scholarly journals Noise Reduction of Atmospheric Emitted Radiance Interferometer (AERI) Observations Using Principal Component Analysis

2006 ◽  
Vol 23 (9) ◽  
pp. 1223-1238 ◽  
Author(s):  
D. D. Turner ◽  
R. O. Knuteson ◽  
H. E. Revercomb ◽  
C. Lo ◽  
R. G. Dedecker
Keyword(s):  
Principal Components ◽  
Principal Component ◽  
Spectral Element ◽  
High Spectral Resolution ◽  
The Arctic ◽  
Atmospheric Variability ◽  
Temporal Sampling ◽  
Noise Filter ◽  
Empirical Function ◽  
Number Of Principal Components

Abstract A principal component noise filter has been applied to ground-based high-spectral-resolution infrared radiance observations collected by the Atmospheric Emitted Radiance Interferometers (AERIs) deployed by the Atmospheric Radiation Measurement (ARM) program. The technique decomposes the radiance observations into their principal components, selects the ones that describe the most variance in the data, and reconstructs the data from these components. An empirical function developed for chemical analysis is utilized to determine the number of principal components to be used in the reconstruction of the data. Statistical analysis of the noise-filtered minus original radiance data, as well as side-by-side analysis of data from two AERI systems utilizing different temporal sampling, demonstrates the ability of the noise filter using this empirical function to retain most of the atmospheric signal above the AERI noise level in the filtered data. The noise filter is applied to data collected at ARM’s tropical, midlatitude, and Arctic sites, demonstrating that the random variability in the data is reduced by 5% to over 450%, depending on the spectral element and location of the instrument. A seasonal analysis of the number of principal components required by the noise filter for each site shows a strong seasonal dependence in the atmospheric variability at the Arctic and midlatitude sites but not at the tropical site.

scholarly journals REPRESENTATION BOUND FOR HUMAN FACIAL MIMIC WITH THE AID OF PRINCIPAL COMPONENT ANALYSIS

2010 ◽  
Vol 10 (03) ◽  
pp. 343-363
Author(s):  
ULRIK SÖDERSTRÖM ◽  
HAIBO LI
Keyword(s):  
Principal Component Analysis ◽  
Facial Expressions ◽  
Principal Components ◽  
Color Image ◽  
Signal To Noise Ratio ◽  
Principal Component ◽  
Component Analysis ◽  
Exact Representation ◽  
Basic Emotions ◽  
Number Of Principal Components

In this paper, we examine how much information is needed to represent the facial mimic, based on Paul Ekman's assumption that the facial mimic can be represented with a few basic emotions. Principal component analysis is used to compact the important facial expressions. Theoretical bounds for facial mimic representation are presented both for using a certain number of principal components and a certain number of bits. When 10 principal components are used to reconstruct color image video at a resolution of 240 × 176 pixels the representation bound is on average 36.8 dB, measured in peak signal-to-noise ratio. Practical confirmation of the theoretical bounds is demonstrated. Quantization of projection coefficients affects the representation, but a quantization with approximately 7-8 bits is found to match an exact representation, measured in mean square error.

scholarly journals A principal component noise filter for high spectral resolution infrared measurements

2004 ◽  
Vol 109 (D23) ◽  
Author(s):  
P. Antonelli ◽  
H. E. Revercomb ◽  
L. A. Sromovsky ◽  
W. L. Smith ◽  
R. O. Knuteson ◽  
...  
Keyword(s):  
Spectral Resolution ◽  
Principal Component ◽  
High Spectral Resolution ◽  
Noise Filter ◽  
Infrared Measurements

scholarly journals PCR, PLS, or OPLS Evaluation of different regression techniques for hypothesis generation

2021 ◽  
Author(s):  
Avani Ahuja
Keyword(s):  
Least Squares ◽  
Partial Least Squares ◽  
Principal Components ◽  
Selection Process ◽  
Principal Component ◽  
Hypothesis Generation ◽  
Multivariate Techniques ◽  
Response Variable ◽  
Number Of Principal Components ◽  
Latent Structures

In the current era of ‘big data’, scientists are able to quickly amass enormous amount of data in a limited number of experiments. The investigators then try to hypothesize about the root cause based on the observed trends for the predictors and the response variable. This involves identifying the discriminatory predictors that are most responsible for explaining variation in the response variable. In the current work, we investigated three related multivariate techniques: Principal Component Regression (PCR), Partial Least Squares or Projections to Latent Structures (PLS), and Orthogonal Partial Least Squares (OPLS). To perform a comparative analysis, we used a publicly available dataset for Parkinson’ disease patien ts. We first performed the analysis using a cross-validated number of principal components for the aforementioned techniques. Our results demonstrated that PLS and OPLS were better suited than PCR for identifying the discriminatory predictors. Since the X data did not exhibit a strong correlation, we also performed Multiple Linear Regression (MLR) on the dataset. A comparison of the top five discriminatory predictors identified by the four techniques showed a substantial overlap between the results obtained by PLS, OPLS, and MLR, and the three techniques exhibited a significant divergence from the variables identified by PCR. A further investigation of the data revealed that PCR could be used to identify the discriminatory variables successfully if the number of principal components in the regression model were increased. In summary, we recommend using PLS or OPLS for hypothesis generation and systemizing the selection process for principal components when using PCR.rewordexplain later why MLR can be used on a dataset with no correlation

scholarly journals Robust PCA via Regularized Reaper with a Matrix-Free Proximal Algorithm

