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H P Chan

Publications and source records attributed to H P Chan.

At least 19 recordsLinked to original sources
PubMed2002

Effects of antioxidants on pyridinoline cross-link formation in culture supernatants of fibroblasts from normal skin and hypertrophic scars.

Free radicals are normally generated in many metabolic pathways. They are closely associated with inflammatory diseases. The aim of this study was to investigate the effects of free radicals and their antioxidants on the formation of pyridinoline using human fibroblasts from normal skin and hypertrophic scars. The significance of the increase in pyridinoline cross-links is that large quantities have been found in hypertrophic scars formed post-burn than in normal skin, and that catalase was effective in reducing the pyridinoline cross-link formation in hypertrophic scars. The pyridinoline cross-link concentration expressed in nM/ micro g hydroxyl proline was found to be higher in the culture supernatants of the fibroblasts from hypertrophic scars (9.04 +/- 2.74) than that of normal skin (7.55 +/- 2.1). When the human fibroblasts from normal skin and hypertrophic scar were subject to hydroxyl radicals generated by the Fenton reaction, there was no significant increase in pyridinoline cross-link concentration (nm/ micro g hydroxyl proline) in the supernatants compared with the control. When the controls plus various treatments with free radicals were subject to different antioxidants, including superoxide dismutase, catalase, glutathione peroxidase, and desferrioxamine, it was found that catalase alone was most effective in scavenging hydroxyl radicals as determined by the decrease in pyridinoline cross-links.

Amino Acids↗
PubMed2001

Digital mammography: observer performance study of the effects of pixel size on the characterization of malignant and benign microcalcifications.

RATIONALE AND OBJECTIVES: The authors performed this study to evaluate the effects of pixel size on the characterization of mammographic microcalcifications by radiologists. MATERIALS AND METHODS: Two-view mammograms of 112 microcalcification clusters were digitized with a laser scanner at a pixel size of 35 microm. Images with pixel sizes of 70, 105, and 140 microm were derived from the 35-microm-pixel size images by averaging neighboring pixels. The malignancy or benignity of the microcalcifications had been determined with findings at biopsy or 2-year follow-up. Region-of-interest images containing the microcalcifications were printed with a laser imager. Seven radiologists participated in a receiver operating characteristic (ROC) study to estimate the likelihood of malignancy. The classification accuracy was quantified with the area under the ROC curve (Az). The statistical significance of the differences in the Az values for different pixel sizes was estimated with the Dorfman-Berbaum-Metz method and the Student paired t test. The variance components were analyzed with a bootstrap method. RESULTS: The higher-resolution images did not result in better classification; the average Az with a pixel size of 35 microm was lower than that with pixel sizes of 70 and 105 microm. The differences in Az between different pixel sizes did not achieve statistical significance. CONCLUSION: Pixel sizes in the range studied do not have a strong effect on radiologists' accuracy in the characterization of microcalcifications. The low specificity of the image features of microcalcifications and the large interobserver and intraobserver variabilities may have prevented small advantages in image resolution from being observed.

Breast Diseases↗
PubMed2001

Analysis of uncertainties in estimates of components of variance in multivariate ROC analysis.

RATIONALE AND OBJECTIVES: Solutions have previously been presented to the problem of estimating the components of variance in the general linear model used for multivariate receiver operating characteristic (ROC) analysis. The case where the variance components do not change across the modalities under comparison was first treated, followed by the case where they are permitted to change. No analysis of uncertainties in these estimates has been presented previously. MATERIALS AND METHODS: For the case where the variance components do not change across modalities, the "jackknife-after-bootstrap" resampling procedure can be used together with conventional linear propagation of variance to solve for the uncertainties in estimates of the components. For the case where the components are permitted to change across modalities, a slight elaboration of this procedure is presented. RESULTS: The approach was validated by Monte Carlo simulations, where uncertainties in estimates of the variance components calculated by the jackknife-after-bootstrap procedure were found to converge in the mean to the Monte Carlo results over many independent trials. The method is exemplified with data from a study of readers-with and without the aid of a computer-assist modality-given the task of discriminating benign from malignant masses in mammography. CONCLUSION: The present approach is relevant to a broad class of problems where estimates of multiple contributions to the variance observed in ROC assessment of diagnostic modalities are desired, in particular, for the assessment of multiple-reader studies of computer-aided diagnosis in radiology where the variance components may change across reading modalities (eg, unaided vs computer-aided reading).

