Misuse of orientation statistics

1982 ◽  
Vol 60 (3) ◽  
pp. 475-477 ◽  
Author(s):  
Stephen B. Childs ◽  
Edward R. Buchler
Keyword(s):  
Order Statistics ◽  
Current Literature ◽  
Second Order ◽  
Circular Data ◽  
Statistical Techniques ◽  
Data Sets ◽  
Second Order Statistics ◽  
First Order ◽  
Orientation Statistics ◽  
Number Of Individuals

Improved statistical techniques for the analysis of circular data have increased our awareness of certain invalid procedures in earlier orientation research. Even now, however, the current literature contains many examples of inappropriately analyzed data sets. In experiments where a number of individuals are each observed more than once, second-order statistics must be used. Twice repeated, first-order statistics do not allow valid conclusions in experiments of this type.

OPTICAL COHERENCE OF A SCALAR WAVE INFLUENCED BY FIRST-ORDER AND SECOND-ORDER STATISTICS OF ITS RANDOM PHASE

2008 ◽  
Vol 08 (02) ◽  
pp. L107-L123 ◽  
Author(s):  
FRANÇOIS CHAPEAU-BLONDEAU ◽  
DENIS GINDRE ◽  
RÉGIS BARILLÉ ◽  
DAVID ROUSSEAU
Keyword(s):  
Order Statistics ◽  
Phase Distribution ◽  
Random Phase ◽  
Second Order ◽  
Phase Correlation ◽  
Partial Coherence ◽  
Scalar Wave ◽  
Optical Wave ◽  
Second Order Statistics ◽  
First Order

We analyze a simple model of a scalar optical wave with partial coherence. The model is devised to describe the influence on the coherence of the wave, of the statistical properties of its random phase, including both the second-order statistics (phase correlation) — which is classic, but also the first-order statistics (phase distribution) — which is nonclassic. Expectedly, upon increasing the disorder of the fluctuating phase through a reduction of its correlation duration, the model shows that the coherence of the wave is always reduced. By contrast, upon increasing the disorder of the fluctuating phase through an increase of its dispersion, the model reveals that the coherence of the wave can sometimes be enhanced. This beneficial consequence of an increase in disorder is related to the phenomenon of stochastic resonance or improvement by noise in signal processing.

scholarly journals Toward Measuring Target Perception: First-Order and Second-Order Deep Network Pipeline for Classification of Fixation-Related Potentials

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Hong Zeng ◽  
Junjie Shen ◽  
Wenming Zheng ◽  
Aiguo Song ◽  
Jia Liu
Keyword(s):  
Order Statistics ◽  
Object Perception ◽  
Representation Learning ◽  
Second Order ◽  
Visual Object ◽  
Second Order Statistics ◽  
First Order ◽  
Related Potentials ◽  
Perceptual Ability

The topdown determined visual object perception refers to the ability of a person to identify a prespecified visual target. This paper studies the technical foundation for measuring the target-perceptual ability in a guided visual search task, using the EEG-based brain imaging technique. Specifically, it focuses on the feature representation learning problem for single-trial classification of fixation-related potentials (FRPs). The existing methods either capture only first-order statistics while ignoring second-order statistics in data, or directly extract second-order statistics with covariance matrices estimated with raw FRPs that suffer from low signal-to-noise ratio. In this paper, we propose a new representation learning pipeline involving a low-level convolution subnetwork followed by a high-level Riemannian manifold subnetwork, with a novel midlevel pooling layer bridging them. In this way, the discriminative power of the first-order features can be increased by the convolution subnetwork, while the second-order information in the convolutional features could further be deeply learned with the subsequent Riemannian subnetwork. In particular, the temporal ordering of FRPs is well preserved for the components in our pipeline, which is considered to be a valuable source of discriminant information. The experimental results show that proposed approach leads to improved classification performance and robustness to lack of data over the state-of-the-art ones, thus making it appealing for practical applications in measuring the target-perceptual ability of cognitively impaired patients with the FRP technique.

scholarly journals Prediction of plant-level tomato biomass and yield using machine learning with unmanned aerial vehicle imagery

2021 ◽  
Author(s):  
Kenichi Tatsumi ◽  
Noa Igarashi ◽  
Xiao Mengxue
Keyword(s):  
Machine Learning ◽  
Standard Deviation ◽  
High Resolution ◽  
Order Statistics ◽  
Second Order ◽  
Machine Learning Algorithms ◽  
Support Vector ◽  
Second Order Statistics ◽  
First Order ◽  
Plant Level