2021 ◽  
Author(s):  
Robert Beinert ◽  
Gabriele Steidl
Keyword(s):  
Principal Components ◽  
High Dimensional Data ◽  
Principal Component ◽  
High Dimensional ◽  
Robust Pca ◽  
Lanczos Process ◽  
Primal Dual ◽  
Curve Method ◽  
Number Of Principal Components ◽  
Matrix Free

AbstractPrincipal component analysis (PCA) is known to be sensitive to outliers, so that various robust PCA variants were proposed in the literature. A recent model, called reaper, aims to find the principal components by solving a convex optimization problem. Usually the number of principal components must be determined in advance and the minimization is performed over symmetric positive semi-definite matrices having the size of the data, although the number of principal components is substantially smaller. This prohibits its use if the dimension of the data is large which is often the case in image processing. In this paper, we propose a regularized version of reaper which enforces the sparsity of the number of principal components by penalizing the nuclear norm of the corresponding orthogonal projector. If only an upper bound on the number of principal components is available, our approach can be combined with the L-curve method to reconstruct the appropriate subspace. Our second contribution is a matrix-free algorithm to find a minimizer of the regularized reaper which is also suited for high-dimensional data. The algorithm couples a primal-dual minimization approach with a thick-restarted Lanczos process. This appears to be the first efficient convex variational method for robust PCA that can handle high-dimensional data. As a side result, we discuss the topic of the bias in robust PCA. Numerical examples demonstrate the performance of our algorithm.

The USAF Multivariate Accommodation Method

1998 ◽  
Vol 42 (10) ◽  
pp. 722-726 ◽  
Author(s):  
Jeffrey A. Hudson ◽  
Gregory F. Zehner ◽  
Richard S. Meindl
Keyword(s):  
Principal Component Analysis ◽  
Body Size ◽  
Statistical Method ◽  
Principal Components ◽  
Principal Component ◽  
Full Understanding ◽  
Multivariate Method ◽  
Number Of Principal Components ◽  
Research And Design ◽  
Selection Of

The USAF has been using a multivariate method for specifying pilot body size for nearly ten years. The Multivariate Accommodation software was originally written for a VMS environment using the statistical package SAS. It is now available for PC computers. The program is based on the CADRE statistical method developed by Bittner (1987), and the Anthropometric Database at the Computerized Anthropometric Research and Design Laboratory (Robinson et al., 1992), and has been very effective in increasing body size accommodation in USAF cockpit designs. The technique relies on principal component analysis which describes the variation of the original multivariate distribution with a set of orthogonal axes (principal components). Selection of the anthropometric measurements, the number of principal components used to represent the variation in their distribution, and a full understanding of the assumptions implicit in the model are all critical in generating useful representative accommodation cases. The authors will discuss previous applications of the method as well as demonstrate its limitations when used outside of cockpit/workstation designs.

scholarly journals Airborne limb-imaging measurements of temperature, HNO<sub>3</sub>, O<sub>3</sub>, ClONO<sub>2</sub>, H<sub>2</sub>O and CFC-12 during the Arctic winter 2015/16: characterization, in-situ validation and comparison to Aura/MLS

2018 ◽  
Author(s):  
Sören Johansson ◽  
Wolfgang Woiwode ◽  
Michael Höpfner ◽  
Felix Friedl-Vallon ◽  
Anne Kleinert ◽  
...  
Keyword(s):  
Cross Sections ◽  
Spectral Resolution ◽  
Trace Gases ◽  
High Spectral Resolution ◽  
The Arctic ◽  
Trace Gas ◽  
Atmospheric Variability ◽  
Mesoscale Structures ◽  
Research Aircraft

