Efficient multiclass ROC approximation by decomposition via confusion matrix perturbation analysis.

ROC analysis has become a standard tool in the design and evaluation of 2-class classification problems. It allows for an analysis that incorporates all possible priors, costs, and operating points, which is important in many real problems, where conditions are often nonideal. Extending this to the multiclass case is attractive, conferring the benefits of ROC analysis to a multitude of new problems. Even though ROC analysis does extend theoretically to the multiclass case, the exponential computational complexity as a function of the number of classes is restrictive. In this paper we show that the multiclass ROC can often be simplified considerably because some ROC dimensions are independent of each other. We present an algorithm that analyses interactions between various ROC dimensions, identifying independent classes, and groups of interacting classes, allowing the ROC to be decomposed. The resultant decomposed ROC hypersurface can be interrogated in a similar fashion to the ideal case, allowing for approaches such as cost-sensitive and Neyman-Pearson optimisation, as well as the volume under the ROC. An extensive bouquet of examples and experiments demonstrates the potential of this methodology.

Subclass problem-dependent design for error-correcting output codes.

A common way to model multi-class classification problems is by means of Error-Correcting Output Codes (ECOC). Given a multi-class problem, the ECOC technique designs a code word for each class, where each position of the code identifies the membership of the class for a given binary problem. A classification decision is obtained by assigning the label of the class with the closest code. One of the main requirements of the ECOC design is that the base classifier is capable of splitting each sub-group of classes from each binary problem. However, we can not guarantee that a linear classifier model convex regions. Furthermore, non-linear classifiers also fail to manage some type of surfaces. In this paper, we present a novel strategy to model multi-class classification problems using sub-class information in the ECOC framework. Complex problems are solved by splitting the original set of classes into sub-classes, and embedding the binary problems in a problem-dependent ECOC design. Experimental results show that the proposed splitting procedure yields a better performance when the class overlap or the distribution of the training objects conceil the decision boundaries for the base classifier. The results are even more significant when one has a sufficiently large training size.

Optical spectroscopy for the classification of malignant lesions of the bronchial tree.

Optical spectroscopy may be used for in vivo, noninvasive distinction of malignant from normal tissue. The aim of our study was to analyze the accuracy of various optical spectroscopic techniques for the classification of cancerous lesions of the bronchial tree. We developed a fiberoptic instrument allowing the measurement of autofluorescence spectroscopy (AFS), diffuse reflectance spectroscopy (DRS), and differential path length spectroscopy (DPS) during bronchoscopy. Spectroscopic measurements were obtained from 191 different endobronchial lesions (63 malignant and 128 nonmalignant) in 107 patients. AFS, DRS, and DPS sensitivity/specificity for the distinction between malignant and nonmalignant bronchial lesions were 73%/82%, 86%/81%, and 81%/88%, respectively. All three optical spectroscopic modalities facilitate an increase of the positive predictive value of autofluorescence bronchoscopy for the detection of endobronchial tumors. Even better results were obtained when the three spectroscopic techniques were combined.

Improving the specificity of fluorescence bronchoscopy for the analysis of neoplastic lesions of the bronchial tree by combination with optical spectroscopy: preliminary communication.

Detection of malignancies of the bronchial tree in an early stage, such as carcinoma in situ (CIS), augments the cure rate considerably. It has been shown that the sensitivity of autofluorescence bronchoscopy is better than white light bronchoscopy for the detection of CIS and dysplastic lesions. Autofluorescence bronchoscopy is, however, characterized by a low specificity with a high rate of false positive findings. In the present paper we propose to combine autofluorescence bronchoscopy with optical spectroscopy to improve the specificity of autofluorescence imaging, while maintaining the high sensitivity. Standard autofluorescence bronchoscopy was used to find suspect lesions in the upper bronchial tree, and these lesions were subsequently characterized spectroscopically using a custom made fiberoptic probe. Autofluorescence spectra of the lesions as well as reflectance spectra were measured. We will show in this preliminary report that the addition of either of these spectroscopic techniques decreases the rate of false positives findings, with the best results obtained when both spectroscopic modalities are combined.

Clinical study for classification of benign, dysplastic, and malignant oral lesions using autofluorescence spectroscopy.

