Probabilities of Correct Classification in Discriminant Analysis

The technique of discriminant analysis is widely used for discriminating arson from nonarson structures. Since in this particular case only two groups are involved viz., the arson and the match groups, the computations required for obtaining a discriminant function are relatively simple. Because of this, it is possible to delete a variable by examining the value of a sub i d sub i where a sub i is the coefficient for the i-th variable in the discriminant function and d sub i is the difference between the means for the arson and the match groups for the i th variable (i=1, 2, ... , p). Thus, if a sub i d sub i is less than 0 then we delete the i th variable from consideration because inclusion of such a varable, increases the probability of misclassification. A prior knowledge of a i d i is particularly useful when we have large numbers of variables to be considered. This will help to reduce the number of discriminant functions one needs to consider in order to arrive at the discriminant function which minimizes the misclassification probability. Frequently, in developing a discriminant function one strives to increase the probability of correct classification. However, this probability reflects two components, viz., the probability of correct classification of known arson structures and the probability of correct classification of known nonarson structures. Even if the overall probability of correct classification is high, it does not necessarily imply, as the illustrations of Boston and New York City indicate, that the resulting discriminant function is also efficient in the sense that more arson cases are correctly classified than the nonarson cases. To this end, a procedure has been suggested to compute the cost of the wrong decision for a discriminant function which can be used to compare the cost of two similar types of discriminant functions. Using the relative cost efficiency criterion, it has been shown that the discriminant function for Newark is more efficient than the discriminant function for either Boston or New York City.

New instruments currently in design for Earth observational remote sensing from space offer promising advancements in the use of remote sensing for soil studies. Due to the enormous quantities of data generated by these high spectral resolution sensors, efficient use will only be feasible if new algorithms are developed to compress the data while maintaining information content. A spectral band selection algorithm is proposed to identify the important spectral bands for compression and classification of soil reflectance data. This algorithm was developed from the shape dominancy concept of Karhunen‐Loeve based optimal features. The high dimensional raw data were first transformed into much lower dimensionality by the derived spectral features. Canonical analysis was then used to transform the data under the maximal separability criterion into their final signal space where the data classification was performed. Soil data sets with and without stratification by soil order and climatic moisture zone were used to test the algorithm. The probabilities of correct classification of soil organic matter content using Landsat Multispectral Scanner (MSS) bands, Thematic Mapper (TM) bands, and the bands identified using the new band selection algorithm, were calculated and compared. The algorithm was successful in finding important spectral bands for soil organic matter content classification. The probabilities of correct classification obtained by using these bands were 0.850 and 0.883 for unstratified data sets, as compared to 0.600 to 0.640 for MSS bands and 0.640 to 0.653 for TM bands. Probabilities of correct classification for climate‐stratified data ranged from 0.910 to 0.980 using the calculated bands. The overall data compression ratio achieved using the algorithm was greater than 10 with no loss in classification accuracy.

To present an effective classification method based on the prevalence of Schistosoma mansoni in the community. We created decision rules (defined by cut-offs for number of positive slides), which account for imperfect sensitivity, both with a simple adjustment of fixed sensitivity and with a more complex adjustment of changing sensitivity with prevalence. To reduce screening costs while maintaining accuracy, we propose a pooled classification method. To estimate sensitivity, we use the De Vlas model for worm and egg distributions. We compare the proposed method with the standard method to investigate differences in efficiency, measured by number of slides read, and accuracy, measured by probability of correct classification. Modelling varying sensitivity lowers the lower cut-off more significantly than the upper cut-off, correctly classifying regions as moderate rather than lower, thus receiving life-saving treatment. The classification method goes directly to classification on the basis of positive pools, avoiding having to know sensitivity to estimate prevalence. For model parameter values describing worm and egg distributions among children, the pooled method with 25 slides achieves an expected 89.9% probability of correct classification, whereas the standard method with 50 slides achieves 88.7%. Among children, it is more efficient and more accurate to use the pooled method for classification of S. mansoni prevalence than the current standard method.

