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Second Order Bilinear Discriminant Analysis for single trial EEG analysis

Christoforos Christoforou, Paul Sajda, Lucas C. Parra
2007 Neural Information Processing Systems  
Here we propose a principled method, based on a bilinear model, in which the algorithm simultaneously learns the best first and second order spatial and temporal features for classification of EEG.  ...  for classification, e.g. event related potentials; and second order methods, in which the feature of interest is the power of the signal, e.g. event related (de)synchronization.  ...  Second order bilinear discriminant analysis 2.1 Problem setting Given a set of sample points D = {X n , y n } N n=1 , X ∈ R D × T , y ∈ {−1, 1} , where X n corresponds to the EEG signal of D channels  ... 
dblp:conf/nips/ChristoforouSP07 fatcat:vvau5oceune6vfcd6akojyhtbm

Second-order properties for multiple-bilinear models

György Terdik
1990 Journal of Multivariate Analysis  
The exact form of the spectral density function shows that there is no way one can discriminate between a linear (non-Gaussian) and a bilinear model based on the second-order properties of the process.  ...  We give a necessary and sufficient condition for the second-order stationarity of multiple bilinear models in terms of the spectral radius of a particular matrix involving the coefficients of the model  ...  An easy consequence of these formulae is that there is no way one would discriminate between the linear (D,=O, j = 1, 2, . ..) d) non-Gaussian and the bilinear process on the basis of the second-order  ... 
doi:10.1016/0047-259x(90)90030-l fatcat:muyf3s3gk5c37k2gqj5txviph4

Multimodal Bilinear Fusion Network with Second-order Attention Based Channel Selection for Land Cover Classification

Xiao Li, Lin Lei, Yuli Sun, Ming Li, Gangyao Kuang
2020 IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing  
The MBFNet consists of three components: the feature extractor, the second-order attention-based channel selection module (SACSM), and the bilinear fusion module.  ...  Then, the SACSM is embedded into each stream, and the fine channel-attention maps with second-order statistics are obtained by bilinear integrating the global averagepooling and global max-pooling information  ...  However, the channel attention maps of CBAM lacked more discriminative second-order statistics.  ... 
doi:10.1109/jstars.2020.2975252 fatcat:kybbaqqdavgljnnce2tgvmyhm4

Compact Bilinear Pooling [article]

Yang Gao, Oscar Beijbom, Ning Zhang, Trevor Darrell
2016 arXiv   pre-print
However, bilinear features are high dimensional, typically on the order of hundreds of thousands to a few million, which makes them impractical for subsequent analysis.  ...  The compact bilinear representations are derived through a novel kernelized analysis of bilinear pooling which provide insights into the discriminative power of bilinear pooling, and a platform for further  ...  Bilinear pooling thus gives a linear classifier the discriminative power of a second order kernel-machine, which may help explain the strong empirical performance observed in previous work [23, 3, 8,  ... 
arXiv:1511.06062v2 fatcat:eithehndyjdcdfwk5o2urvx6qq

Compact Bilinear Pooling

Yang Gao, Oscar Beijbom, Ning Zhang, Trevor Darrell
2016 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)  
However, bilinear features are high dimensional, typically on the order of hundreds of thousands to a few million, which makes them impractical for subsequent analysis.  ...  The compact bilinear representations are derived through a novel kernelized analysis of bilinear pooling which provide insights into the discriminative power of bilinear pooling, and a platform for further  ...  Bilinear pooling thus gives a linear classifier the discriminative power of a second order kernel-machine, which may help explain the strong empirical performance observed in previous work [23, 3, 8,  ... 
doi:10.1109/cvpr.2016.41 dblp:conf/cvpr/GaoBZD16 fatcat:ik3q4hhngbf5nkwrsqt5u4bxza

Face Recognition Using Modular Bilinear Discriminant Analysis [chapter]

Muriel Visani, Christophe Garcia, Jean-Michel Jolion
2006 Lecture Notes in Computer Science  
In this paper, we present a new approach for face recognition, named Modular Bilinear Discriminant Analysis (MBDA).  ...  In a first step, a set of experts is created, each one being trained independently on specific face regions using a new supervised technique named Bilinear Discriminant Analysis (BDA).  ...  We therefore propose an iterative procedure that we call Bilinear Discriminant Analysis.  ... 
doi:10.1007/11590064_3 fatcat:lqssjrudqnfwxmmmdmriduu2xu

Multi-Objective Matrix Normalization for Fine-grained Visual Recognition

Shaobo Min, Hantao Yao, Hongtao Xie, Zheng-Jun Zha, Yongdong Zhang
2020 IEEE Transactions on Image Processing  
These three regularizers can not only stabilize the second-order information, but also compact the bilinear features and promote model generalization.  ...  Recent methods have shown that the matrix power normalization can stabilize the second-order information in bilinear features, but some problems, e.g., redundant information and over-fitting, remain to  ...  Inspired by the second-order descriptors, the bilinear pooling is first proposed by Lin et al. [7] to capture the second-order information for FGVC.  ... 
doi:10.1109/tip.2020.2977457 pmid:32149637 fatcat:w5syyp7emnhxfp63yydnar3v5q

Page 5855 of Mathematical Reviews Vol. , Issue 87j [page]

1987 Mathematical Reviews  
However, in this paper it is shown that some of the third-order moments do not vanish for some superdiagonal and diagonal bilinear models and the pattern of nonzero moments can be used to discriminate  ...  for some bilinear models they will all be zero, and hence are of no use in discriminating between true white noise and some bilinear models.  ... 

