27,445 research outputs found
Modified confidence intervals for the Mahalanobis distance
Reiser (2001) proposes a method of forming confidence interval for a Mahalanobis distance that yields intervals which have exactly the nominal coverage, but sometimes the interval is View the MathML source (0,0). We consider the case where Mahalanobis distance quantifies the difference between an individual and a population mean, and suggest a modification that avoids implausible intervals
Mahalanobis Distance for Class Averaging of Cryo-EM Images
Single particle reconstruction (SPR) from cryo-electron microscopy (EM) is a
technique in which the 3D structure of a molecule needs to be determined from
its contrast transfer function (CTF) affected, noisy 2D projection images taken
at unknown viewing directions. One of the main challenges in cryo-EM is the
typically low signal to noise ratio (SNR) of the acquired images. 2D
classification of images, followed by class averaging, improves the SNR of the
resulting averages, and is used for selecting particles from micrographs and
for inspecting the particle images. We introduce a new affinity measure, akin
to the Mahalanobis distance, to compare cryo-EM images belonging to different
defocus groups. The new similarity measure is employed to detect similar
images, thereby leading to an improved algorithm for class averaging. We
evaluate the performance of the proposed class averaging procedure on synthetic
datasets, obtaining state of the art classification.Comment: Final version accepted to the 14th IEEE International Symposium on
Biomedical Imaging (ISBI 2017
The Mahalanobis distance for functional data with applications to classification
This paper presents a general notion of Mahalanobis distance for functional data that
extends the classical multivariate concept to situations where the observed data are
points belonging to curves generated by a stochastic process. More precisely, a new
semi-distance for functional observations that generalize the usual Mahalanobis distance
for multivariate datasets is introduced. For that, the development uses a regularized
square root inverse operator in Hilbert spaces. Some of the main characteristics of the
functional Mahalanobis semi-distance are shown. Afterwards, new versions of several
well known functional classification procedures are developed using the Mahalanobis
distance for functional data as a measure of proximity between functional observations.
The performance of several well known functional classification procedures are
compared with those methods used in conjunction with the Mahalanobis distance for
functional data, with positive results, through a Monte Carlo study and the analysis of
two real data examplesFinancial support by MEC
project ECO2012-38442 is gratefully acknowledge
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