Classification with Set-Valued Decision Functions

The fusion of multiple Computer Aided Detection/Computer Aided Classification (CAD/CAC) algorithms has been shown to be effective in reducing the false alarm rate associated with the automated classification of bottom mine-like objects when applied to side-scan sonar images taken in Very Shallow Water (VSW) environments [C.M. Ciany et al., 2001],[C.M. Ciany et al., 2000]. The fusion of CAD/CAC algorithms from Raytheon and NSWC Coastal Systems Station (CSS) also has been demonstrated in the shallow water environment on a single sonar data set [C.M. Ciany et al., 2002]. This paper extends the shallow water CAD/CAC/Fusion performance analysis to an additional set of sonar data taken in the Gulf of Mexico during June 1998, and adds the outputs of a third CAD/CAC algorithm from Lockheed Martin to the fusion processing. The fusion algorithm accepts the classification confidence levels and associated contact locations from the three different CAD/CAC algorithms, clusters the contacts based on the distance between their locations, and then declares a valid target when a clustered contact passes a prescribed fusion criterion. Four different fusion criteria are evaluated: the first based on the Fisher Discriminant, the second and third based on simple and constrained binary combinations of the multiple CAD/CAC processor outputs, and the fourth based on a constrained optimization approach that minimizes the total number of false alarms over the clustering distance and cluster confidence factor thresholds for a given probability of correct classification. The resulting performance of the four fusion algorithms is compared, and the overall performance benefit of a significant reduction of false alarms at high correct classification probabilities is quantified.

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.

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.

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.

Using Monte Carlo methods, the relationship is investigated between the actual probability of correct classification using the calculated linear discriminant function and the estimate of this probability which can be easily obtained by estimating the Miahalanobis distance between the two populations. Graphs are given for obtaining conservative confidence intervals for the probabilities of correct classification, given the estimated probability. For a given number of variates used to calculate the discriminant function the estimate of the probability becomes more satisfactory in terms of length of confidence interval as the size of the sample increases. For a given sample size, the estimate of the probability becomes less satisfactory as the number of variates is increased from two to ten. Tables with several percentiles in the distribution of these ratios are also included. Data for graphs and tables were obtained by Monte Carlo methods.

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.

This study uses a hybrid high order Markov Chains Model to predict direction of exchange rate, gold price and stock market returns with the Artificial Neural Network Algorithm as an estimator of transition probability matrix. Many forecasting techniques are used to examine the direction of returns forecasting in the literature such as Markov Chains Model and Artificial Neural Network Algorithm. In this study, it is aimed to combine these two techniques and to utilize the predict values of the Artificial Neural Network Algorithm for calculate transition probabilities matrix. Calculations show that the hybrid model gives high correct classification probabilities besides of well approximated transition probabilities. Returns series of USD/TRY exchange rate, closing price of Borsa Istanbul Stock Exchange and gold prices cover the period of 01/01/2003 and 31/01/2016. All series are obtained from database of Central Bank of Turkey. As a result, although the transition probabilities almost equal to 0.5 and so estimation of these series are not easy, the transition probabilities and correct classification probabilities gained from the hybrid model provide substantial information related to direction of returns forecasting. Besides, estimated model provide valuable information to individual investors and companies, and could help them to take position against to risks.

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

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.

Performance of automatic target recognition (ATR) systems depends on numerous factors including the mission description, operating conditions, sensor modality, and ATR algorithm itself. Performance prediction models sensitive to these factors could be applied to ATR algorithm design, mission planning, sensor resource management, and data collection design for algorithm verification. Ideally, such a model would return measures of performance (MOPs) such as probability of detection (Pd), correct classification (Pc), and false alarm (Pfa), all as a function of the relevant predictor variables. Here we discuss the challenges of model-based and data-based approaches to performance prediction, concentrating especially on the synthetic aperture radar (SAR) modality. Our principal conclusion for model-based performance models (predictive models derived from fundamental physics- and statistics-based considerations) is that analytical progress can be made for performance of ATR system components, but that performance prediction for an entire ATR system under realistic conditions will likely require the combined use of Monte Carlo simulations, analytical development, and careful comparison to MOPs from real experiments. The latter are valuable for their high-fidelity, but have a limited range of applicability. Our principal conclusion for data-based performance models (that fit empirically derived MOPs) offer a potentially important means for extending the utility of empirical results. However, great care must be taken in their construction due to the necessarily sparse sampling of operating conditions, the high-dimensionality of the input space, and the diverse character of the predictor variables. Also the applicability of such models for extrapolation is an open question.

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...

In this article we propose a new linear model for regression/classification of matrix input data. The algorithm for parameter estimation is constructed, some properties of the model are analyzed. The proposed model was applied for various binary classification problems, experimentally demonstrated, that in the case of small training sample, this model can be more efficient than standard techniques. In each experiment the training sample was selected randomly, the results (correct classification probabilities on the testing set) were averaged, statistical hypothesis about efficiency of the models were tested. By signed rank test most of the results are statistically significant. Bibl. 9 (in English; summaries in English, Russian and Lithuanian).

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.