Autofluorescence spectroscopy shows promising results for detection and staging of oral (pre-)malignancies. To improve staging reliability, we develop and compare algorithms for lesion classification. Furthermore, we examine the potential for detecting invisible tissue alterations. Autofluorescence spectra are recorded at six excitation wavelengths from 172 benign, dysplastic, and cancerous lesions and from 97 healthy volunteers. We apply principal components analysis (PCA), artificial neural networks, and red/green intensity ratio's to separate benign from (pre-)malignant lesions, using four normalization techniques. To assess the potential for detecting invisible tissue alterations, we compare PC scores of healthy mucosa and surroundings/contralateral positions of lesions. The spectra show large variations in shape and intensity within each lesion group. Intensities and PC score distributions demonstrate large overlap between benign and (pre-)malignant lesions. The receiver-operator characteristic areas under the curve (ROC-AUCs) for distinguishing cancerous from healthy tissue are excellent (0.90 to 0.97). However, the ROC-AUCs are too low for classification of benign versus (pre-)malignant mucosa for all methods (0.50 to 0.70). Some statistically significant differences between surrounding/contralateral tissues of benign and healthy tissue and of (pre-)malignant lesions are observed. We can successfully separate healthy mucosa from cancers (ROC-AUC>0.9). However, autofluorescence spectroscopy is not able to distinguish benign from visible (pre-)malignant lesions using our methods (ROC-AUC<0.65). The observed significant differences between healthy tissue and surroundings/contralateral positions of lesions might be useful for invisible tissue alteration detection.

The MDF discrimination measure: Fisher in disguise.

Recently, a discrimination measure for feature extraction for two-class data, called the maximum discriminating (MDF) measure (Talukder and Casasent [Neural Networks 14 (2001) 1201-1218]), was introduced. In the present paper, it is shown that the MDF discrimination measure produces exactly the same results as the classical Fisher criterion, on the condition that the two prior probabilities are chosen to be equal. The effect of unequal priors on the efficiency of the measures is also discussed.

Linear dimensionality reduction via a heteroscedastic extension of LDA: the Chernoff criterion.

We propose an eigenvector-based heteroscedastic linear dimension reduction (LDR) technique for multiclass data. The technique is based on a heteroscedastic two-class technique which utilizes the so-called Chernoff criterion, and successfully extends the well-known linear discriminant analysis (LDA). The latter, which is based on the Fisher criterion, is incapable of dealing with heteroscedastic data in a proper way. For the two-class case, the between-class scatter is generalized so to capture differences in (co)variances. It is shown that the classical notion of between-class scatter can be associated with Euclidean distances between class means. From this viewpoint, the between-class scatter is generalized by employing the Chernoff distance measure, leading to our proposed heteroscedastic measure. Finally, using the results from the two-class case, a multiclass extension of the Chernoff criterion is proposed. This criterion combines separation information present in the class mean as well as the class covariance matrices. Extensive experiments and a comparison with similar dimension reduction techniques are presented.

Spherical and Hyperbolic Embeddings of Data.

Many computer vision and pattern recognition problems may be posed as the analysis of a set of dissimilarities between objects. For many types of data, these dissimilarities are not euclidean (i.e., they do not represent the distances between points in a euclidean space), and therefore cannot be isometrically embedded in a euclidean space. Examples include shape-dissimilarities, graph distances and mesh geodesic distances. In this paper, we provide a means of embedding such non-euclidean data onto surfaces of constant curvature. We aim to embed the data on a space whose radius of curvature is determined by the dissimilarity data. The space can be either of positive curvature (spherical) or of negative curvature (hyperbolic). We give an efficient method for solving the spherical and hyperbolic embedding problems on symmetric dissimilarity data. Our approach gives the radius of curvature and a method for approximating the objects as points on a hyperspherical manifold without optimisation. For objects which do not reside exactly on the manifold, we develop a optimisation-based procedure for approximate embedding on a hyperspherical manifold. We use the exponential map between the manifold and its local tangent space to solve the optimisation problem locally in the euclidean tangent space. This process is efficient enough to allow us to embed data sets of several thousand objects. We apply our method to a variety of data including time warping functions, shape similarities, graph similarity and gesture similarity data. In each case the embedding maintains the local structure of the data while placing the points in a metric space.

Automated colorectal cancer diagnosis for whole-slice histopathology.

