scholarly journals Parameters estimate of Riemannian Gaussian distribution in the manifold of covariance matrices

2016 ◽  
Author(s):  
Paolo Zanini ◽  
Marco Congedo ◽  
Christian Jutten ◽  
Salem Said ◽  
Yannick Berthoumieu
Keyword(s):  
Gaussian Distribution ◽  
Covariance Matrices

Determining the Optimal Number of Clusters by an Extended RPCL Algorithm

1999 ◽  
Vol 3 (6) ◽  
pp. 467-473 ◽  
Author(s):  
Xin Li ◽  
◽  
Man Wai Mak ◽  
Chi Kwong Li
Keyword(s):  
Gaussian Distribution ◽  
Error Rate ◽  
Basis Function ◽  
Recognition Accuracy ◽  
Speaker Verification ◽  
Optimal Number ◽  
Covariance Matrices ◽  
Training Data ◽  
Number Of Clusters ◽  
Optimal Number Of Clusters

Determining an appropriate number of clusters is a difficult yet important problem that the rival penalized competitive learning (RPCL) algorithm was designed to solve, but its performance is not satifactory with overlapping clusters or cases where input vectors contain dependent components. We address this problem by incorporating full covariance matrices into the original RPCL algorithm. The resulting extended RPCL algorithm progressively eliminates units whose clusters contain only a small amount of training data. The algorithm is used to determine the number of clusters in a Gaussian distribution. It is also used to optimize the architecture of elliptical basis function networks for speaker verification and vowel classification. We found that covariance matrices obtained by the extended RPCL algorithm have a better representation of clusters than those obtained by the original RPCL algorithm, resulting in a lower verification error rate in speaker verification and a higher recognition accuracy in vowel classification.

Structure images of Si, Ge and Mos2 crystals and some application to radiation damage studies

1978 ◽  
Vol 36 (1) ◽  
pp. 292-293 ◽  
Author(s):  
K. Izui ◽  
T. Nishida ◽  
S. Furuno ◽  
H. Otsu ◽  
S. Kuwabara
Keyword(s):  
Radiation Damage ◽  
Exposure Time ◽  
Gaussian Distribution ◽  
Intensity Distribution ◽  
Chromatic Aberration ◽  
Magnetic Lens

Recently we have observed the structure images of silicon in the (110), (111) and (100) projection respectively, and then examined the optimum defocus and thickness ranges for the formation of such images on the basis of calculations of image contrasts using the n-slice theory. The present paper reports the effects of a chromatic aberration and a slight misorientation on the images, and also presents some applications of structure images of Si, Ge and MoS2 to the radiation damage studies.(1) Effect of a chromatic aberration and slight misorientation: There is an inevitable fluctuation in the amount of defocus due to a chromatic aberration originating from the fluctuations both in the energies of electrons and in the magnetic lens current. The actual image is a results of superposition of those fluctuated images during the exposure time. Assuming the Gaussian distribution for defocus, Δf around the optimum defocus value Δf0, the intensity distribution, I(x,y) in the image formed by this fluctuation is given by

Quadratic Discriminant Analysis of Spatially Correlated Data

2001 ◽  
Vol 6 (2) ◽  
pp. 15-28 ◽  
Author(s):  
K. Dučinskas ◽  
J. Šaltytė
Keyword(s):  
Discriminant Function ◽  
Error Rate ◽  
Gaussian Random Field ◽  
Correlated Data ◽  
Covariance Matrices ◽  
Classification Rule ◽  
Spatial Correlations ◽  
Linear Quadratic ◽  
Spatial Correlation Function ◽  
Spatially Correlated

The problem of classification of the realisation of the stationary univariate Gaussian random field into one of two populations with different means and different factorised covariance matrices is considered. In such a case optimal classification rule in the sense of minimum probability of misclassification is associated with non-linear (quadratic) discriminant function. Unknown means and the covariance matrices of the feature vector components are estimated from spatially correlated training samples using the maximum likelihood approach and assuming spatial correlations to be known. Explicit formula of Bayes error rate and the first-order asymptotic expansion of the expected error rate associated with quadratic plug-in discriminant function are presented. A set of numerical calculations for the spherical spatial correlation function is performed and two different spatial sampling designs are compared.

Pemberian Umpan Balik Dalam Meningkatkan Hasil Belajar dan Minat Belajar Mahasiswa

2015 ◽  
Vol 4 (3) ◽  
Author(s):  
Seruni Seruni ◽  
Nurul Hikmah
Keyword(s):  
Information Technology ◽  
Learning Outcomes ◽  
Test Data ◽  
Random Sampling ◽  
Covariance Matrices ◽  
Test Results ◽  
Immediate Feedback ◽  
Statistics Course ◽  
Independent Variable ◽  
Descriptive Statistical Analysis

<p>The purpose of this study is to find and analyze the effect of feedback on <br />learning outcomes in mathematics and an interest in basic statistics course. The <br />population in this study are affordable Information Technology Student cademic Year 2012/2013 Semester II Indraprasta PGRI University of South Jakarta. Sample The study sample was obtained through random sampling. This study used an experimental method to the analysis using the MANOVA test. This study has three variables, consisting of: one independent variable, namely the provision of feedback (immediate and delayed), and two dependent variable is the result of interest in the study of mathematics and basic statistics course. The data was collected for the test results to learn mathematics, and a questionnaire for the interest in basic statistics course. Collected data were analyzed using the MANOVA test. Before the data were analyzed, first performed descriptive statistical analysis and test data analysis requirements (test data normality and homogeneity of covariance matrices). The results show that the learning outcomes of interest in mathematics and basic statistics course for students who are given immediate feedback higher than students given feedback delayed. <br /><br /></p>

Sign in / Sign up

Export Citation Format

Share Document