Soft Classification Methods Research Articles

Augmentation of Soft Partition with a Granular Prototype Based Fuzzy C-Means

Clustering is a fundamental cornerstone in unsupervised learning, playing a pivotal role in various data mining techniques. The precise and efficient classification of data stands as a central focus for numerous researchers and practitioners alike. In this study, we design an effective soft partition classification method which refines and extends the prototype of the well-known Fuzzy C-Means clustering algorithm. Specifically, the developed scheme employs membership function to extend the prototypes into a series of granular prototypes, thus achieving a deeper revelation of the structure of the data. This process softly divides the data into core and extended parts. The core part can be succinctly encapsulated through several information granules, whereas the extended part lacks discernible geometry and requires formal descriptors (such as membership formulas). Our objective is to develop information granules that shape the core structure within the dataset, delineate their characteristics, and explore the interaction among these granules that result in their deformation. The granular prototypes become the main component of the information granules and provide an optimization space for traditional prototypes. Subsequently, we apply quantum-behaved particle swarm optimization to identify the optimal partition matrix for the data. This optimized matrix significantly enhances the partition performance of the data. Experimental results provide substantial evidence of the effectiveness of the proposed approach.

PLS class modelling using error correction output code matrices, entropy and NIR spectroscopy to detect deficiencies in pastry doughs

Biscuits are a highly demanded product worldwide. Its success makes their manufacture process a challenging task, needing new strategies to maintain the high production levels and a high-quality standard. This is determined by two key processes: the kneading and the rolling. This manuscript aims to reflect the improvements that the application of a novel soft multiclass compliant classification method (PLS2-CM) entails regarding the traditional chemometric class modelling. With this new approach, the intention is to detect possible deficiencies in biscuit doughs (excess of water, lack of water or little kneading time) during both industrial processes by using NIR spectroscopy.In PLS2-CM, the coding of the classes is done using an Error Correcting Code Matrix (ECOC), which implies to employ several binary learners so that their number and structure are not predetermined beforehand but are function of the data set to be modelled. The optimization criterion in PLS2-CM is the sensitivity and specificity matrix evaluated by the Diagonal Modified Confusion Entropy (DMCEN), a new index inspired by the Shannon's entropy that is more sensitive to changes in the elements of that matrix than the usual total efficiency. The results obtained according to this index are better with this new soft classification method than the ones obtained when using other soft class modelling techniques such as soft independent modelling of class analogy (SIMCA) or unequal dispersed classes (UNEQ).In this work it is shown that it is possible to completely distinguish a correct kneaded dough from another defective one with a specificity equal to 1 during the kneading process, but the class corresponding with water deficit dough, accepts a very high percentage (80 % in training and 92 % in prediction) of the excess-water dough spectra. Despite that, after the fermentation and during the rolling process, the same doughs are modelled with complete sensitivity and specificity in prediction (100 %), which indicates that the physico-chemical changes produced during the fermentation are decisive to characterize the absence of defects in biscuit doughs kneading by NIR spectroscopy.

Sentiment Analysist of the TPKS Law on Twitter Using InSet Lexicon with Multinomial Naïve Bayes and Support Vector Machine Based on Soft Voting

Abstract. The Indonesian Sexual Violence Law (TPKS Law) is a law that regulates forms of sexual violence. The TPKS Law reaped pros and cons in the drafting process and was officially ratified on April 12th, 2022. However, after being ratified, pros and cons can still be found and supervision is needed over the implementation of the law.
 Purpose: This study was conducted to identify the application and accuracy of soft voting on multinomial naïve Bayes and support vector machine algorithm, also to find out public opinion on the TPKS Law as a support tool in evaluating the law.
 Methods/Study design/approach: The method used is InSet lexicon for labeling with the soft voting classification method on the multinomial naive Bayes and support vector machine algorithm.
 Result/Findings: The accuracy obtained by applying 10 k-fold cross validation in soft voting is 84.31%, which uses a weight of 1:3 for multinomial naive Bayes and support vector machines. Soft voting obtains better accuracy than its standalone predictor, and also works well for sentiment analysis of the TPKS Law.
 Novelty/Originality/Value: This study using two combined lexicons (Colloquial Indonesian lexicon and the InaNLP formalization dictionary) in normalization process and using InSet lexicon as automatic labeling for sentiment analysis on TPKS Law.