Abstract. The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA) was operated on board the German High Altitude and LOng range (HALO) research aircraft during the PGS (POLSTRACC/GW-LCYCLE/SALSA) aircraft campaigns in the Arctic winter 2015/2016. Research flights were conducted from 17 December 2015 until 18 March 2016 between 80° W–30° E longitude and 25° N–87° N latitude. From the GLORIA infrared limb emission measurements, two dimensional cross sections of temperature, HNO3, O3, ClONO2, H2O and CFC-12 are retrieved. During 15 scientific flights of the PGS campaigns the GLORIA instrument measured more than 15 000 atmospheric profiles at high spectral resolution. Dependent on flight altitude and tropospheric cloud cover, the profiles retrieved from the measurements typically range between 5 and 14 km, and vertical resolutions between 400 m and 1000 m are achieved. The estimated total (random and systematic) 1σ errors are in the range of 1 to 2 K for temperature and 10 % to 20 % relative error for the discussed trace gases. Comparisons to in-situ instruments deployed on board HALO have been performed. Over all flights of this campaign the median differences and median absolute deviations between in-situ and GLORIA observations are −0.75 K ± 0.88 K for temperature, −0.03 ppbv ± 0.85 ppbv for HNO3, −3.5 ppbv ± 116.8 ppbv for O3, −15.4 pptv ± 102.8 pptv for ClONO2, −0.13 ppmv ± 0.63 ppmv for H2O and −19.8 pptv ± 46.9 pptv for CFC-12. These differences are mainly within the expected performances of the cross-compared instruments. Events with stronger deviations are explained by atmospheric variability and different sampling characteristics of the instruments. Additionally comparisons of GLORIA HNO3 and O3 with measurements of the Aura Microwave Limb Sounder (MLS) instrument show highly consistent structures in trace gas distributions and illustrate the potential of the high spectral resolution limb-imaging GLORIA observations for resolving narrow mesoscale structures in the UTLS.

scholarly journals A Corrected Criterion for Selecting the Optimum Number of Principal Components

2016 ◽  
Vol 38 (3) ◽  
Author(s):  
Hannes Kazianka ◽  
Jürgen Pilz
Keyword(s):  
Principal Components ◽  
Bayesian Model ◽  
Selection Criterion ◽  
Principal Component ◽  
Optimum Number ◽  
The Novel ◽  
Probabilistic Pca ◽  
Hyper Spectral ◽  
Number Of Principal Components ◽  
Approximate Bayesian

Determining the optimum number of components to be retained is a key problem in principal component analysis (PCA). Besides the rule of thumb estimates there exist several sophisticated methods for automatically selecting the dimensionality of the data. Based on the probabilistic PCA model Minka (2001) proposed an approximate Bayesian model selection criterion. In this paper we correct this criterion and present a modified version. We compare the novel criterion with various other approaches in a simulationstudy. Furthermore, we use it for finding the optimum number of principal components in hyper-spectral skin cancer images.

On Reliability and Number of Principal Components: Joinder with Cliff and Kaiser

1992 ◽  
Vol 75 (3) ◽  
pp. 929-930 ◽  
Author(s):  
Oliver C. S. Tzeng
Keyword(s):  
Principal Component Analysis ◽  
Principal Components ◽  
Correlation Matrix ◽  
Principal Component ◽  
Component Analysis ◽  
Number Of Factors ◽  
Number Of Principal Components ◽  
Scree Test

This note summarizes my remarks on the application of reliability of the principal component and the eigenvalue-greater-than-1 rule for determining the number of factors in principal component analysis of a correlation matrix. Due to the unpredictability and uselessness of the reliability approach and the Kaiser-Guttman rule, research workers are encouraged to use other methods such as the scree test.

scholarly journals Adaptive dimensionality reduction for neural network-based online principal component analysis

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0248896
Author(s):  
Nico Migenda ◽  
Ralf Möller ◽  
Wolfram Schenck
Keyword(s):  
Neural Network ◽  
Principal Component Analysis ◽  
Dimensionality Reduction ◽  
Principal Components ◽  
Principal Component ◽  
Component Analysis ◽  
Optimal Number ◽  
Streaming Data ◽  
Number Of Principal Components ◽  
Incremental Pca

“Principal Component Analysis” (PCA) is an established linear technique for dimensionality reduction. It performs an orthonormal transformation to replace possibly correlated variables with a smaller set of linearly independent variables, the so-called principal components, which capture a large portion of the data variance. The problem of finding the optimal number of principal components has been widely studied for offline PCA. However, when working with streaming data, the optimal number changes continuously. This requires to update both the principal components and the dimensionality in every timestep. While the continuous update of the principal components is widely studied, the available algorithms for dimensionality adjustment are limited to an increment of one in neural network-based and incremental PCA. Therefore, existing approaches cannot account for abrupt changes in the presented data. The contribution of this work is to enable in neural network-based PCA the continuous dimensionality adjustment by an arbitrary number without the necessity to learn all principal components. A novel algorithm is presented that utilizes several PCA characteristics to adaptivly update the optimal number of principal components for neural network-based PCA. A precise estimation of the required dimensionality reduces the computational effort while ensuring that the desired amount of variance is kept. The computational complexity of the proposed algorithm is investigated and it is benchmarked in an experimental study against other neural network-based and incremental PCA approaches where it produces highly competitive results.

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