalt roofing shingle pyrolysis, and (c) 95% shingle pyrolysis and 5% gasoline. The asterisk (*) symbols in panel (c) indicate positions where there is a noticeable difference between the two TIC shown panels (b) and (c).

Similar tests were made with two contributing components (ISO and MPD, A2 and A3 from Table 1). In the first test, the dataset was comprised of factors A2 (1–15%,), A3 (1–15%), S1–S5 (65–93%), and 5% noise. This sample has a rank of seven and DRMAD correctly predicted seven principal factors in a dataset. When seven factors are retained for target transformation, the class-conditional probability density functions shown in Fig. 9a are obtained (hGas = 0.037, hISO = 0.009 and hMPD = 0.007). The graph in Fig. 9a shows the larger correlations and strongly overlapped distributions for library spectra from the ISO and MPD class. The P(vij[rLL,1]) graph as a function of rLL is shown in Fig. 9b. The value of P(vij[rLL,1]) rapidly approaches 0.5 for the MPD and ISO classes as rLL drops to 0.96 and the posterior probabilities remain

fairly constant down to rLL of 0.8. As rLL approaches one, the P(vij[rLL,1]) curves in Fig. 9b can be seen to diverge as a result of the imperfect overlap of the two class-conditional distributions shown in Fig. 9a. The similar P(vij[rLL,1]) values for the ISO and MPD classes for rLL on the interval [0.8, 0.95] reflect the fact that these classes were both represented in the data set, and as a softclassification, these values would direct the analyst to consider the possibility of a sample containing two analytes. When the test was repeated with each spectrum comprised of A2 and A3 in the range of 1–5%, random noise of 5% and one of the five substrates S1–S5, accounting for the remainder (85–93%), DRMAD indicated the presence of eight primary factors, rather than seven, which corresponds to the rank of the data matrix. The

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Fig. 9. (a) Kernel probability distribution functions calculated by Eqs. (6)–(8) (hGas = 0.037, hISO = 0.009 and hMPD = 0.007) from the distributions of r for Gas (solid line), MPD (long dash) and ISO (short dash), (b) posterior probability calculated by Eq. (9) as a function of rLL.

P(vij[rLL,1]) values vary between 0.33 and 0.67 for ISO and MPD at rLL > 0.96. The P(vij[rLL,1]) values for MPD and ISO are stable at approximately 0.5 each for 0.8 < rLL < 0.95, reflecting the composition of the sample. In a final set of simulation studies, the Gas example was repeated four times, each with a data matrix rank of 11 prepared by including substrates S1–S10, gasoline A1 at varying levels, and 5%

381

noise in each case. The maximum contributions of A1 were set at 5, 30, 50 and 70% respectively, in the four tests. In each test, the dataset consisted of 10 spectra and the rank of the data matrix exceeded the number of spectra. There is no guarantee in a real dataset that the number of spectra will exceed the number of factors. Therefore, it is of interest to examine the case where the number of chemical factors exceeds the number of spectra. In the tests with 5, 30 and 50% A1 contribution, DRMAD indicated only one principal factor and target factor analysis resulted in the classconditional distribution curves shown in Fig. 10a–c, respectively. In each case, the class-conditional distribution for Gas (solid line) reflects higher correlation coefficients than observed for ISO or MPD classes; however, the distributions for all classes reveal low correlations. These results emphasize the need to examine the p(rjvi) curves. If all of the class-conditional distributions reflect poor agreement between the test and predicted spectra, the analyst may wish to not classify the samples as positive for ignitable liquid residue. This approach can be formalized by requiring that 1  Ii[1,rLL] > a if P(vij[rLL,1]) is to be calculated for class vi, where a is the probability of observing r > rLL (i.e., a statistical significance level). In the case of a maximum of 70% A1, two principal factors were indicated by DRMAD and the resulting p(rjvi) curves are shown in Fig. 10d. The results from this calculation also emphasize the need to maximize the number of spectra relative to the possible number of contributing factors, and the importance of a strong analyte signal. 3.2. Laboratory-scale burn studies A series of 20 laboratory-scale burn tests were conducted as described in the experimental section. The ASTM class and volume of ignitable liquid was varied, as was the number and type of substrate included in each set of burns. The number of burn samples combined in a test was also varied. Table 2 presents a list

Fig. 10. Kernel probability density functions for Gas (solid line), MPD (long dash) and ISO (short dash) obtained from the analysis of a dataset containing A1 in (a) 5%, (b) 30%, (c) 50% and (d) 70% contributions. Each of the 10 spectra also contained one of the substrates S1–S10 and 5% noise.