Analysis of Variance↗
PubMed2001

Computer-aided characterization of mammographic masses: accuracy of mass segmentation and its effects on characterization.

Mass segmentation is used as the first step in many computer-aided diagnosis (CAD) systems for classification of breast masses as malignant or benign. The goal of this paper was to study the accuracy of an automated mass segmentation method developed in our laboratory, and to investigate the effect of the segmentation stage on the overall classification accuracy. The automated segmentation method was quantitatively compared with manual segmentation by two expert radiologists (R1 and R2) using three similarity or distance measures on a data set of 100 masses. The area overlap measures between R1 and R2, the computer and R1, and the computer and R2 were 0.76 +/- 0.13, 0.74 +/- 0.11, and 0.74 +/- 0.13, respectively. The interobserver difference in these measures between the two radiologists was compared with the corresponding differences between the computer and the radiologists. Using three similarity measures and data from two radiologists, a total of six statistical tests were performed. The difference between the computer and the radiologist segmentation was significantly larger than the interobserver variability in only one test. Two sets of texture, morphological, and spiculation features, one based on the computer segmentation, and the other based on radiologist segmentation, were extracted from a data set of 249 films from 102 patients. A classifier based on stepwise feature selection and linear discriminant analysis was trained and tested using the two feature sets. The leave-one-case-out method was used for data sampling. For case-based classification, the area Az under the receiver operating characteristic (ROC) curve was 0.89 and 0.88 for the feature sets based on the radiologist segmentation and computer segmentation, respectively. The difference between the two ROC curves was not statistically significant.

Algorithms↗
PubMed2001

Automated registration of breast lesions in temporal pairs of mammograms for interval change analysis--local affine transformation for improved localization.

Analysis of interval change is important for mammographic interpretation. The aim of this study is to evaluate the use of an automated registration technique for computer-aided interval change analysis in mammography. Previously we developed a regional registration technique for identifying masses on temporal pairs of mammograms. In the current study, we improved lesion registration by including a local alignment step. Initially, the lesion position on the prior mammogram was estimated based on the breast geometry. An initial fan-shaped search region was then defined on the prior mammogram. In the second stage, the location of the fan-shaped region on the prior mammogram was refined by warping, based on an affine transformation and simplex optimization in a local region. In the third stage, a search for the best match between the lesion template from the current mammogram and a structure on the prior mammogram was carried out within the search region. This technique was evaluated on 124 temporal pairs of mammograms containing biopsyproven masses. Eighty-seven percent of the estimated lesion locations resulted in an area overlap of at least 50% with the true lesion locations and an average distance of 2.4 +/- 2.1 mm between their centroids. The average distance between the estimated and the true centroid of the lesions on the prior mammogram over all 124 temporal pairs was 4.2 +/- 5.7 mm. The registration accuracy was improved in comparison with our previous study that used a data set of 74 temporal pairs of mammograms. This improvement in accuracy resulted from the improved geometry estimation and the local affine transformation.

Biophysical Phenomena↗
PubMed2001

Computerized image analysis: estimation of breast density on mammograms.

An automated image analysis tool is being developed for the estimation of mammographic breast density. This tool may be useful for risk estimation or for monitoring breast density change in prevention or intervention programs. In this preliminary study, a data set of 4-view mammograms from 65 patients was used to evaluate our approach. Breast density analysis was performed on the digitized mammograms in three stages. First, the breast region was segmented from the surrounding background by an automated breast boundary-tracking algorithm. Second, an adaptive dynamic range compression technique was applied to the breast image to reduce the range of the gray level distribution in the low frequency background and to enhance the differences in the characteristic features of the gray level histogram for breasts of different densities. Third, rule-based classification was used to classify the breast images into four classes according to the characteristic features of their gray level histogram. For each image, a gray level threshold was automatically determined to segment the dense tissue from the breast region. The area of segmented dense tissue as a percentage of the breast area was then estimated. To evaluate the performance of the algorithm, the computer segmentation results were compared to manual segmentation with interactive thresholding by five radiologists. A "true" percent dense area for each mammogram was obtained by averaging the manually segmented areas of the radiologists. We found that the histograms of 6% (8 CC and 8 MLO views) of the breast regions were misclassified by the computer, resulting in poor segmentation of the dense region. For the images with correct classification, the correlation between the computer-estimated percent dense area and the "truth" was 0.94 and 0.91, respectively, for CC and MLO views, with a mean bias of less than 2%. The mean biases of the five radiologists' visual estimates for the same images ranged from 0.1% to 11%. The results demonstrate the feasibility of estimating mammographic breast density using computer vision techniques and its potential to improve the accuracy and reproducibility of breast density estimation in comparison with the subjective visual assessment by radiologists.

