Partial Class Memberships Research Articles

Validation of soft classification models using partial class memberships: An extended concept of sensitivity & co. applied to grading of astrocytoma tissues

We use partial class memberships in soft classification to model uncertain labeling and mixtures of classes. Partial class memberships are not restricted to predictions, but may also occur in reference labels (ground truth, gold standard diagnosis) for training and validation data.Classifier performance is usually expressed as fractions of the confusion matrix, like sensitivity, specificity, negative and positive predictive values. We extend this concept to soft classification and discuss the bias and variance properties of the extended performance measures. Ambiguity in reference labels translates to differences between best-case, expected and worst-case performance. We show a second set of measures comparing expected and ideal performance which is closely related to regression performance, namely the root mean squared error RMSE and the mean absolute error MAE.All calculations apply to classical crisp as well as to soft classification (partial class memberships as well as one-class classifiers). The proposed performance measures allow to test classifiers with actual borderline cases. In addition, hardening of e.g. posterior probabilities into class labels is not necessary, avoiding the corresponding information loss and increase in variance.We implemented the proposed performance measures in R package “softclassval” which is available from CRAN and at softclassval.r-forge.r-project.org.Our reasoning as well as the importance of partial memberships for chemometric classification is illustrated by a real-word application: astrocytoma brain tumor tissue grading (80 patients, 37,000 spectra) for finding surgical excision borders. As borderline cases are the actual target of the analytical technique, samples which are diagnosed to be borderline cases must be included in the validation.

Raman spectroscopic grading of astrocytoma tissues: using soft reference information

Gliomas are the most frequent primary brain tumours. During neurosurgical treatment, locating the exact tumour border is often difficult. This study assesses grading of astrocytomas based on Raman spectroscopy for a future application in intra-surgical guidance. Our predictive classification models distinguish the surgically relevant classes "normal tissue" and "low" and "high grade astrocytoma" in Raman maps of moist bulk samples (80 patients) acquired with a fibre-optic probe. We introduce partial class memberships as a strategy to utilize borderline cases for classification. Borderline cases supply the most valuable training and test data for our application. They are (a) examples of the sought boundary and (b) the cases for which new diagnostics are needed. Besides, the number of suitable training samples increases considerably: soft logistic regression (LR) utilizes 85% more spectra and 50% more patients than linear discriminant analysis (LDA). The predictive soft LR models achieve ca. 85, 67 and 84% (normal, low and high grade) sensitivity and specificity. We discuss the different heuristics of LR and LDA in the light of borderline samples. While we focus on prediction, the spectroscopic interpretation of the predictive models agrees with previous descriptive studies. Unsaturated lipids are used to differentiate between normal and tumour tissues, while the total lipid content prominently contributes to the determination of the tumour grade. The high-wavenumber region above 2,800 cm(-1) alone did not allow successful grading. We give a proof of concept for Raman spectroscopic grading of moist astrocytoma tissues and propose to include borderline samples into classifier training and testing.

Supervised learning algorithms for multi-class classification problems with partial class memberships

In several application domains such as biology, computer vision, social network analysis and information retrieval, multi-class classification problems arise in which data instances not simply belong to one particular class, but exhibit a partial membership to several classes. Existing machine learning or fuzzy set approaches for representing this type of fuzzy information mainly focus on unsupervised methods. In contrast, we present in this article supervised learning algorithms for classification problems with partial class memberships, where class memberships instead of crisp class labels serve as input for fitting a model to the data. Using kernel logistic regression (KLR) as a baseline method, first a basic one-versus-all approach is proposed, by replacing the binary-coded label vectors with [0,1]-valued class memberships in the likelihood. Subsequently, we use this KLR extension as base classifier to construct one-versus-one decompositions, in which partial class memberships are transformed and estimated in a pairwise manner. Empirical results on synthetic data and a real-world application in bioinformatics confirm that our approach delivers promising results. The one-versus-all method yields the best computational efficiency, while the one-versus-one methods are preferred in terms of predictive performance, especially when the observed class memberships are heavily unbalanced.

Potential Improvements in the Characterization of Forest Canopy Gaps Caused by Windthrow Using Fine Spatial Resolution Multispectral Data: Comparing Hard and Soft Classification Techniques

Abstract Gaps often form in forest canopies due to windthrow and have important management and ecological implications. Remote sensing has considerable potential for the provision of information on gap properties but this has not been fully realized. This is largely due to the use of conventional (hard, one-pixel one-class) image analysis techniques and imagery with a relatively coarse spatial resolution. This article investigates the potential to extract information on gap properties from fine spatial resolution airborne thematic mapper imagery using soft classification techniques that allow image pixels to have multiple and partial class membership. It is shown that a standard hard maximum likelihood classification may be used to derive an accurate map of the land cover of a forested site (95.1%) from which gaps in a canopy of Sitka spruce were accurately identified (94.5%). The maximum likelihood classification was also softened by outputting probabilities of class membership for each pixel. Softening the classification increased the information on gap properties that could be extracted from the data. In particular, the accuracy with which key gap properties, such as gap area, perimeter length and shape, were estimated was higher in the outputs of the softened than hard classification. Thus, while strong correlations between the remotely sensed and ground data estimates of gap area (r ≥ 0.96) and perimeter (r ≥ 0.87), based on a sample of 36 gaps, were derived from all classifications, the accuracy with which gap properties were estimated was generally highest when a soft classification was used. For example, the use of a soft rather than hard classification resulted in the root mean square error in estimating gap area declining from 144.90 to 132.87 m2. Furthermore, the soft classification allowed the sharpness of the gap boundary to be estimated, enabling further gap properties to be inferred. In particular, the soft classification output enabled the direction of the wind event causing the initial damage to be estimated, and it may aid the definition of sites with a future risk of windthrow. FOR. SCI. 49(3):444–454.

