Estimation of Error Rates in Several-Population Discriminant Analysis

1982 ◽  
Vol 19 (1) ◽  
pp. 57-61 ◽  
Author(s):  
Stephen C. Hora ◽  
James B. Wilcox

Researchers seeking to estimate the classification accuracy of linear discriminant functions in a more than two-population setting have had little guidance as to the most appropriate technique. The authors review the available techniques and present an additional alternative which combines features of the U-method and the recently developed posterior probability estimator. The new alternative is compared with other methods by Monté Carlo simulation.

Author(s):  
Ahmed.T. Sahlol ◽  
Aboul Ella Hassanien

There are still many obstacles for achieving high recognition accuracy for Arabic handwritten optical character recognition system, each character has a different shape, as well as the similarities between characters. In this chapter, several feature selection-based bio-inspired optimization algorithms including Bat Algorithm, Grey Wolf Optimization, Whale optimization Algorithm, Particle Swarm Optimization and Genetic Algorithm have been presented and an application of Arabic handwritten characters recognition has been chosen to see their ability and accuracy to recognize Arabic characters. The experiments have been performed using a benchmark dataset, CENPARMI by k-Nearest neighbors, Linear Discriminant Analysis, and random forests. The achieved results show superior results for the selected features when comparing the classification accuracy for the selected features by the optimization algorithms with the whole feature set in terms of the classification accuracy and the processing time. The experiments have been performed using a benchmark dataset, CENPARMI by k-Nearest neighbors, Linear Discriminant Analysis, and random forests. The achieved results show superior results for the selected features when comparing the classification accuracy for the selected features by the optimization algorithms with the whole feature set in terms of the classification accuracy and the processing time.


Author(s):  
Rong-Hua Li ◽  
Shuang Liang ◽  
George Baciu ◽  
Eddie Chan

Singularity problems of scatter matrices in Linear Discriminant Analysis (LDA) are challenging and have obtained attention during the last decade. Linear Discriminant Analysis via QR decomposition (LDA/QR) and Direct Linear Discriminant analysis (DLDA) are two popular algorithms to solve the singularity problem. This paper establishes the equivalent relationship between LDA/QR and DLDA. They can be regarded as special cases of pseudo-inverse LDA. Similar to LDA/QR algorithm, DLDA can also be considered as a two-stage LDA method. Interestingly, the first stage of DLDA can act as a dimension reduction algorithm. The experiment compares LDA/QR and DLDA algorithms in terms of classification accuracy, computational complexity on several benchmark datasets and compares their first stages. The results confirm the established equivalent relationship and verify their capabilities in dimension reduction.


Sensors ◽  
2020 ◽  
Vol 20 (23) ◽  
pp. 6763
Author(s):  
Mads Jochumsen ◽  
Imran Khan Niazi ◽  
Muhammad Zia ur Rehman ◽  
Imran Amjad ◽  
Muhammad Shafique ◽  
...  

Brain- and muscle-triggered exoskeletons have been proposed as a means for motor training after a stroke. With the possibility of performing different movement types with an exoskeleton, it is possible to introduce task variability in training. It is difficult to decode different movement types simultaneously from brain activity, but it may be possible from residual muscle activity that many patients have or quickly regain. This study investigates whether nine different motion classes of the hand and forearm could be decoded from forearm EMG in 15 stroke patients. This study also evaluates the test-retest reliability of a classical, but simple, classifier (linear discriminant analysis) and advanced, but more computationally intensive, classifiers (autoencoders and convolutional neural networks). Moreover, the association between the level of motor impairment and classification accuracy was tested. Three channels of surface EMG were recorded during the following motion classes: Hand Close, Hand Open, Wrist Extension, Wrist Flexion, Supination, Pronation, Lateral Grasp, Pinch Grasp, and Rest. Six repetitions of each motion class were performed on two different days. Hudgins time-domain features were extracted and classified using linear discriminant analysis and autoencoders, and raw EMG was classified with convolutional neural networks. On average, 79 ± 12% and 80 ± 12% (autoencoders) of the movements were correctly classified for days 1 and 2, respectively, with an intraclass correlation coefficient of 0.88. No association was found between the level of motor impairment and classification accuracy (Spearman correlation: 0.24). It was shown that nine motion classes could be decoded from residual EMG, with autoencoders being the best classification approach, and that the results were reliable across days; this may have implications for the development of EMG-controlled exoskeletons for training in the patient’s home.


1977 ◽  
Vol 19 (81) ◽  
pp. 679-680
Author(s):  
N.F. Drozdovskaya

Abstract The existing methods of predicting avalanche danger often do not meet users’ demands because of the empiric character of the insufficient volume of information used. In such forecasts the contribution of each individual parameter into the prognostic information is unknown, and this is very important when studying such an event as avalanche formation, which is conditioned by a complex interaction of numerous factors, including snow accumulation, the state of snow thickness, and the conditions of its development. It is obvious that such problems can be successfully solved by statistical methods, and that explains the growing interest in numerical methods of avalanche forecasting. Problems of multi-dimensional observations arises in many scientific fields. The method suited for this problem is discriminant analysis, the purpose of which is to divide a multi-dimensional observation vector into predetermined classes. This study considers the prognostic (diagnostic) problems of fresh-snow avalanches released during snowfall or in the two days after it has ceased. The theoretical basis is a complex of statistical methods: correlation and dispersion analysis, “sifting" for the choice of predictors’ informative groups, construction of linear parametric discriminant functions, predictions based on training sample, and verification of discriminant functions based on independent material. The archive used in the study consisted of 500 avalanching cases and 1 300 non-avalanching ones. All situations were grouped according to geomorphological characteristics. Each situation is described by eight meteorological characteristics. The results of classification of snowfall situations into avalanching and non-avalanching ones are as follows: reliability of ρ is from 75% to 91%, H from 0.15 to 0.51; based on independent material the reliability of ρ is from 63% to 85%, H from 0.10 to 0.56. This paper has been accepted in revised form for publication in a later issue of the Journal of Glaciology.


2021 ◽  
Vol 47 ◽  
Author(s):  
Kęstutis Dučinskas ◽  
Lina Dreižienė

Paper deals with statistical classification of spatial data as a part of widely applicable statistical approach to pattern recognition. Error rates in supervised classification of Gaussian random field observation into one of two populations specified by different constant means and common stationary geometric anisotropic covariance are considered. Formula for the exact Bayesian error rate is derived. The influence of the ratio of anisotropy to the error rates is evaluated numerically for the case of complete parametric certainty.


1985 ◽  
Vol 63 (4) ◽  
pp. 735-743 ◽  
Author(s):  
Bernard R. Baum ◽  
L. Grant Bailey

Material of the diploid (HBD) and tetraploid (HBT) Hordeum bulbosum collected in the Mediterranean and Near East areas was examined for 14 morphometric characters. Exploratory data analysis revealed that cilia on the margins of the glumes of the central spikelets may or may not be present in HBT but are never present in HBD. The data were submitted to various kinds of discriminant analysis in which group assignment was based on ploidy level. When presence–absence of cilia on glume margins is used in combination with the resulting linear discriminant functions (DF) there is about 91% probability of correct identification; with DF alone there is about 81% probability. The results of discriminant analysis provided justification, in the opinion of the authors, to regard HBD and HBT as separate taxa at the level of subspecies, namely H. bulbosum subsp. bulbosum and H. bulbosum L. subsp. nodosum (L.) Baum.


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