Biophysical Phenomena↗
PubMed2001

Improvement of mammographic mass characterization using spiculation meausures and morphological features.

We are developing new computer vision techniques for characterization of breast masses on mammograms. We had previously developed a characterization method based on texture features. The goal of the present work was to improve our characterization method by making use of morphological features. Toward this goal, we have developed a fully automated, three-stage segmentation method that includes clustering, active contour, and spiculation detection stages. After segmentation, morphological features describing the shape of the mass were extracted. Texture features were also extracted from a band of pixels surrounding the mass. Stepwise feature selection and linear discriminant analysis were employed in the morphological, texture, and combined feature spaces for classifier design. The classification accuracy was evaluated using the area Az under the receiver operating characteristic curve. A data set containing 249 films from 102 patients was used. When the leave-one-case-out method was applied to partition the data set into trainers and testers, the average test Az for the task of classifying the mass on a single mammographic view was 0.83 +/- 0.02, 0.84 +/- 0.02, and 0.87 +/- 0.02 in the morphological, texture, and combined feature spaces, respectively. The improvement obtained by supplementing texture features with morphological features in classification was statistically significant (p = 0.04). For classifying a mass as malignant or benign, we combined the leave-one-case-out discriminant scores from different views of a mass to obtain a summary score. In this task, the test Az value using the combined feature space was 0.91 +/- 0.02. Our results indicate that combining texture features with morphological features extracted from automatically segmented mass boundaries will be an effective approach for computer-aided characterization of mammographic masses.

Automation↗
PubMed2001

Selection of an optimal neural network architecture for computer-aided detection of microcalcifications--comparison of automated optimization techniques.

Many computer-aided diagnosis (CAD) systems use neural networks (NNs) for either detection or classification of abnormalities. Currently, most NNs are "optimized" by manual search in a very limited parameter space. In this work, we evaluated the use of automated optimization methods for selecting an optimal convolution neural network (CNN) architecture. Three automated methods, the steepest descent (SD), the simulated annealing (SA), and the genetic algorithm (GA), were compared. We used as an example the CNN that classifies true and false microcalcifications detected on digitized mammograms by a prescreening algorithm. Four parameters of the CNN architecture were considered for optimization, the numbers of node groups and the filter kernel sizes in the first and second hidden layers, resulting in a search space of 432 possible architectures. The area Az under the receiver operating characteristic (ROC) curve was used to design a cost function. The SA experiments were conducted with four different annealing schedules. Three different parent selection methods were compared for the GA experiments. An available data set was split into two groups with approximately equal number of samples. By using the two groups alternately for training and testing, two different cost surfaces were evaluated. For the first cost surface, the SD method was trapped in a local minimum 91% (392/432) of the time. The SA using the Boltzman schedule selected the best architecture after evaluating, on average, 167 architectures. The GA achieved its best performance with linearly scaled roulette-wheel parent selection; however, it evaluated 391 different architectures, on average, to find the best one. The second cost surface contained no local minimum. For this surface, a simple SD algorithm could quickly find the global minimum, but the SA with the very fast reannealing schedule was still the most efficient. The same SA scheme, however, was trapped in a local minimum on the first cost surface. Our CNN study demonstrated that, if optimization is to be performed on a cost surface whose characteristics are not known a priori, it is advisable that a moderately fast algorithm such as a SA using a Boltzman cooling schedule be used to conduct an efficient and thorough search, which may offer a better chance of reaching the global minimum.

Algorithms↗
PubMed2001

Analysis of temporal changes of mammographic features: computer-aided classification of malignant and benign breast masses.

A new classification scheme was developed to classify mammographic masses as malignant and benign by using interval change information. The masses on both the current and the prior mammograms were automatically segmented using an active contour method. From each mass, 20 run length statistics (RLS) texture features, 3 speculation features, and 12 morphological features were extracted. Additionally, 20 difference RLS features were obtained by subtracting the prior RLS features from the corresponding current RLS features. The feature space consisted of the current RLS features, the difference RLS features, the current and prior speculation features, and the current and prior mass sizes. Stepwise feature selection and linear discriminant analysis classification were used to select and merge the most useful features. A leave-one-case-out resampling scheme was used to train and test the classifier using 140 temporal image pairs (85 malignant, 55 benign) obtained from 57 biopsy-proven masses (33 malignant, 24 benign) in 56 patients. An average of 10 features were selected from the 56 training subsets: 4 difference RLS features, 4 RLS features, and 1 speculation feature from the current image, and 1 speculation feature from the prior, were most often chosen. The classifier achieved an average training Az of 0.92 and a test Az of 0.88. For comparison, a classifier was trained and tested using features extracted from the 120 current single images. This classifier achieved an average training Az of 0.90 and a test Az of 0.82. The information on the prior image significantly (p = 0.015) improved the accuracy for classification of the masses.

