$$\kappa $$-Circulant Maximum Variance Bases

2021 ◽  
pp. 17-29
Author(s):  
Christopher Bonenberger ◽  
Wolfgang Ertel ◽  
Markus Schneider
Keyword(s):  
2020 ◽  
pp. 1-11
Author(s):  
Mayamin Hamid Raha ◽  
Tonmoay Deb ◽  
Mahieyin Rahmun ◽  
Tim Chen

Face recognition is the most efficient image analysis application, and the reduction of dimensionality is an essential requirement. The curse of dimensionality occurs with the increase in dimensionality, the sample density decreases exponentially. Dimensionality Reduction is the process of taking into account the dimensionality of the feature space by obtaining a set of principal features. The purpose of this manuscript is to demonstrate a comparative study of Principal Component Analysis and Linear Discriminant Analysis methods which are two of the highly popular appearance-based face recognition projection methods. PCA creates a flat dimensional data representation that describes as much data variance as possible, while LDA finds the vectors that best discriminate between classes in the underlying space. The main idea of PCA is to transform high dimensional input space into the function space that displays the maximum variance. Traditional LDA feature selection is obtained by maximizing class differences and minimizing class distance.


2005 ◽  
Vol 23 (2) ◽  
pp. 609-624 ◽  
Author(s):  
K. E. J. Huttunen ◽  
J. Slavin ◽  
M. Collier ◽  
H. E. J. Koskinen ◽  
A. Szabo ◽  
...  

Abstract. Sudden impulses (SI) in the tail lobe magnetic field associated with solar wind pressure enhancements are investigated using measurements from Cluster. The magnetic field components during the SIs change in a manner consistent with the assumption that an antisunward moving lateral pressure enhancement compresses the magnetotail axisymmetrically. We found that the maximum variance SI unit vectors were nearly aligned with the associated interplanetary shock normals. For two of the tail lobe SI events during which Cluster was located close to the tail boundary, Cluster observed the inward moving magnetopause. During both events, the spacecraft location changed from the lobe to the magnetospheric boundary layer. During the event on 6 November 2001 the magnetopause was compressed past Cluster. We applied the 2-D Cartesian model developed by collier98 in which a vacuum uniform tail lobe magnetic field is compressed by a step-like pressure increase. The model underestimates the compression of the magnetic field, but it fits the magnetic field maximum variance component well. For events for which we could determine the shock normal orientation, the differences between the observed and calculated shock propagation times from the location of WIND/Geotail to the location of Cluster were small. The propagation speeds of the SIs between the Cluster spacecraft were comparable to the solar wind speed. Our results suggest that the observed tail lobe SIs are due to lateral increases in solar wind dynamic pressure outside the magnetotail boundary.


2013 ◽  
Vol 798-799 ◽  
pp. 761-764
Author(s):  
Ming Xia Xiao

A new technique that combines maximum variance method and morphology was presented for Synthetic Aperture Radar (SAR) image segmentation in target detection. Firstly, using the first-order differential method to enhance the original image for highlighting edge details of the image; then using the maximum variance method to calculate the gray threshold and segment the image; lastly, the mathematical morphology was used to processing the segmented image, which could prominently improve the segmentation effects. Experiments show that this algorithm can obtain accurate segmentation results, and have a good effect on noise suppression, edge detail protection and operation time.


2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Lei Luo ◽  
Chao Zhang ◽  
Yongrui Qin ◽  
Chunyuan Zhang

With the explosive growth of the data volume in modern applications such as web search and multimedia retrieval, hashing is becoming increasingly important for efficient nearest neighbor (similar item) search. Recently, a number of data-dependent methods have been developed, reflecting the great potential of learning for hashing. Inspired by the classic nonlinear dimensionality reduction algorithm—maximum variance unfolding, we propose a novel unsupervised hashing method, named maximum variance hashing, in this work. The idea is to maximize the total variance of the hash codes while preserving the local structure of the training data. To solve the derived optimization problem, we propose a column generation algorithm, which directly learns the binary-valued hash functions. We then extend it using anchor graphs to reduce the computational cost. Experiments on large-scale image datasets demonstrate that the proposed method outperforms state-of-the-art hashing methods in many cases.


SIAM Review ◽  
2006 ◽  
Vol 48 (4) ◽  
pp. 681-699 ◽  
Author(s):  
Jun Sun ◽  
Stephen Boyd ◽  
Lin Xiao ◽  
Persi Diaconis

2008 ◽  
Vol 41 (11) ◽  
pp. 3287-3294 ◽  
Author(s):  
Bo Li ◽  
De-Shuang Huang ◽  
Chao Wang ◽  
Kun-Hong Liu

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