Correlation Codes in Neuronal Populations

Maoz Shamir, Haim Sompolinsky
2001 Neural Information Processing Systems  
Here we study the efficiency of coding information in the second order statistics of the population responses.  ...  We propose a bilinear readout model for extracting information from correlation codes, and evaluate its performance in discrimination and estimation tasks.  ...  Secondly, we inquire how information in the second order statistics can be efficiently extracted.  ... 
dblp:conf/nips/ShamirS01 fatcat:hkxmxtqujba3zjwgaghzdxpbba

The Analytic Bilinear Discrimination of Single-Trial EEG Signals in Rapid Image Triage

Ke Yu, Hasan AI-Nashash, Nitish Thakor, Xiaoping Li, Pedro A. Valdes-Sosa
2014 PLoS ONE  
Being a first-order discriminator, LDA is usually preceded by the feature extraction of electroencephalogram (EEG) signals, as multi-density EEG data are of second order.  ...  The linear discriminant analysis (LDA) method is a classical and commonly utilized technique for dimensionality reduction and classification in brain-computer interface (BCI) systems.  ...  On the other hand, bilinear discriminant analysis (BDA) [32] and 2-dimensional linear discriminant analysis (2DLDA) [33] extend LDA by iteratively optimizing bilinear projections instead of one LDA  ... 
doi:10.1371/journal.pone.0100097 pmid:24933017 pmcid:PMC4059712 fatcat:gfulifj7mbbxdm2ke2slb64efa

Bilinear image translation for temporal analysis of photo collections

Theophile Dalens, Mathieu Aubry, Josef Sivic
2019 IEEE Transactions on Pattern Analysis and Machine Intelligence  
To isolate and transfer time dependent appearance variations, we introduce a new trainable bilinear factor separation module.  ...  Others have looked at identifying parts of images that are temporally discriminative in order to date historical objects in photographs [39] .  ...  The second term encourages that for the generated images M (I, y) the discriminator output for period y, D y should be zero.  ... 
doi:10.1109/tpami.2019.2950317 pmid:31675318 fatcat:tl3l3w2aqvb4ff5ifnyudxyj5a

Temporal Attention augmented Bilinear Network for Financial Time-Series Data Analysis [article]

Dat Thanh Tran, Alexandros Iosifidis, Juho Kanniainen, Moncef Gabbouj
2017 arXiv   pre-print
The resulting network is highly interpretable, given its ability to highlight the importance and contribution of each temporal instance, thus allowing further analysis on the time instances of interest  ...  In this paper, we propose a neural network layer architecture that incorporates the idea of bilinear projection as well as an attention mechanism that enables the layer to detect and focus on crucial temporal  ...  For example, popular discriminant and regression criteria were extended for tensor inputs, such as Multilinear Discriminant Analysis (MDA) [41] , Multilinear Class-specific Discriminant Analysis (MCSDA  ... 
arXiv:1712.00975v1 fatcat:vqgcwtk5fndijmvi7hoxglybyi

A Vehicle Detection Algorithm Based on Deep Belief Network

Hai Wang, Yingfeng Cai, Long Chen
2014 The Scientific World Journal  
In the algorithm, the proposed 2D-DBN architecture uses second-order planes instead of first-order vector as input and uses bilinear projection for retaining discriminative information so as to determine  ...  The bilinear projection maps original second-order output of lower layer to a small bilinear space without reducing discriminative information.  ...  In the algorithm, the proposed 2D-DBN architecture uses second-order planes instead of first-order vector as input and uses bilinear projection for retaining discriminative information so as to determine  ... 
doi:10.1155/2014/647380 pmid:24959617 pmcid:PMC4052056 fatcat:kb3m3v6aorghjmlaxccsqkzy3i

Bilinear Discriminant Analysis for Face Recognition [chapter]

Muriel Visani, Christophe Garcia, Jean-Michel Jolion
2005 Lecture Notes in Computer Science  
In this paper, a new statistical projection method called Bilinear Discriminant Analysis (BDA) is presented.  ...  Linear Discriminant Analysis (RoLDA), through an iterative algorithm using a generalized bilinear projectionbased Fisher criterion.  ...  We therefore propose an iterative procedure that we call Bilinear Discriminant Analysis.  ... 
doi:10.1007/11552499_28 fatcat:govndsb5tba4todowipm2ord3e

Aircraft Type Recognition in Remote Sensing Images: Bilinear Discriminative Extreme Learning Machine Framework

Baojun Zhao, Wei Tang, Yu Pan, Yuqi Han, Wenzheng Wang
2021 Electronics  
To solve the above problems, we propose the bilinear discriminative extreme learning machine (ELM) network (BD-ELMNet), which integrates the advantages of the CNN, autoencoder (AE), and ELM.  ...  The bilinear pooling model uses the feature association information for feature fusion to enhance the substantial distinction of features.  ...  In the high-order feature extraction module, the bilinear pool model is used as the high-order feature extractor of the BD-ELMNet, which extracts second-order statistical information by calculating the  ... 
doi:10.3390/electronics10172046 fatcat:nl32ybgumra4bk6qs4uyirisja
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