Abstract Background The objective of this study is twofold. First, ascertain the important variables that predict tomato yields from plant height (PH) and vegetation index (VI) maps. The maps were derived from images taken by unmanned aerial vehicles (UAVs). Second, examine the accuracy of predictions of tomato fresh shoot masses (SM), fruit weights (FW), and the number of fruits (FN) from multiple machine learning algorithms using selected variable sets. To realize our objective, ultra-high-resolution RGB and multispectral images were collected by a UAV on ten days in 2020’s tomato growing season. From these images, 756 total variables, including first- (e.g., average, standard deviation, skewness, range, and maximum) and second-order (e.g., gray-level co-occurrence matrix features and growth rates of PH and VIs) statistics for each plant, were extracted. Several selection algorithms (i.e., Boruta, DALEX, genetic algorithm, least absolute shrinkage and selection operator, and recursive feature elimination) were used to select the variable sets useful for predicting SM, FW, and FN. Random forests, ridge regressions, and support vector machines were used to predict the yield using the top five selected variable sets. Results First-order statistics of PH and VIs collected during the early to mid-fruit formation periods, about one month prior to harvest, were important variables for predicting SM. Similar to the case for SM, variables collected approximately one month prior to harvest were important for predicting FW and FN. Furthermore, variables related to PH were unimportant for prediction. Compared with predictions obtained using only first-order statistics, those obtained using the second-order statistics of VIs were more accurate for FW and FN. Conclusions In addition to basic statistics (e.g., average and standard deviation), we derived second-order statistics of PH and VIs at the plant level using the ultra-high resolution UAV images. Our findings indicated that our variable selection method reduced the number variables needed for tomato yield prediction, improving the efficiency of phenotypic data collection and assisting with the selection of high-yield lines within breeding programs.

scholarly journals Prediction of plant-level tomato biomass and yield using machine learning with unmanned aerial vehicle imagery

Plant Methods ◽  
2021 ◽  
Vol 17 (1) ◽  
Author(s):  
Kenichi Tatsumi ◽  
Noa Igarashi ◽  
Xiao Mengxue
Keyword(s):  
Machine Learning ◽  
Standard Deviation ◽  
High Resolution ◽  
Order Statistics ◽  
Second Order ◽  
Machine Learning Algorithms ◽  
Support Vector ◽  
Second Order Statistics ◽  
First Order ◽  
Plant Level

Abstract Background The objective of this study is twofold. First, ascertain the important variables that predict tomato yields from plant height (PH) and vegetation index (VI) maps. The maps were derived from images taken by unmanned aerial vehicles (UAVs). Second, examine the accuracy of predictions of tomato fresh shoot masses (SM), fruit weights (FW), and the number of fruits (FN) from multiple machine learning algorithms using selected variable sets. To realize our objective, ultra-high-resolution RGB and multispectral images were collected by a UAV on ten days in 2020’s tomato growing season. From these images, 756 total variables, including first- (e.g., average, standard deviation, skewness, range, and maximum) and second-order (e.g., gray-level co-occurrence matrix features and growth rates of PH and VIs) statistics for each plant, were extracted. Several selection algorithms (i.e., Boruta, DALEX, genetic algorithm, least absolute shrinkage and selection operator, and recursive feature elimination) were used to select the variable sets useful for predicting SM, FW, and FN. Random forests, ridge regressions, and support vector machines were used to predict the yield using the top five selected variable sets. Results First-order statistics of PH and VIs collected during the early to mid-fruit formation periods, about one month prior to harvest, were important variables for predicting SM. Similar to the case for SM, variables collected approximately one month prior to harvest were important for predicting FW and FN. Furthermore, variables related to PH were unimportant for prediction. Compared with predictions obtained using only first-order statistics, those obtained using the second-order statistics of VIs were more accurate for FW and FN. The prediction accuracy of SM, FW, and FN by models constructed from all variables (rRMSE = 8.8–28.1%) was better than that from first-order statistics (rRMSE = 10.0–50.1%). Conclusions In addition to basic statistics (e.g., average and standard deviation), we derived second-order statistics of PH and VIs at the plant level using the ultra-high resolution UAV images. Our findings indicated that our variable selection method reduced the number variables needed for tomato yield prediction, improving the efficiency of phenotypic data collection and assisting with the selection of high-yield lines within breeding programs.

Second-order statistics of natural images

2003 ◽  
Vol 52-54 ◽  
pp. 467-472 ◽  
Author(s):  
Hauke Bartsch ◽  
Klaus Obermayer
Keyword(s):  
Order Statistics ◽  
Second Order ◽  
Natural Images ◽  
Second Order Statistics
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