Deep Learning Approach for Emotion Recognition Analysis in Text Streams

Social media sites employ various approaches to track feelings, including diagnosing neurological problems, including fear, in people or assessing a population public sentiment. One essential obstacle for automatic emotion recognition principles is variable with fluctuating limitations, language, and interpretation shifts. Therefore, in this paper, a deep learning-based emotion recognition (DL-EM) system has been proposed to describe the various relational effects in emotional groups. A soft classification method is suggested to quantify the tendency and allocate a message to each emotional class. A supervised framework for emotions in text streaming messages is developed and tested. Two of the major activities are offline teaching assignments and interactive emotion classification techniques. The first challenge offers templates in text responses to describe sentiment. The second activity includes implementing a two-stage framework to identify live broadcasts of text messages for dedicated emotion monitoring.

Dimensionality Reduction and Classification of Hyperspectral Remote Sensing Image Feature Extraction

Terrain classification is an important research direction in the field of remote sensing. Hyperspectral remote sensing image data contain a large amount of rich ground object information. However, such data have the characteristics of high spatial dimensions of features, strong data correlation, high data redundancy, and long operation time, which lead to difficulty in image data classification. A data dimensionality reduction algorithm can transform the data into low-dimensional data with strong features and then classify the dimensionally reduced data. However, most classification methods cannot effectively extract dimensionality-reduced data features. In this paper, different dimensionality reduction and machine learning supervised classification algorithms are explored to determine a suitable combination method of dimensionality reduction and classification for hyperspectral images. Soft and hard classification methods are adopted to achieve the classification of pixels according to diversity. The results show that the data after dimensionality reduction retain the data features with high overall feature correlation, and the data dimension is drastically reduced. The dimensionality reduction method of unified manifold approximation and projection and the classification method of support vector machine achieve the best terrain classification with 99.57% classification accuracy. High-precision fitting of neural networks for soft classification of hyperspectral images with a model fitting correlation coefficient (R2) of up to 0.979 solves the problem of mixed pixel decomposition.

A Multi-Stage Approach Combining Very High-Resolution Satellite Image, GIS Database and Post-Classification Modification Rules for Habitat Mapping in Hong Kong

Identification and mapping of various habitats with sufficient spatial details are essential to support environmental planning and management. Considering the complexity of diverse habitat types in a heterogeneous landscape, a context-dependent mapping framework is expected to be superior to traditional classification techniques. With the aim to produce a territory-wide habitat map in Hong Kong, a three-stage mapping procedure was developed to identify 21 habitats by combining very-high-resolution satellite images, geographic information system (GIS) layers and knowledge-based modification rules. In stage 1, several classification methods were tested to produce initial results with 11 classes from a WorldView-2/3 image mosaic using a combination of spectral, textural, topographic and geometric variables. In stage 2, modification rules were applied to refine the classification results based on contextual properties and ancillary data layers. Evaluation of the classified maps showed that the highest overall accuracy was obtained from pixel-based random forest classification (84.0%) and the implementation of modification rules led to an average 8.8% increase in the accuracy. In stage 3, the classification scheme was expanded to all 21 habitats through the adoption of additional rules. The resulting habitat map achieved >80% accuracy for most of the evaluated classes and >70% accuracy for the mixed habitats when validated using field-collected points. The proposed mapping framework was able to utilize different information sources in a systematic and controllable workflow. While transitional mixed habitats were mapped using class membership probabilities and a soft classification method, the identification of other habitats benefited from the hybrid use of remote-sensing classification and ancillary data. Adaptive implementation of classification procedures, development of appropriate rules and combination with spatial data are recommended when producing an integrated and accurate map.