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Table 2 Laboratory test burn data, corresponding to results from Table 3. Specific volume use in each test burn is given as a footnote to the table. Test no.

IL class

IL volumea

ILRC SRN

Substrates

1 2

Gas Gas

A C

116 116

3

Gas

D

116

4

Gas

E

116

5

Gas

D

116

6 7 8

Gas Gas Gas

B B F

258 385 116

9

Gas

E

116

HPD ISO ISO AR MPD MPD NA NP OXY OXY OXY

A A B A A B A A A B B

206 87 87 59 30 30 241 243 174 248 407

Polyester carpet and padding, Yellow pine, fiberglass insulation, polyurethane foam mattress, vinyl flooring, PET polyester carpet, and carpet padding Yellow pine, fiberglass insulation, polyurethane foam mattress, vinyl flooring, PET polyester carpet, and carpet padding Yellow pine, fiberglass insulation, polyurethane foam mattress, vinyl flooring, PET polyester carpet, and carpet padding Poplar, fiberglass insulation, olefin/nylon carpet Oak, nylon rope, and roofing shingles Teak, cotton t-shirt, cork tiles Cork board, vinyl, polyester quilt batting, nylon-olefin mix carpet, carpet padding, cherry wood PET polyester carpet, carpet padding, cotton, cork board, vinyl. Polyester carpet and padding Polyester carpet and padding Douglas Fir Polyester carpet and padding Polyester carpet and padding Douglas Fir Polyester carpet and padding Polyester carpet and padding Polyester carpet and padding Olefin carpet, cherry wood, vinyl Olefin carpet, oak, fiberglass insulation

10 11 12 13 14 15 16 17 18 19 20

a IL volumes (mL) A: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 1.0, 1.5, 2.0; B: 0.2, 0.5, 1.0, 1.5, 2.0; C: 1.0; D: 0.2; E: 0.05; F: 0.025.

of the substrates, the volumes of ignitable liquid, ASTM classification of the ignitable liquid and the ILRC sample reference number (SRN) used in each burn. The TIS resulting from the multiple samples associated with each burn were analyzed by target factor

analysis and the results were analyzed as described above. The ignitable liquids in the library used for target transformation comprised the ASTM classes and specifying light (L), medium (M) and heavy (H) sub-classifications for the petroleum distillate (PD) and aromatic (AR) classes. The library of 358 TIS contained 25 Gas, 3 HAR, 47 HPD, 34 ISO, 7 LAR, 23 LPD, 17 MAR, 95 MPD, 17 NA, 16 NP and 71 OXY ignitable liquids. The 20 tests containing ignitable liquid were analyzed by target factor analysis with Bayesian classification using Eq. (9) and assigning membership to the class with the largest posterior probability. The correct classification percentage was calculated as rLL was varied and P(vij[rLL,1]) was calculated for all classes. A maximum 80% correct classification was obtained in the region of rLL 0.94–0.97, as shown in Fig. 11. Table 3 summarizes the performance at rLL = 0.95, with the largest posterior probability for each test highlighted in bold text, and posterior probabilities less than 0.001 are represented by 0 to simplify reading of the table. The ASTM class of the ignitable liquid used in the burn is shown in the second column of Table 3, and the volume range of ignitable liquid (mL) used in the series of burns is given in column 3. For a list of the exact volumes used in each test, the reader is referred to Table 2. All ASTM E1618 primary classes were represented in the test, with the gasoline class utilized in the largest number of tests. In four of the twenty burns, the highest calculated posterior probability did not correspond to the ASTM class of the ignitable liquid used in the test. Only one gasoline sample (Test 8) was incorrectly classified. The data matrix for the incorrectly classified Gas sample had a rank that exceeded the number of samples in the dataset and the volume of gasoline used was extremely small, 0.025 mL. Examination of the total ion spectra from the burn samples did not reveal any chromatographic peaks corresponding to components of the gasoline sample used in the burn. Both of the ISO samples (Tests 11 and 12) were classified incorrectly, one as OXY (Test 11) and the other as NA (Test 12). In Test 11, the chromatographic peaks corresponding to components of the ignitable liquid used in the burn were extremely weak or not present, while peaks from pyrolysis products were strong. In Test 12, the highest posterior probability (0.52) was calculated for the NA class, while the second highest posterior probability (0.436) was calculated for the ISO class. The NA and ISO classes have very similar total ion spectra, and in a previous study, the similarity of

