scholarly journals Cross-Subject Assistance: Inter- and Intra-Subject Maximal Correlation for Enhancing the Performance of SSVEP-Based BCIs

2021 ◽  
Vol 29 ◽  
pp. 517-526
Author(s):  
Haoran Wang ◽  
Yaoru Sun ◽  
Fang Wang ◽  
Lei Cao ◽  
Wei Zhou ◽  
...  
Keyword(s):  
Maximal Correlation

The rate of convergence of extremes of stationary normal sequences

1983 ◽  
Vol 15 (01) ◽  
pp. 54-80 ◽  
Author(s):  
Holger Rootzén
Keyword(s):  
Rate Of Convergence ◽  
Joint Distribution ◽  
Point Processes ◽  
Rates Of Convergence ◽  
Joint Distribution Function ◽  
Maximal Correlation ◽  
Standard Normal ◽  
Image Position ◽  
The Right ◽  
Right Order

Let {ξ; t = 1, 2, …} be a stationary normal sequence with zero means, unit variances, and covariances let be independent and standard normal, and write . In this paper we find bounds on which are roughly of the order where ρ is the maximal correlation, ρ =sup {0, r 1 , r 2, …}. It is further shown that, at least for m-dependent sequences, the bounds are of the right order and, in a simple example, the errors are evaluated numerically. Bounds of the same order on the rate of convergence of the point processes of exceedances of one or several levels are obtained using a ‘representation' approach (which seems to be of rather wide applicability). As corollaries we obtain rates of convergence of several functionals of the point processes, including the joint distribution function of the k largest values amongst ξ1, …, ξn.

scholarly journals Estimating Visual Field Mean Deviation using Optical Coherence Tomographic Nerve Fiber Layer Measurements in Glaucoma Patients

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Ou Tan ◽  
David S. Greenfield ◽  
Brian A. Francis ◽  
Rohit Varma ◽  
Joel S. Schuman ◽  
...  
Keyword(s):  
Visual Field ◽  
Nerve Fiber ◽  
Weighted Averaging ◽  
Mean Deviation ◽  
Optical Coherence ◽  
Fiber Layer ◽  
Nerve Fiber Layer ◽  
Maximal Correlation ◽  
Advanced Stages ◽  
Higher Sensitivity

AbstractTo construct an optical coherence tomography (OCT) nerve fiber layer (NFL) parameter that has maximal correlation and agreement with visual field (VF) mean deviation (MD). The NFL_MD parameter in dB scale was calculated from the peripapillary NFL thickness profile nonlinear transformation and VF area-weighted averaging. From the Advanced Imaging for Glaucoma study, 245 normal, 420 pre-perimetric glaucoma (PPG), and 289 perimetric glaucoma (PG) eyes were selected. NFL_MD had significantly higher correlation (Pearson R: 0.68 vs 0.55, p < 0.001) with VF_MD than the overall NFL thickness. NFL_MD also had significantly higher sensitivity in detecting PPG (0.14 vs 0.08) and PG (0.60 vs 0.43) at the 99% specificity level. NFL_MD had better reproducibility than VF_MD (0.35 vs 0.69 dB, p < 0.001). The differences between NFL_MD and VF_MD were −0.34 ± 1.71 dB, −0.01 ± 2.08 dB and 3.54 ± 3.18 dB and 7.17 ± 2.68 dB for PPG, early PG, moderate PG, and severe PG subgroups, respectively. In summary, OCT-based NFL_MD has better correlation with VF_MD and greater diagnostic sensitivity than the average NFL thickness. It has better reproducibility than VF_MD, which may be advantageous in detecting progression. It agrees well with VF_MD in early glaucoma but underestimates damage in moderate~advanced stages.

Optimal couplings are totally positive and more

2004 ◽  
Vol 41 (A) ◽  
pp. 321-332 ◽  
Author(s):  
Paul Glasserman ◽  
David D. Yao
Keyword(s):  
Transportation Problem ◽  
Random Variables ◽  
Total Positivity ◽  
Bivariate Distribution ◽  
Discrete Distributions ◽  
Optimal Solutions ◽  
Totally Positive ◽  
Maximal Correlation ◽  
Optimal Coupling

An optimal coupling is a bivariate distribution with specified marginals achieving maximal correlation. We show that optimal couplings are totally positive and, in fact, satisfy a strictly stronger condition we call the nonintersection property. For discrete distributions we illustrate the equivalence between optimal coupling and a certain transportation problem. Specifically, the optimal solutions of greedily-solvable transportation problems are totally positive, and even nonintersecting, through a rearrangement of matrix entries that results in a Monge sequence. In coupling continuous random variables or random vectors, we exploit a characterization of optimal couplings in terms of subgradients of a closed convex function to establish a generalization of the nonintersection property. We argue that nonintersection is not only stronger than total positivity, it is the more natural concept for the singular distributions that arise in coupling continuous random variables.

On statistical independence and zero correlation in several dimensions

1960 ◽  
Vol 1 (4) ◽  
pp. 492-496 ◽  
Author(s):  
H. O. Lancaster
Keyword(s):  
Canonical Form ◽  
Arbitrary Number ◽  
Random Variables ◽  
Summable Function ◽  
Statistical Independence ◽  
Bivariate Distributions ◽  
Canonical Correlations ◽  
Zero Correlation ◽  
Maximal Correlation

Bivariate distributions, subject to a condition of φ2 boundedness to be defined later, can be written in a canonical form. Sarmanov [4] used such a form to deduce that two random variables are independent if and only if the maximal correlation of any square summable function, ξ (x1), of the first variable with any square summable function, η(x2), of the second variable is zero. This is equivalent to the condition that the canonical correlations are all zero. The theorem of Sarmanov [4] was proved without any restriction in Lancaster [2] and the proof is now extended to an arbitrary number of dimensions.

Sign in / Sign up

Export Citation Format

Share Document