This report describes the hardware system and the set of algorithms we have developed for detecting damage in cables for the Advanced Development and Process Technologies (ADAPT) Program. This program is part of the W80 Life Extension Program (LEP). The system could be generalized for application to other systems in the future. Critical cables can undergo various types of damage (e.g. short circuits, open circuits, punctures, compression) that manifest as changes in the dielectric/impedance properties of the cables. For our specific problem, only one end of the cable is accessible, and no exemplars of actual damage are available. This work addresses the detection of dielectric/impedance anomalies in transient time domain reflectometry (TDR) measurements on the cables. The approach is to interrogate the cable using time domain reflectometry (TDR) techniques, in which a known pulse is inserted into the cable, and reflections from the cable are measured. The key operating principle is that any important cable damage will manifest itself as an electrical impedance discontinuity that can be measured in the TDR response signal. Machine learning classification algorithms are effectively eliminated from consideration, because only a small number of cables is available for testing; so a sufficient sample size is not attainable. Nonetheless, a key requirement is to achieve very high probability of detection and very low probability of false alarm. The approach is to compare TDR signals from possibly damaged cables to signals or an empirical model derived from reference cables that are known to be undamaged. This requires that the TDR signals are reasonably repeatable from test to test on the same cable, and from cable to cable. Empirical studies show that the repeatability issue is the 'long pole in the tent' for damage detection, because it is has been difficult to achieve reasonable repeatability. This one factor dominated the project. The two-step model-based approach is summarized as follows: Step 1, Cable Modeling: Given input-output TDR signals s(n) and x{sub U}(n) for a cable known to be free of damage, system identification algorithms are used to compute a dynamic prediction-error cable model that has output {cflx x}{sub U}(n). The model is declared valid when the innovations e{sub U}(n) = x{sub U}(n) {cflx x}{sub U}(n) satisfy a statistical zero-mean whiteness test. This validated model output is then used as a known reference to which other cables can be compared. Step 2, Cable Testing: The TDR output signal x{sub D}(n) from a cable under test is compared with the model output {cflx x}{sub U}(n) by computing the innovations e{sub D}(n) = x{sub D}(n) {cflx x}{sub U}(n). The innovations are tested using a short-term whiteness test statistic, which employs a statistical confidence interval. If the cable passes the test, this implies that the model is valid and the cable is declared undamaged. If the cable fails the test, this indicates a model mismatch, which means that the cable's dielectric properties have changed; and this implies that the cable is damaged. The test threshold is adjusted to maximize probability of detection and minimize probability of false alarm according to an empirically determined receiver operating characteristic (ROC) curve. An associated confidence interval on the probability of correct classification is also provided. The effectiveness of the algorithm is demonstrated using measured TDR signals for undamaged and damaged cables. Experimental and algorithmic methods for coping with repeatability issues are presented. The model-based damage detection algorithms have been shown to perform well for some representative examples of real TDR signals acquired using the two-dimensional (2D) mockup fixture. If the damage causes a short circuit, then damage detection performance is generally good to excellent. Examples include the cases demonstrated in this report for cuts and pinholes. If the damage does not cause a short circuit, then damage detection performance is generally poor to fair. Examples include the cases demonstrated in this report for crushes and partial cuts.

BackgroundMost studies of epidemic detection focus on their start and rarely on the whole signal or the end of the epidemic. In some cases, it may be necessary to retrospectively identify outbreak signals from surveillance data. Our study aims at evaluating the ability of change point analysis (CPA) methods to locate the whole disease outbreak signal. We will compare our approach with the results coming from experts’ signal inspections, considered as the gold standard method.MethodsWe simulated 840 time series, each of which includes an epidemic-free baseline (7 options) and a type of epidemic (4 options). We tested the ability of 4 CPA methods (Max-likelihood, Kruskall-Wallis, Kernel, Bayesian) methods and expert inspection to identify the simulated outbreaks. We evaluated the performances using metrics including delay, accuracy, bias, sensitivity, specificity and Bayesian probability of correct classification (PCC).ResultsA minimum of 15 h was required for experts for analyzing the 840 curves and a maximum of 25 min for a CPA algorithm. The Kernel algorithm was the most effective overall in terms of accuracy, bias and global decision (PCC = 0.904), compared to PCC of 0.848 for human expert review.ConclusionsFor the aim of retrospectively identifying the start and end of a disease outbreak, in the absence of human resources available to do this work, we recommend using the Kernel change point model. And in case of experts’ availability, we also suggest to supplement the Human expertise with a CPA, especially when the signal noise difference is below 0.Electronic supplementary materialThe online version of this article (doi:10.1186/s12911-016-0271-x) contains supplementary material, which is available to authorized users.