In this study, we propose a computational diagnosis system for detecting the colorectal cancer from histopathological slices. The computational analysis was usually performed on patch level where only a small part of the slice is covered. However, slice-based classification is more realistic for histopathological diagnosis. The developed method combines both textural and structural features from patch images and proposes a two level classification scheme. In the first level, the patches in slices are classified into possible classes (adenomatous, inflamed, cancer and normal) and the distribution of the patches into these classes is considered as the information representing the slices. Then the slices are classified using a logistic linear classifier. In patch level, we obtain the correct classification accuracies of 94.36% and 96.34% for the cancer and normal classes, respectively. However, in slice level, the accuracies of the 79.17% and 92.68% are achieved for cancer and normal classes, respectively.

Image dissimilarity-based quantification of lung disease from CT.

In this paper, we propose to classify medical images using dissimilarities computed between collections of regions of interest. The images are mapped into a dissimilarity space using an image dissimilarity measure, and a standard vector space-based classifier is applied in this space. The classification output of this approach can be used in computer aided-diagnosis problems where the goal is to detect the presence of abnormal regions or to quantify the extent or severity of abnormalities in these regions. The proposed approach is applied to quantify chronic obstructive pulmonary disease in computed tomography (CT) images, achieving an area under the receiver operating characteristic curve of 0.817. This is significantly better compared to combining individual region classifications into an overall image classification, and compared to common computerized quantitative measures in pulmonary CT.

Autofluorescence and diffuse reflectance spectroscopy for oral oncology.

BACKGROUND AND OBJECTIVES: Autofluorescence and diffuse reflectance spectroscopy have been used separately and combined for tissue diagnostics. Previously, we assessed the value of autofluorescence spectroscopy for the classification of oral (pre-)malignancies. In the present study, we want to determine the contributions of diffuse reflectance and autofluorescence spectroscopy to diagnostic performance. STUDY DESIGN/MATERIALS AND METHODS: Autofluorescence and diffuse reflectance spectra were recorded from 172 oral lesions and 70 healthy volunteers. Autofluorescence spectra were corrected in first order for blood absorption effects using diffuse reflectance spectra. Principal Components Analysis (PCA) with various classifiers was applied to distinguish (1) cancer and (2) all lesions from healthy oral mucosa, and (3) dysplastic and malignant lesions from benign lesions. Autofluorescence and diffuse reflectance spectra were evaluated separately and combined. RESULTS: The classification of cancer versus healthy mucosa gave excellent results for diffuse reflectance as well as corrected autofluorescence (Receiver Operator Characteristic (ROC) areas up to 0.98). For both autofluorescence and diffuse reflectance spectra, the classification of lesions versus healthy mucosa was successful (ROC areas up to 0.90). However, the classification of benign and (pre-)malignant lesions was not successful for raw or corrected autofluorescence spectra (ROC areas <0.70). For diffuse reflectance spectra, the results were slightly better (ROC areas up to 0.77). CONCLUSIONS: The results for plain and corrected autofluorescence as well as diffuse reflectance spectra were similar. The relevant information for distinguishing lesions from healthy oral mucosa is probably sufficiently contained in blood absorption and scattering information, as well as in corrected autofluorescence. However, neither type of information is capable of distinguishing benign from dysplastic and malignant lesions. Combining autofluorescence and reflectance only slightly improved the results.

Autofluorescence characteristics of healthy oral mucosa at different anatomical sites.

BACKGROUND AND OBJECTIVES: Autofluorescence spectroscopy is a promising tool for oral cancer detection. Its reliability might be improved by using a reference database of spectra from healthy mucosa. We investigated the influence of anatomical location on healthy mucosa autofluorescence. STUDY DESIGN/MATERIALS AND METHODS: Spectra were recorded from 97 volunteers using seven excitation wavelengths (350-450 nm), 455-867 nm emission. We studied intensity and applied principal component analysis (PCA) with classification algorithms. Class overlap estimates were calculated. RESULTS: We observed differences in fluorescence intensity between locations. These were significant but small compared to standard deviations (SD). Normalized spectra looked similar for locations, except for the dorsal side of the tongue (DST) and the vermilion border (VB). Porphyrin-like fluorescence was observed frequently, especially at DST. PCA and classification confirmed VB and DST to be spectrally distinct. The remaining locations showed large class overlaps. CONCLUSIONS: No relevant systematic spectral differences have been observed between most locations, allowing the use of one large reference database. For DST and VB separate databases are required.