Table 3 Posterior probabilities P(vij[0.95,1]) from laboratory-scale burn tests using the ignitable liquid (IL) classes and volumes reported. The number of samples analyzed and number of substrates (Sub.) used in each burn are also given. Posterior probabilities less than 0.001 are reported as 0 and the highest posterior probability for each burn is indicated in bold text. No.

IL

Vol. (mL)a

Samples

Sub.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Gas Gas Gas Gas Gas Gas Gas Gas Gas HPD ISO ISO LAR MPD MPD NA NP OXY OXY OXY

0.1–2 1 0.2 0.05 0.2 0.2–2 0.2–2 0.025 0.05 0.11–2 0.1–2 0.2–2 0.1–2 0.1–2 0.2–2 0.1–2 0.1–2 0.1–2 0.2–2 0.2–2

9 9 6 6 5 5 5 5 5 9 9 5 9 9 5 9 9 9 5 5

2 6 6 6 7 3 3 6 5 2 2 1 2 2 1 2 2 2 3 3

a

See Table 2 for a list of volumes used in each burn.

Posterior probability Gas

HAR

HPD

ISO

LAR

LPD

MAR

MPD

NA

NP

OXY

0.766 0.933 0.934 0.884 0.906 0.958 0.995 0.123 0.907 0.040 0 0 0.034 0 0 0 0 0 0.804 0

0.007 0 0 0 0 0 0 0 0 0.243 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0.640 0 0.001 0 0.266 0.274 0.004 0.014 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0.436 0 0.006 0.006 0.053 0 0 0 0

0.006 0 0 0 0.008 0 0 0 0 0 0 0 0.899 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0.040 0.024 0.011 0.097 0.067 0 0.016 0.059 0 0

0.222 0.066 0.065 0.047 0.081 0.036 0 0.012 0.076 0 0 0 0.001 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0.003 0 0.372 0.341 0 0.117 0.228 0 0

0 0 0 0 0 0 0 0 0 0 0 0.520 0 0 0 0.938 0 0 0 0

0 0 0 0 0 0 0 0 0 0.061 0 0 0 0.232 0.288 0 0.836 0.311 0 0

0 0 0.001 0.069 0.005 0.006 0.005 0.865 0.017 0.016 0.960 0.017 0.055 0.028 0.024 0.005 0.018 0.402 0.197 1.000

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was not visible in the total ion spectra of the burn samples. In 16 of the 20 burn samples (80%), the largest calculated posterior probability corresponded to the class of ignitable liquid used in the burn. In previous studies of ignitable liquids that had not been exposed to fire conditions, the correct classification rate for ASTM classes, based on highest similarity of total ion spectra, was shown to be 83% [10]. When the calculations were repeated at rLL = 0.95 with a significance level of 0.01, three samples (9, 11 and 18) were not classified because none of the classes met the requirement 1  Ii[1,rLL] > 0.01. Fourteen of the remaining 17 samples were correctly classified (82% correct classification). 3.3. Large-scale burn studies

Fig. 11. Optimization of correct classification percentage as a function of rLL for 20 laboratory test burns, see Table 2.

these two classes was evident as they appeared adjacent in a heat map display of the similarities. The incorrectly calculated posterior probability in Test 12 is attributed to the inability to adequately distinguish between ISO and NA classes using the total ion spectrum. The final test where the largest posterior probability did not correspond to the ASTM class of the ignitable liquid used in the burn was Test 19. In this test, an OXY sample was classified as Gas. While this seems to be a rather strange misclassification, the oxygenated ignitable liquid used in the burn contained isoparaffinic compounds, cycloalkanes, C2- and C3-alkyl benzenes, and the oxygenated component (2-butoxyethanol) was visible at lower intensities in the total ion spectrum. Several of the components from the ignitable liquid are also present in gasoline, and this may account for the large posterior probability calculated for the gasoline class. The oxygenated component was lost in the burn and