Algorithms↗
PubMed2000

Phototimer setup for CR imaging.

A study was performed to investigate the feasibility of using the standard deviation (sigma) of the pixel values in a computed radiography (CR) image and a measure of the median incident exposure on the imaging plate (IP) as parameters for setting up phototimers in a CR system. Slabs of Lucite 4-, 6-, and 8-in.-thick were imaged with a CR system at 70, 90, and 125 kVp at various mA s values both with grid and without grid. Incident IP exposures were measured with an ionization chamber. Images were analyzed on a workstation. The sigma's in the "flat field" images were found to be approximately related to the mean incident exposure E by the relationship: sigma is proportional to E(-1/2), indicating the quantum-noise-limited operation of the system. Derived relationships between the reading sensitivity of the (IP) reader (S number) and sigma can be used to obtain images with a specific noise level. At our institution, where a 400 speed screen-film system is used for general radiography and 200 speed for chest radiography, radiologists generally find CR image quality acceptable when sigma < or = 11 (S< or =400) for general radiography (50-90 kVp), and sigma < or =8 (S< or =200) for chest radiography (125 kVp). However, factors other than the amount of x-ray quanta that form the useful image, such as the image processing mode and the amount of collimation, may affect both the sensitivity value and the image quality.

Humans↗
PubMed2000

Stereomammography: evaluation of depth perception using a virtual 3D cursor.

We are evaluating the usefulness of stereomammography in improving breast cancer diagnosis. One area that we are investigating is whether the improved depth perception associated with stereomammography might be significantly enhanced with the use of a virtual 3D cursor. A study was performed to evaluate the accuracy of absolute depth measurements made in stereomammograms with such a cursor. A biopsy unit was used to produce digital stereo images of a phantom containing 50 low contrast fibrils (0.5 mm diam monofilaments) at depths ranging from 1 to 11 mm, with a minimum spacing of 2 mm. Half of the fibrils were oriented perpendicular (vertical) and half parallel (horizontal) to the stereo shift direction. The depth and orientation of each fibril were randomized, and the horizontal and vertical fibrils crossed, simulating overlapping structures in a breast image. Left and right eye images were generated by shifting the x-ray tube from +2.5 degrees to -2.5 degrees relative to the image receptor. Three observers viewed these images on a computer display with stereo glasses and adjusted the position of a cross-shaped virtual cursor to best match the perceived location of each fibril. The x, y, and z positions of the cursor were indicated on the display. The z (depth) coordinate was separately calibrated using known positions of fibrils in the phantom. The observers analyzed images of two configurations of the phantom. Thus, each observer made 50 vertical filament depth measurements and 50 horizontal filament depth measurements. These measurements were compared with the true depths. The correlation coefficients between the measured and true depths of the vertically oriented fibrils for the three observers were 0.99, 0.97, and 0.89 with standard errors of the estimates of 0.39 mm, 0.83 mm, and 1.33 mm, respectively. Corresponding values for the horizontally oriented fibrils were 0.91, 0.28, and 0.08, and 1.87 mm, 4.19 mm, and 3.13 mm. All observers could estimate the absolute depths of vertically oriented objects fairly accurately in digital stereomammograms; however, only one observer was able to accurately estimate the depths of horizontally oriented objects. This may relate to different aptitudes for stereoscopic visualization. The orientations of most objects in actual mammograms are combinations of horizontal and vertical. Further studies are planned to evaluate absolute depth measurements of fibrils oriented at various intermediate angles and of objects of different shapes. The effects of the shape and contrast of the virtual cursor and the stereo shift angle on the accuracy of the depth measurements will also be investigated.

Biophysical Phenomena↗
PubMed2000

Feature selection and classifier performance in computer-aided diagnosis: the effect of finite sample size.