The paper describes an approach to parametric optimization of an IR imaging system. This approach is based on minimization of image distortion of a multi-bar test object. The quality of imaging system is defined by a probability of correct pixel classification. This probability characterizes an error of image binarization. The paper represents the mathematical model that binds the probability of correct pixel classification with parameters of an imaging system such as focal length, aperture diameter, dimensions of photosensitive element, integration time and etc. It allows to get the merit function for parametric optimization and to identify the optimal relationship between spatial resolution and temperature resolution.

Detection of Mastitis in Dairy Cattle by Use of Mixture Models for Repeated Somatic Cell Scores: A Bayesian Approach via Gibbs Sampling

Calculation of the probability of correct classification in probabilistic bagged k-Nearest Neighbours

In many pattern recognition/classification problem the true class conditional model and class probabilities are approximated for reasons of reducing complexity and/or of statistical estimation. The...

We seek to understand the extraction of radar micro-Doppler signals generated by human motions at long range and with a front-view to use them as a biometric. We describe micro-Doppler algorithms used for the detection and tracking, and detail the gait features that can be extracted. We have measurements of multiple human subjects in outdoor but low-clutter backgrounds for identification and find that at long range and front-view, the probability of correct classification can be over 80%. However, the micro-Doppler signals are dependent on the direction of motion, and we discuss methods to reduce the effect of the direction of motion. These radar biometric features can serve as identifying features in a scene with multiple subjects. Ground truth using video and GPS is used to validate the radar data.

Receiver operating characteristic curve analysis of clinical risk models

This paper is concerned with the development of a system for the classification of military munitions and unexploded ordnance (UXO) in shallow underwater environments. A Matched Subspace Classifier (MSC) is used in conjunction with Acoustic Color (AC) features generated from the raw sonar returns for munition characterization. Our classification hypothesis is that spectral content of the sonar backscatter display unique acoustic signatures providing good discrimination between different classes of detected contacts. The system is exclusively trained using synthetic sonar data and then tested using real data sets collected from a side-looking sonar system. These data sets were collected using underwater objects in relatively controlled and clutter-free environments. Classification results are presented using standard performance metrics such as probability of correct classification (P CC ), probability of false alarm (P FA ) in Receiver Operating Characteristic (ROC) curves, and confusion matrices.

This paper focuses on the experimental evaluation of a range image segmentation system which partitions range data into homogeneous surface patches using estimates of the sign of the mean and Gaussian curvatures. The authors report the results of an extensive testing program aimed at investigating the behavior of important experimental parameters such as the probability of correct classification and the accuracy of curvature estimates, measured over variations of significant segmentation variables. Evaluation methods in computer vision are often unstructured and subjective: this paper contributes a useful example of extensive experimental assessment of surface-based range segmentation. >

We consider the $M$-ary classification problem via crowdsourcing, where crowd workers respond to simple binary questions and the answers are aggregated via decision fusion. The workers have a reject option to skip answering a question when they do not have the expertise, or when the confidence of answering that question correctly is low. We further consider that there are spammers in the crowd who respond to the questions with random guesses. Under the payment mechanism that encourages the reject option, we study the behavior of honest workers and spammers, whose objectives are to maximize their monetary rewards. To accurately characterize human behavioral aspects, we employ prospect theory to model the rationality of the crowd workers, whose perception of costs and probabilities are distorted based on some value and weight functions, respectively. Moreover, we estimate the number of spammers and employ a weighted majority voting decision rule, where we assign an optimal weight for every worker to maximize the system performance. The probability of correct classification and asymptotic system performance are derived. We also provide simulation results to demonstrate the effectiveness of our approach.

A learning-based classification problem with a large number of classes is considered. The error-correcting-output-codes (ЕСОС) scheme is optimized. An initial binary matrix is formed at random so that the number of its rows is equal to the number of classes and each column corresponds to the union of several classes in two macroclasses. In the ЕСОС approach, a binary classification problem is solved for every object to be recognized and for every union. The object is assigned to the class with the nearest code row. A generalization of the ЕСОС approach is presented in which a discrete optimization problem is solved to find optimal unions, probabilities of correct classification are used in dichotomy problems, and the degree of dichotomy informativeness is taken into account. If the solution algorithms for the dichotomy problems are correct, the recognition algorithm for the original problem is correct as well.