Twelve large-scale burns were conducted in 2.4 m  2.4 m  6.1 m Konex boxes that had been built-out on the inside and furnished with common household furnishings as described in the experimental section. Due to the high costs of these experiments, the number of experiments conducted was limited; however, the large-scale burn samples are considered to be more representative of actual fire debris samples encountered in forensic examinations. Fig. 12a shows one of the containers prior to burning and Fig. 12b and c show two containers after extinguishment of the fires. The container shown in Fig. 12b depicts a representative amount of damage sustained by most of the containers, while Fig. 12c shows a much higher degree of damage sustained in some of the containers. These images emphasize the complexity of the matrix and nature of the problem addressed in this work. Fig. 12c also shows numbered sample markers indicating the positions were samples were collected from this particular burn. Most of the samples came from the floor and included carpet and carpet padding or laminate flooring. Burned plastics, paper, clothing, sheetrock and furniture also contributed to the various samples. The temperatures were monitored during the course of the fire with four thermocouples placed as indicated in Fig. 13(a). Temperatures in the large-scale burns typically maximized around 700–800 8C. A plot of the temperatures in one of the large-scale burns is shown as a function of time in Fig. 13(b). Thermocouples T1 and T2 were positioned near the ceiling in the structure and thermocouples T3 and T4 were located approximately 1.2 m above the floor.

Fig. 12. (a) An example container prior to burning, (b) a representative amount of damage sustained by most of the containers, and (c) sample collection markers shown in a container sustaining a high degree of damage from the burn.

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Fig. 13. (a) Schematic showing the layout of large-scale burn containers with the positions of thermocouples indicated as T1–T4. (b) Temperature recorded by thermocouples T1–T4 during a 6-min burn.

Four of the 12 burns were conducted with ignitable liquids from two classes; three with Gas and MPD and one with Gas and HPD. In the three burns with Gas and MPD, the two liquids were poured along separate trails. In the burn with Gas and HPD, the two liquids were poured as a blend on a single trail. In the remaining eight burns, an ignitable liquid from a single ASTM class was used. A detailed list of ignitable liquids used is given in Table 4. The number of fire debris samples collected from each testburn ranged from 11 to 13, see Table 4, column 3. Table 4 also gives the P(vij[0.95,1]) for each class. Assigning the ignitable liquid to the class with the highest posterior probability, 83% of the samples (10 of 12 burns) were assigned to either the single liquid used, or one of the two liquids used in the test. This rate does not differ significantly from that observed in the laboratory burns. The

incorrectly assigned Container 7 was burned with Gas and MPD, but assigned to NP. The P(vij[0.95,1]) values for NP and MPD in Container 7 were 0.310 and 0.300, respectively. In a previous study, the distillates and the naphthenic paraffinic classes were shown to have very similar total ion spectra [10]. The large posterior probability (0.31) calculated for the NP class is attributed to the similarity between the NP and MPD total ion spectra. The incorrectly assigned Container 8 was also burned with Gas and MPD, but assigned to OXY. Examination of the total ion chromatogram for samples taken from this burn did not reveal any peaks attributable to ignitable liquid residue. In these experiments, as in a real structural fire, it is not possible to control the amount of ignitable liquid residue remaining in the fire debris. Notably, in the other container burned with Gas and MPD,

Table 4 Posterior probabilities P(vij[0.95,1]) from large-scale burn tests using the ignitable liquid (IL) classes reported. The numbers of samples analyzed from each burn are also given. Posterior probabilities less than 0.001 are reported as 0 and the largest posterior probability is given in bold text. The volume of each IL used in each burn was 500 mL, see Section 2. Container