In computer-aided diagnosis (CAD), a frequently used approach for distinguishing normal and abnormal cases is first to extract potentially useful features for the classification task. Effective features are then selected from this entire pool of available features. Finally, a classifier is designed using the selected features. In this study, we investigated the effect of finite sample size on classification accuracy when classifier design involves stepwise feature selection in linear discriminant analysis, which is the most commonly used feature selection algorithm for linear classifiers. The feature selection and the classifier coefficient estimation steps were considered to be cascading stages in the classifier design process. We compared the performance of the classifier when feature selection was performed on the design samples alone and on the entire set of available samples, which consisted of design and test samples. The area Az under the receiver operating characteristic curve was used as our performance measure. After linear classifier coefficient estimation using the design samples, we studied the hold-out and resubstitution performance estimates. The two classes were assumed to have multidimensional Gaussian distributions, with a large number of features available for feature selection. We investigated the dependence of feature selection performance on the covariance matrices and means for the two classes, and examined the effects of sample size, number of available features, and parameters of stepwise feature selection on classifier bias. Our results indicated that the resubstitution estimate was always optimistically biased, except in cases where the parameters of stepwise feature selection were chosen such that too few features were selected by the stepwise procedure. When feature selection was performed using only the design samples, the hold-out estimate was always pessimistically biased. When feature selection was performed using the entire finite sample space, the hold-out estimates could be pessimistically or optimistically biased, depending on the number of features available for selection, the number of available samples, and their statistical distribution. For our simulation conditions, these estimates were always pessimistically (conservatively) biased if the ratio of the total number of available samples per class to the number of available features was greater than five.

Algorithms↗
PubMed2000

Adverse effects of increased body weight on quantitative measures of mammographic image quality.

OBJECTIVE: The purpose of our study was to show that compressed breast thickness on mammograms in overweight and obese women exceeds the thickness in normal-weight women and that increased thickness results in image degradation. SUBJECTS AND METHODS: Three hundred consecutive routine mammograms were reviewed. Patients were categorized according to body mass index. Compression thickness, compressive force, kilovoltage, and milliampere-seconds were recorded. Geometric unsharpness and contrast degradation were calculated for each body mass index category. RESULTS: Body mass index categories were lean (3%), normal (36%), overweight (36%), and obese (25%). Body mass index was directly correlated with compressed thickness. In the mediolateral oblique view, the mean thickness of the obese category exceeded normal thickness by 18 mm (p < 0.01), corresponding to a 32% increase in geometric unsharpness. Mean obese thickness exceeded lean thickness by 33 mm (p < 0.01), corresponding to a 79% increase in unsharpness. Similar trends were observed for the craniocaudal view. In the mediolateral oblique projection, there was an increase of 1.0 kVp (p < 0.01) for obese compared with normal and 1.7 kVp (p < 0.01) between lean and obese, corresponding, respectively, to a 16% and a 25% decrease in image contrast because of scatter and kilovoltage changes. Milliampere-seconds increased by 47% on the mediolateral oblique images in the obese category compared with normal body mass index. CONCLUSION: An increased body mass index was associated with greater compressed breast thickness, resulting in increased geometric unsharpness, decreased image contrast, and greater potential for motion unsharpness.

Adult↗
PubMed1999

Classification of malignant and benign masses based on hybrid ART2LDA approach.

A new type of classifier combining an unsupervised and a supervised model was designed and applied to classification of malignant and benign masses on mammograms. The unsupervised model was based on an adaptive resonance theory (ART2) network which clustered the masses into a number of separate classes. The classes were divided into two types: one containing only malignant masses and the other containing a mix of malignant and benign masses. The masses from the malignant classes were classified by ART2. The masses from the mixed classes were input to a supervised linear discriminant classifier (LDA). In this way, some malignant masses were separated and classified by ART2 and the less distinguishable benign and malignant masses were classified by LDA. For the evaluation of classifier performance, 348 regions of interest (ROI's) containing biopsy proven masses (169 benign and 179 malignant) were used. Ten different partitions of training and test groups were randomly generated using an average of 73% of ROI's for training and 27% for testing. Classifier design, including feature selection and weight optimization, was performed with the training group. The test group was kept independent of the training group. The performance of the hybrid classifier was compared to that of an LDA classifier alone and a backpropagation neural network (BPN). Receiver operating characteristics (ROC) analysis was used to evaluate the accuracy of the classifiers. The average area under the ROC curve (A(z)) for the hybrid classifier was 0.81 as compared to 0.78 for the LDA and 0.80 for the BPN. The partial areas above a true positive fraction of 0.9 were 0.34, 0.27 and 0.31 for the hybrid, the LDA and the BPN classifier, respectively. These results indicate that the hybrid classifier is a promising approach for improving the accuracy of classification in CAD applications.