Hierarchical method and hyperspectral images for classification of blood stains on colored and printed fabrics

This work describes the development of methodology based on the hierarchical soft classification method by combining multivariate analysis techniques and Hyperspectral Near Infrared Images (HSI-NIR) to confirm identification of bloodstains on colored and printed fabrics. The term hierarchical is used to designate that the classification is done sequentially on smaller parts of the data such as first splitting the data into human and non-human etc. Human Blood (HB) and Animal Blood (AB) stains and stains from different commercial products (Common False Positives-CFP) were deposited on ten different fabrics of two types (five synthetic and five cotton-based) and hyperspectral imagens were acquired. The best pre-processing techniques were spectral smoothing (Savitzky-Golay filter, 11 point), Standard Normal Variate (SNV), and Generalized Least Squared Weighted (GLSW) performed in that sequence, to reduce the influence of the fabric on the model. Principal Component Analysis (PCA) models for samples prepared on synthetic fabrics demonstrated a great potential as a filter in discriminating blood samples from common false positives than the models built for samples prepared on cotton fabrics. This was done in a SIMCA-like fashion. The Partial Least Squared Discriminant Analysis (PLS-DA) model was used only to separate HB from AB samples for samples prepared on synthetic fabrics. For the samples prepared on cotton fabric, PLS-DA was also needed to discriminate some CFP from blood samples. PCA and PLS-DA were combined in a hierarchical structure to result in a single aggregated soft classification model. The hierarchical classification model built by a fusion of PCA and PLS-DA showed 100% sensitivity and 98% specificity in distinguishing between HB and Animal Blood and False Positive Samples in synthetic fabric. For stains prepared on cotton fabrics, the hierarchical model showed 95% sensitivity and 98% specificity.

Fluvial gravel bar mapping with spectral signal mixture analysis

ABSTRACT The paper presents a method for mapping fluvial gravel bars based on Sentinel-2 and Landsat imagery. The proposed method therefore uses spectral signal mixture analysis (SSMA) because its results allow the development of land cover fraction maps for surface water, gravel, and vegetation. The method is validated on a spatially heterogeneous mountainous area in the upper Soča river basin in north-west Slovenia, Central Europe. Unmixing results in highly accurate fraction maps with MAE of around 0.1. Gravel fractions are mapped the most accurately, indicating that the approach can be used successfully for fluvial gravel bar mapping. Endmember sets selected automatically perform slightly worse (MAE higher by at most 0.05) than sets selected manually based on high resolution reference data. Both Sentinel-2 and Landsat imagery can be used for accurate mapping with differences between the two remote sensing systems within 0.05 MAE. For the study area, the SSMA-based soft classification method is more accurate for land cover mapping than a Spectral Angle Mapping-based hard classification. The method is promising for an effective use in other cases where highly accurate subpixel information is needed, because it is able to detect small-scale changes that could go unnoticed with hard classification mapping.

Classification of Grain Maize (Zea mays L.) from Different Geographical Origins with FTIR Spectroscopy—a Suitable Analytical Tool for Feed Authentication?

Feed is substantial in the production of animal food products and subject to regulations about traceability in the European Union. The geographical origin as one feature of authenticity was approached by spectroscopic techniques such as Fourier transform infrared spectroscopy. This fast and non-destructive method may be used to identify suspicious samples and initiate further investigations. The aim of the feasibility study was the development of classification models based on authentic grain maize samples from three different countries. Grain maize was used as demonstrator for unprocessed feed materials due to its wide cultivation and trade. Attenuated total reflexion Fourier transform infrared spectroscopy and multivariate analyses were applied to differentiate grain maize samples by their geographical origin (Ukraine, USA, Peru). Several sample preparations and data preprocessings were tested based on the results of a hard and a soft classification method. Model validation was performed with separate test sets and permutation tests. The use of an optimal data preprocessing resulted in 100% sensitivity for solid samples in both classification models, whereas oil extraction resulted in 100% and 70% sensitivity, respectively. These findings indicate the feasibility of FTIR spectroscopy combined with multivariate classification to verify the geographical origin of grain maize.