Fully-fuzzy supervised classification of sub-urban land cover from remotely sensed imagery: Statistical and artificial neural network approaches

Fully-fuzzy classification approaches have attracted increasing interest recently. These approaches allow for multiple and partial class memberships at the level of individual pixels and accommodate fuzziness in all three stages of a supervised classification of remotely sensed imagery. A fully-fuzzy classification strategy may be deemed more objective and correct than partially-fuzzy approaches where fuzziness is only accommodated in one or two of the three classification stages. This paper describes two approaches to the fully-fuzzy classification of remotely sensed imagery: a statistical approach based on a modified fuzzy c-means clustering algorithm performed in a supervised mode and an artificial neural network based approach. This is followed by the documentation of a case study using Landsat Thematic Mapper (TM) data of an Edinburgh suburb. Both approaches were applied to derive fully-fuzzy classifications of land cover, with fuzzy ground data, critical for training and testing the classifications, derived from indicator kriging. Results confirmed the superiority of fully-fuzzy over their respective partially-fuzzy classification counterparts, which is beneficial given their more relaxed requirements for training pixels (i.e. training pixels need not be pure). Similar accuracies were obtained with the artificial neural network and statistical approaches to classification. It is suggested that due emphasis must be placed on derivation and analysis of fuzzy ground data as well as fuzzy classified data in order to further improve fully-fuzzy classifications.

Approaches for the production and evaluation of fuzzy land cover classifications from remotely-sensed data

Abstract Remote sensing is an attractive source of data for land cover mapping applications. Mapping is generally achieved through the application of a conventional statistical classification, which allocates each image pixel to a land cover class. Such approaches are inappropriate for mixed pixels, which contain two or more land cover classes, and a fuzzy classification approach is required. When pixels may have multiple and partial class membership measures of the strength of class membership may be output and, if strongly related to the land cover composition, mapped to represent such fuzzy land cover. This type of representation can be derived by softening the output of a conventional ‘hard’ classification or using a fuzzy classification. The accuracy of the representation provided by a fuzzy classification is, however, difficult to evaluate. Conventional measures of classification accuracy cannot be used as they are appropriate only for ‘hard’ classifications. The accuracy of a classification may, ho...

Cross-entropy for the evaluation of the accuracy of a fuzzy land cover classification with fuzzy ground data

Fuzzy classifications have been used to represent land cover when pixels may have multiple and partial class membership. A fuzzy classification can be derived by softening the output of a conventional “hard” classification. Thus, for example, the probabilities of class membership may be derived from a conventional probability-based classification and mapped to represent the land cover of a site. The accuracy of the representation provided by a fuzzy classification is, however, difficult to evaluate. Conventional measures of classification accuracy cannot be used since they are appropriate only for “hard” classifications. The accuracy of a classification may, however, be indicated by the way in which the probability of class membership is partitioned between the classes and this may be expressed by entropy measures. Here cross-entropy is proposed as a means of evaluating the accuracy of a fuzzy classification, by illustrating how closely a fuzzy classification represents land cover when multiple and partial class membership is a feature of both the remotely sensed and ground data sets. Cross-entropy is calculated from the probability distributions of class membership derived from the remotely sensed and ground data sets. The use of cross-entropy as an indicator of classification accuracy was investigated with reference to land cover classifications of two contrasting test sites. The results show that cross-entropy may be used to indicate the accuracy of the representation of land cover when the classification of the remotely sensed data and ground data are both fuzzy.

Non-classificatory analysis and representation of heathland vegetation from remotely sensed imagery

Remotely sensed imagery are an attractive source of data for vegetation mapping. Conventional image classification routines used to produce thematic maps from remotely sensed imagery rely on a one-pixel-one-class approach and generate discrete thematic units. Where the environmental phenomena to be mapped exhibit gradients such a representation is inappropriate. This paper discusses the representation of semi-natural vegetation, drawing on examples of heathland vegetation that lie along continua. Two alternative approaches to the representation of heathland vegetation are examined, both of which aim to model the continuous character of the vegetation with measures of the strength of membership to ‘discrete classes’, namely probabilities of class membership from a maximum likelihood classification and fuzzy membership functions from the fuzzy c-means algorithm. Since both approaches imply partial class membership they can be considered as non-classificatory, even though the measures of the strength of class membership may be derived from classification routines. The measures of class membership generated from both approaches were found to be significantly correlated to the variations in heathland composition along a transect which graded from dry heath to wet heath/bog. Furthermore for cases drawn from the class end-points both approaches were able to discriminate class membership accurately.

Classification of electrocardiographic signals: a fuzzy pattern matching approach

In this paper we will deal with the problem of classification and interpretation of electrocardiograms (ECG) in the presence of uncertain environment. The problem can be conveniently handled in a general framework of pattern recognition. Uncertainty that is evident there relates both to (i) a perception perspective established in the classification process as well as (ii) final class assignment. Due to this type of uncertainty which essentially derives from a lack of sharp boundaries (i.e. precise definitions) of the features of the signal and the partial class membership (that is characteristic for unclear, borderline cases) of individual signals a methodology of fuzzy set theory is appropriate. Within this framework it will be clarified how all perception properties concerning signal processing and its interpretation can be handled.