IL

Samples

1 2 3 4 5 6 7 8 9 10 11 12

Gas Gas + MPD MPD OXY Gas Gas Gas + MPD Gas + MPD Gas + HPD LPD NP ISO

12 12 12 11 14 13 12 13 13 12 12 12

Posterior probability Gas

HAR

HPD

ISO

LAR

LPD

MAR

MPD

NA

NP

OXY

0.925 0.017 0.032 0.254 0.511 0.895 0.038 0.001 0.004 0.012 0.002 0.300

0 0 0 0 0 0 0 0 0 0 0 0

0.002 0.418 0.248 0.037 0 0 0.248 0 0.724 0.021 0.159 0.020

0 0 0.009 0 0 0 0.003 0 0 0 0 0.359

0 0 0 0 0.275 0 0 0 0 0 0 0.002

0.017 0 0.093 0 0.041 0 0.063 0 0 0.442 0.030 0.011

0 0 0.043 0 0.084 0.049 0.019 0 0 0 0 0.058

0 0.511 0.302 0.006 0 0 0.300 0 0.173 0.453 0.331 0.047

0 0 0 0 0 0 0 0 0 0 0 0.158

0 0 0.247 0 0 0 0.310 0 0.027 0 0.455 0

0.056 0.054 0.028 0.703 0.089 0.057 0.019 0.998 0.073 0.072 0.024 0.046

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Fig. 14. Class-conditional kernel probability distributions obtained from large scale burn of Container 1. The ordering of curves in each panel is solid, short dash and long dash: (a) Gas, HAR and HPD; (b) ISO, LAR and LPD; (c) MAR, MPD and NA; (d) NP and OXY.

Container 2, the MPD posterior probability was 0.511, while the posterior probability for Gas was only 0.17. However, in Container 2, the posterior probability for HPD, which is chemically very similar to highly evaporated gasoline, was 0.418. In Container 9, the posterior probability for the HPD was 0.724, while the posterior probability for Gas was only 0.004. The second highest posterior probability in Container 9 was MPD at 0.173. This result may also reflect the chemical similarity of highly evaporated gasoline and an HPD. The class-conditional probability distribution functions obtained from target factor analysis of the burn data from Container 1 are shown in Fig. 14a–d. Fig. 14a shows distribution functions for Gas, HAR and HPD as solid, short dash and long dash respectively. Fig. 14b shows the ISO, LAR and LPD distributions as solid, short dash and long dash respectively. Fig. 14c shows the MAR, MPD and NA distributions as solid, short dash and long dash respectively. Fig. 14d shows the NP and OXY distributions as solid and short dash respectively. The P(vij[0.95,1]) for this container was predominated by the Gas class (see Table 4). When the calculations are repeated at rLL = 0.95 with a significance level of 0.01, only Container 4 was not classified due to none of the classes meeting the requirement 1  Ii[1,rLL] > 0.01. Following this single failure to classify, and assigning the ignitable liquid to the class with the highest posterior probability, 82% of the samples (9 of 11 classified burns) were assigned to either the only liquid used, or one of the two liquids used in the test. 4. Conclusions A Bayesian soft classification method combined with target factor analysis has been described and tested on the analysis of fire debris data. Unlike most classification methods, the Bayesian-TFA method is designed to work in the presence of interfering

background contributions. The method also provides the analyst with a posterior probability of ASTM class assignment and the associated risk, which should aid in the assignment of difficult samples. The overall performance achieved in this initial test of the method was approximately 75–80% correct classification of fire debris samples from laboratory burns and large-scale burns. The disadvantages of the method are that it requires the analysis of data from multiple samples taken from a single fire scene, rather than a single sample, and the number of samples should exceed the ‘‘chemical rank’’ of the data, a condition that may be difficult to ensure in real samples. Acknowledgements This project was supported by Award No.2008-DN-BX-K069, awarded by the National Institute of Justice, Office of Justice Programs, U.S. Department of Justice. The opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect those of the Department of Justice. References [1] ASTM, Test Method for ignitable liquid residues in extracts from fire debris samples by gas chromatography-mass spectrometry (E1618-10), American Society for Testing and Materials, ASTM International, West Conshohocken, PA, 2010, 2006. [2] R.O. Duda, P.E. Hart, D.G. Stork, Pattern Classification, John Wiley & Sons, Inc, New York, 2001. [3] M.E. Sigman, M.R. Williams, Application of covariance mapping to the analysis of complex mixtures by GC–MS, Anal. Chem. 78 (2006) 1713–1718. [4] M.E. Sigman, M.R. Williams, R.G. Ivy, Comparative analysis of gasolines by covariance mapping and gas chromatography–mass spectrometry, Anal. Chem. 79 (2007) 3462–3468. [5] L. Frasinski, J.K. Codling, P.A. Hatherly, Covariance mapping: a correlation method applied to multiphoton multiple ionization, Science 246 (1989) 1029–1031.

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