Weighted Direct Nonlinear Regression for Effective Image Interpolation

This paper proposes a learning-based image interpolation method based on weighted direct nonlinear regression. It attempts to learn the nonlinear relationship between the low-resolution patches and their corresponding high-resolution patches by using an external database of natural images. In the training phase, without being initialized to the same size as the high-resolution patches using bicubic interpolation, low-resolution patches are directly used for training, which will reduce the number of parameters. Dictionary learning combined with nearest neighbor searching based on the normalized correlation coefficient in the entire training set is proposed as a soft classification method. Afterward, a single hidden-layer feed-forward network with random input weights is adopted to learn the direct nonlinear mapping for the regression in each class. In the interpolation phase, the strategy of weighting multiple estimations is applied to enhance the interpolation performance. Furthermore, a refinement process is proposed to improve the interpolation performance with sharper edges and richer details. Extensive experimental results demonstrate that our proposed method is not only effective and efficient but also outperforms many state-of-the-art methods.

Shoreline mapping: how do Fuzzy Sigmoidal, Bayesian, and Demspter-Shafer classifications perform for different types of coasts?

ABSTRACTThis study examined Fuzzy Sigmoidal, Bayesian, and Demspter-Shafer classifications to map shorelines in Kuala Terengganu, Malaysia for different types of coasts (CT). These three soft classification methods were applied to simulated Satellite Pour l’Observation de la Terre-5 (SPOT-5 with 10 and 20 m spatial resolutions) images covering the three shoreline locations which were typically different in shape and orientation: (a) rocky breakwater coasts (CT-1), (b) rocky and sandy airport coasts (CT-2), and (c) sandy beach coasts (CT-3) for predicting shorelines. Visual inspection and statistical measures showed that variations in accuracies were evident, predominantly due to differences in CTs; mapping accuracy decreased with an increase of spatial resolution, but accuracy increased if shorelines were aligned exact parallel to the column of pixel grid. Sigmoidal can predict shoreline over the CT-3 areas with greater accuracy than the other two methods and has less dependence on spatial resolutions for across the CTs. But effective use of Bayesian membership function for mapping shoreline over certain small and narrow jetty-like structures makes this classifier also efficient. The soft classifier assessed in this study produced reliable shoreline maps and should help shoreline change detection and monitoring from coarser spatial resolution imagery.

Shoreline mapping: how do Fuzzy Sigmoidal, Bayesian, and Demspter-Shafer classifications perform for different types of coasts?

ABSTRACTThis study examined Fuzzy Sigmoidal, Bayesian, and Demspter-Shafer classifications to map shorelines in Kuala Terengganu, Malaysia for different types of coasts. These three soft classification methods were applied to simulated Satellite Pour l’Observation de la Terre-5 (SPOT-5 with 10 and 20 m spatial resolutions) images covering the three shoreline locations which were typically different in shape and orientation: (a) rocky breakwater coasts (CT-1), (b) rocky and sandy airport coasts (CT-2), and (c) sandy beach coasts (CT-3) for predicting shorelines. Visual inspection and statistical measures showed that variations in accuracies were evident, predominantly due to differences in CTs; mapping accuracy decreased with an increase of spatial resolution, but accuracy increased if shorelines were aligned exact parallel to the column of pixel grid. Sigmoidal can predict shoreline over the CT-3 areas with greater accuracy than the other two methods and has less dependence on spatial resolutions for across the CTs. But effective use of Bayesian membership function for mapping shoreline over certain small and narrow jetty-like structures makes this classifier also efficient. The soft classifier assessed in this study produced reliable shoreline maps and should help shoreline change detection and monitoring from coarser spatial resolution imagery.

Automatic sub-pixel coastline extraction based on spectral mixture analysis using EO-1 Hyperion data

