scholarly journals Brain Function Network: Higher Order vs. More Discrimination

2021 ◽  
Vol 15 ◽  
Author(s):  
Tingting Guo ◽  
Yining Zhang ◽  
Yanfang Xue ◽  
Lishan Qiao ◽  
Dinggang Shen
Keyword(s):  
Individual Differences ◽  
Order Statistics ◽  
Brain Regions ◽  
Higher Order ◽  
Binary Matrix ◽  
Discriminative Ability ◽  
Second Order Statistics ◽  
Additional Information ◽  
Mental Diseases ◽  
High Order Statistics

Brain functional network (BFN) has become an increasingly important tool to explore individual differences and identify neurological/mental diseases. For estimating a “good” BFN (with more discriminative information for example), researchers have developed various methods, in which the most popular and simplest is Pearson's correlation (PC). Despite its empirical effectiveness, PC only encodes the low-order (second-order) statistics between brain regions. To model high-order statistics, researchers recently proposed to estimate BFN by conducting two sequential PCs (denoted as PC2 in this paper), and found that PC2-based BFN can provide additional information for group difference analysis. This inspires us to think about (1) what will happen if continuing the correlation operation to construct much higher-order BFN by PCn (n>2), and (2) whether the higher-order correlation will result in stronger discriminative ability. To answer these questions, we use PCn-based BFNs to predict individual differences (Female vs. Male) as well as identify subjects with mild cognitive impairment (MCI) from healthy controls (HCs). Through experiments, we have the following findings: (1) with the increase of n, the discriminative ability of PCn-based BFNs tends to decrease; (2) fusing the PCn-based BFNs (n>1) with the PC1-based BFN can generally improve the sensitivity for MCI identification, but fail to help the classification accuracy. In addition, we empirically find that the sequence of BFN adjacency matrices estimated by PCn (n = 1,2,3,⋯ ) will converge to a binary matrix with elements of ± 1.

scholarly journals Coordinated multivoxel coding beyond univariate effects is not likely to be observable in fMRI data

2021 ◽  
Author(s):  
Mansooreh Pakravan ◽  
Ali Ghazizadeh
Keyword(s):  
Order Statistics ◽  
Brain Regions ◽  
Simultaneous Recording ◽  
Higher Order ◽  
Higher Order Statistics ◽  
Distributed Coding ◽  
Additional Information ◽  
Neuronal Populations ◽  
Increased Sensitivity ◽  
Multivariate Responses

Simultaneous recording of activity across brain regions can contain additional information compared to regional recordings done in isolation. In particular, multivariate pattern analysis (MVPA) across voxels has been interpreted as evidence for distributed coding of cognitive or sensorimotor processes beyond what can be gleaned from a collection of univariate responses (UVR) using functional magnetic resonance imaging (fMRI). Here, we argue that regardless of patterns revealed, conventional MVPA is merely a decoding tool with increased sensitivity arising from considering a large number of 'weak classifiers' (i.e. single voxels) in higher dimensions. We propose instead that 'real' multivoxel coding should result in changes in higher-order statistics across voxels between conditions such as second-order multivariate responses (sMVR). Surprisingly, analysis of conditions with robust multivariate responses (MVR) revealed by MVPA failed to show significant sMVR in two species (humans and macaques). Further analysis showed that while both MVR and sMVR can be readily observed in the spiking activity of neuronal populations, the slow and nonlinear hemodynamic coupling and low spatial resolution of fMRI activations make the observation of higher-order statistics between voxels highly unlikely. These results reveal inherent limitations of fMRI signals for studying coordinated coding across voxels. Together, these findings suggest that care should be taken in interpreting significant MVPA results as representing anything beyond a collection of univariate effects.