Biopsy↗
PubMed1999

Combined adaptive enhancement and region-growing segmentation of breast masses on digitized mammograms.

As an ongoing effort to develop a computer aid for detection of masses on mammograms, we recently designed an object-based region-growing technique to improve mass segmentation. This segmentation method utilizes the density-weighted contrast enhancement (DWCE) filter as a pre-processing step. The DWCE filter adaptively enhances the contrast between the breast structures and the background. Object-based region growing was then applied to each of the identified structures. The region-growing technique uses gray-scale and gradient information to adjust the initial object borders and to reduce merging between adjacent or overlapping structures. Each object is then classified as a breast mass or normal tissue based on extracted morphological and texture features. In this study we evaluated the sensitivity of this combined segmentation scheme and its ability to reduce false positive (FP) detections on a data set of 253 digitized mammograms, each of which contained a biopsy-proven breast mass. It was found that the segmentation scheme detected 98% of the 253 biopsy-proven breast masses in our data set. After final FP reduction, the detection resulted in 4.2 FP per image at a 90% true positive (TP) fraction and 2.0 FPs per image at an 80% TP fraction. The combined DWCE and object-based region growing technique increased the initial detection sensitivity, reduced merging between neighboring structures, and reduced the number of FP detections in our automated breast mass detection scheme.

Biophysical Phenomena↗
PubMed1999

Design and evaluation of an external filter technique for exposure equalization in mammography.

We are developing an external filter method for equalizing x-ray exposure in the peripheral region of the breast. This method requires the use of only a limited number of custom-built filters for different breast shapes in a given view. This paper describes the design methodology for these external filters. The filter effectiveness was evaluated through a simulation study on 171 mediolateral and 196 craniocaudal view digitized mammograms and through imaging of a breast phantom. The degree of match between the simulated filter and the individual 3-D exposure profiles at the breast periphery was quantified. An analysis was performed to investigate the effect of filter misalignment. The simulation study indicates that the filter is effective in equalizing exposures for more than 80% of the breast images in our database. The tolerance in filter misalignment was estimated to be about +/- 2 mm for the CC view and +/- 1 mm for the MLO view at the image plane. Some misalignment artifacts were demonstrated with simulated filtered mammograms.

Biophysical Phenomena↗
PubMed1999

Classifier design for computer-aided diagnosis: effects of finite sample size on the mean performance of classical and neural network classifiers.

Classifier design is one of the key steps in the development of computer-aided diagnosis (CAD) algorithms. A classifier is designed with case samples drawn from the patient population. Generally, the sample size available for classifier design is limited, which introduces variance and bias into the performance of the trained classifier, relative to that obtained with an infinite sample size. For CAD applications, a commonly used performance index for a classifier is the area, Az, under the receiver operating characteristic (ROC) curve. We have conducted a computer simulation study to investigate the dependence of the mean performance, in terms of Az, on design sample size for a linear discriminant and two nonlinear classifiers, the quadratic discriminant and the backpropagation neural network (ANN). The performances of the classifiers were compared for four types of class distributions that have specific properties: multivariate normal distributions with equal covariance matrices and unequal means, unequal covariance matrices and unequal means, and unequal covariance matrices and equal means, and a feature space where the two classes were uniformly distributed in disjoint checkerboard regions. We evaluated the performances of the classifiers in feature spaces of dimensionality ranging from 3 to 15, and design sample sizes from 20 to 800 per class. The dependence of the resubstitution and hold-out performance on design (training) sample size (Nt) was investigated. For multivariate normal class distributions with equal covariance matrices, the linear discriminant is the optimal classifier. It was found that its Az-versus-1/Nt curves can be closely approximated by linear dependences over the range of sample sizes studied. In the feature spaces with unequal covariance matrices where the quadratic discriminant is optimal, the linear discriminant is inferior to the quadratic discriminant or the ANN when the design sample size is large. However, when the design sample is small, a relatively simple classifier, such as the linear discriminant or an ANN with very few hidden nodes, may be preferred because performance bias increases with the complexity of the classifier. In the regime where the classifier performance is dominated by the 1/Nt term, the performance in the limit of infinite sample size can be estimated as the intercept (1/Nt= 0) of a linear regression of Az versus 1/Nt. The understanding of the performance of the classifiers under the constraint of a finite design sample size is expected to facilitate the selection of a proper classifier for a given classification task and the design of an efficient resampling scheme.

Computer Simulation↗