Many megacities (such as Shanghai) are located in coastal areas, therefore, coastline monitoring is critical for urban security and urban development sustainability. A shoreline is defined as the intersection between coastal land and a water surface and features seawater edge movements as tides rise and fall. Remote sensing techniques have increasingly been used for coastline extraction; however, traditional hard classification methods are performed only at the pixel-level and extracting subpixel accuracy using soft classification methods is both challenging and time consuming due to the complex features in coastal regions. This paper presents an automatic sub-pixel coastline extraction method (ASPCE) from high-spectral satellite imaging that performs coastline extraction based on spectral mixture analysis and, thus, achieves higher accuracy. The ASPCE method consists of three main components: 1) A Water-Vegetation-Impervious-Soil (W-V-I-S) model is first presented to detect mixed W-V-I-S pixels and determine the endmember spectra in coastal regions; 2) The linear spectral mixture unmixing technique based on Fully Constrained Least Squares (FCLS) is applied to the mixed W-V-I-S pixels to estimate seawater abundance; and 3) The spatial attraction model is used to extract the coastline. We tested this new method using EO-1 images from three coastal regions in China: the South China Sea, the East China Sea, and the Bohai Sea. The results showed that the method is accurate and robust. Root mean square error (RMSE) was utilized to evaluate the accuracy by calculating the distance differences between the extracted coastline and the digitized coastline. The classifier’s performance was compared with that of the Multiple Endmember Spectral Mixture Analysis (MESMA), Mixture Tuned Matched Filtering (MTMF), Sequential Maximum Angle Convex Cone (SMACC), Constrained Energy Minimization (CEM), and one classical Normalized Difference Water Index (NDWI). The results from the three test sites indicated that the proposed ASPCE method extracted coastlines more efficiently than did the compared methods, and its coastline extraction accuracy corresponded closely to the digitized coastline, with 0.39 pixels, 0.40 pixels, and 0.35 pixels in the three test regions, showing that the ASPCE method achieves an accuracy below 12.0 m (0.40 pixels). Moreover, in the quantitative accuracy assessment for the three test sites, the ASPCE method shows the best performance in coastline extraction, achieving a 0.35 pixel-level at the Bohai Sea, China test site. Therefore, the proposed ASPCE method can extract coastline more accurately than can the hard classification methods or other spectral unmixing methods.

A COMPARISON OF SUB-PIXEL MAPPING METHODS FOR COASTAL AREAS

Abstract. This paper presents the comparisons of three soft classification methods and three sub-pixel mapping methods for the classification of coastal areas at sub-pixel level. Specifically, SPOT-7 multispectral images covering the coastal area of Perth are selected as the experiment dataset. For the soft classification, linear spectral unmixing model, supervised fully-fuzzy classification method and the support vector machine are applied to generate the fraction map. Then for the sub-pixel mapping, the sub-pixel/pixel attraction model, pixel swapping and wavelets method are compared. Besides, the influence of the correct fraction constraint is explored. Moreover, a post-processing step is implemented according to the known spatial knowledge of coastal areas. The accuracy assessment of the fraction values indicates that support vector machine generates the most accurate fraction result. For sub-pixel mapping, wavelets method outperforms the other two methods with overall classification accuracy of 91.79% and Kappa coefficient of 0.875 after the post-processing step and it also performs best for waterline extraction with mean distance of 0.71m to the reference waterline. In this experiment, the use of correct fraction constraint decreases the classification accuracy of sub-pixel mapping methods and waterline extraction. Finally, the post-processing step improves the accuracy of sub-pixel mapping methods, especially for those with correct coefficient constraint. The most significant improvement of overall accuracy is as much as 4% for the sub-pixel/pixel attraction model with correct coefficient constraint.

A COMPARISON OF SUB-PIXEL MAPPING METHODS FOR COASTAL AREAS

This paper presents the comparisons of three soft classification methods and three sub-pixel mapping methods for the classification of coastal areas at sub-pixel level. Specifically, SPOT-7 multispectral images covering the coastal area of Perth are selected as the experiment dataset. For the soft classification, linear spectral unmixing model, supervised fully-fuzzy classification method and the support vector machine are applied to generate the fraction map. Then for the sub-pixel mapping, the sub-pixel/pixel attraction model, pixel swapping and wavelets method are compared. Besides, the influence of the correct fraction constraint is explored. Moreover, a post-processing step is implemented according to the known spatial knowledge of coastal areas. The accuracy assessment of the fraction values indicates that support vector machine generates the most accurate fraction result. For sub-pixel mapping, wavelets method outperforms the other two methods with overall classification accuracy of 91.79% and Kappa coefficient of 0.875 after the post-processing step and it also performs best for waterline extraction with mean distance of 0.71m to the reference waterline. In this experiment, the use of correct fraction constraint decreases the classification accuracy of sub-pixel mapping methods and waterline extraction. Finally, the post-processing step improves the accuracy of sub-pixel mapping methods, especially for those with correct coefficient constraint. The most significant improvement of overall accuracy is as much as 4% for the sub-pixel/pixel attraction model with correct coefficient constraint.