Optimal Sequential Detection of Stimuli from Multiunit Recordings Taken in Densely Populated Brain Regions

2012 ◽  
Vol 24 (4) ◽  
pp. 895-938 ◽  
Author(s):  
Nir Nossenson ◽  
Hagit Messer
Keyword(s):  
Order Statistics ◽  
Single Neuron ◽  
Brain Regions ◽  
Second Order ◽  
Detection Scheme ◽  
Second Order Statistics ◽  
Optimal Detector ◽  
Electrode Voltage ◽  
The Subject ◽  
High Pass

We address the problem of detecting the presence of a recurring stimulus by monitoring the voltage on a multiunit electrode located in a brain region densely populated by stimulus reactive neurons. Published experimental results suggest that under these conditions, when a stimulus is present, the measurements are gaussian with typical second-order statistics. In this letter we systematically derive a generic, optimal detector for the presence of a stimulus in these conditions and describe its implementation. The optimality of the proposed detector is in the sense that it maximizes the life span (or time to injury) of the subject. In addition, we construct a model for the acquired multiunit signal drawing on basic assumptions regarding the nature of a single neuron, which explains the second-order statistics of the raw electrode voltage measurements that are high-pass-filtered above 300 Hz. The operation of the optimal detector and that of a simpler suboptimal detection scheme is demonstrated by simulations and on real electrophysiological data.

Adaptive Beamforming for Noncircular Signals

2012 ◽  
Vol 429 ◽  
pp. 318-323
Author(s):  
You Gen Xu ◽  
Zhi Wen Liu
Keyword(s):  
Order Statistics ◽  
Source Separation ◽  
Adaptive Beamforming ◽  
Second Order ◽  
High Order ◽  
Convergence Speed ◽  
Second Order Statistics ◽  
Noncircular Signals ◽  
High Order Statistics

Many manmade signals have nonzero noncircularity coefficients such as those used in AM, BPSK, and ASK systems. They are called noncircular signals which have coexisted moment and conjugate moment at the second-order. This redundancy is herein exploited to derive a blind scheme for source separation and classification based on the NonCircularity REstoral (NCRE4) filtering. The present blind scheme has three major advantages: 1) involves only the second-order statistics (SOS) and has a faster convergence speed than the traditional high-order statistics (HOS) methods; and 2) does not require any a prioriknowledge about the content and/or direction of the signal-of-interest (SOI).

scholarly journals A New Method of Blind Source Separation Using Single-Channel ICA Based on Higher-Order Statistics

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Guangkuo Lu ◽  
Manlin Xiao ◽  
Ping Wei ◽  
Huaguo Zhang
Keyword(s):  
Order Statistics ◽  
Single Channel ◽  
Multiple Input Multiple Output ◽  
Higher Order ◽  
Stationary Time Series ◽  
Measured Signal ◽  
Step Method ◽  
Real World Data ◽  
Input Multiple Output ◽  
High Order Statistics

Methods of utilizing independent component analysis (ICA) give little guidance about practical considerations for separating single-channel real-world data, in which most of them are nonlinear, nonstationary, and even chaotic in many fields. To solve this problem, a three-step method is provided in this paper. In the first step, the measured signal which is assumed to be piecewise higher order stationary time series is introduced and divided into a series of higher order stationary segments by applying a modified segmentation algorithm. Then the state space is reconstructed and the single-channel signal is transformed into a pseudo multiple input multiple output (MIMO) mode using a method of nonlinear analysis based on the high order statistics (HOS). In the last step, ICA is performed on the pseudo MIMO data to decompose the single channel recording into its underlying independent components (ICs) and the interested ICs are then extracted. Finally, the effectiveness and excellence of the higher order single-channel ICA (SCICA) method are validated with measured data throughout experiments. Also, the proposed method in this paper is proved to be more robust under different SNR and/or embedding dimension via explicit formulae and simulations.

Higher order versus second order statistics in ultrasound image deconvolution

1997 ◽  
Vol 44 (6) ◽  
pp. 1409-1416 ◽  
Author(s):  
U.R. Abeyratne ◽  
A.P. Petropulu ◽  
J.M. Reid ◽  
T. Golas ◽  
E. Conant ◽  
...  
Keyword(s):  
Order Statistics ◽  
Ultrasound Image ◽  
Higher Order ◽  
Second Order ◽  
Image Deconvolution ◽  
Second Order Statistics

Evaluation of a new Power Quality index, based in Higher Order Statistics

2017 ◽  
Vol 1 (15) ◽  
pp. 37-42
Author(s):  
J.M. Sierra-Fernández ◽  
J.J. González De La Rosa ◽  
A. Agüera-Pérez ◽  
J.C. Palomares Salas ◽  
O. Florencias-Oliveros
Keyword(s):  
Order Statistics ◽  
Power Quality ◽  
Quality Index ◽  
Higher Order ◽  
Higher Order Statistics
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