SAR Image Despeckling by Soft Classification

We propose a new approach to synthetic aperture radar (SAR) despeckling, based on the combination of multiple alternative estimates of the same data. The many despeckling methods proposed in the literature possess different and often complementary strengths and weaknesses. Given a reliable pixelwise characterization of the image, one can take advantage of this diversity by selecting the most appropriate combination of estimators for each image region. Following this paradigm, we develop a simple algorithm where only two state-of-the-art despeckling tools, characterized by complementary properties, are linearly combined. To ensure the smooth combination of contributes, thus avoiding new artifacts, we propose a novel soft classification method, where a basic estimate of homogeneity is improved through nonlocal and multiresolution processing steps. The results of a number of experiments conducted on both synthetic and real-world SAR images are very promising, thus confirming the potential of the proposed approach.

Large‐margin classification with multiple decision rules

Binary classification is a common statistical learning problem in which a model is estimated on a set of covariates for some outcome, indicating the membership of one of two classes. In the literature, there exists a distinction between hard and soft classification. In soft classification, the conditional class probability is modeled as a function of the covariates. In contrast, hard classification methods only target the optimal prediction boundary. While hard and soft classification methods have been studied extensively, not much work has been performed to compare the actual tasks of hard and soft classification. In this paper, we propose a spectrum of statistical learning problems that span the hard and soft classification tasks based on fitting multiple decision rules to the data. By doing so, we reveal a novel collection of learning tasks of increasing complexity. We study the problems using the framework of large‐margin classifiers and a class of piecewise linear convex surrogates, for which we derive statistical properties and a corresponding sub‐gradient descent algorithm. We conclude by applying our approach to simulation settings and a magnetic resonance imaging (MRI) dataset from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study.

Hybrid system based on bijective soft and neural network for Egyptian neonatal jaundice diagnosis

Neonatal jaundice or hyperbilirubinemia and its evolution to acute bilirubin encephalopathy ABE and kernicterus are an important, yet avoidable, origin of newborn deaths, re-hospitalisations and disabilities generally. In this study, a new supervised hybrid bijective soft set neural network-based classification method is introduced for prediction of Egyptian neonatal jaundice dataset. Early prediction and classification of diseases would provide support to doctors for making decision of patient concerning the type of treatment. The hybrid bijective soft set neural network BISONN approach integrates both bijective soft set and back propagation neural network for the diagnosis of diseases. The experimental results are acquired by examining the proposed method on neonatal jaundice. The acquired results demonstrate that the hybrid bijective soft set neural network method can deliver expressively more accurate and consistent predictive accuracy than well-known algorithms such as bijective soft set classifier, back propagation network, multi-layered perceptron, decision table and naive Bayes classification algorithms.

Mapping Cropland Distributions Using a Hard and Soft Classification Model

Accurate and timely information regarding the location and area of major crop types has significant economic, food, policy, and environmental implications. Both hard and soft classification methods are used throughout the growing season to generate cropland distribution maps using multiple remotely sensed data. Hard classification models (HCMs) yield good results in large homogeneous areas where pure pixels are dominant, but they fail in fragmented areas where mixed pixels are dominant. Conversely, soft classification models (SCMs) are thought to have greater accuracy in fragmented areas than in regions with pure pixels. To take advantage of both methods, we develop a hard and SCM (HSCM) based on existing HCMs and SCMs, and test it using data from simulated images as well as actual satellite data from southeast Beijing, China. The model assessment was performed using three statistical metrics at scales ranging from 1 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\times$</tex></formula> 1 to 10 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\times$</tex></formula> 10 pixels. The results reveal that the HSCM has the highest classification accuracy and produces more reasonable cropland distribution maps than those produced by either HCMs or SCMs. Moreover, the theory and methods employed in developing the HSCM provide a unifying framework for mapping land cover types, and they can be applied to different HCMs and SCMs beyond those currently in use.

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

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.