Régionalisation du régime des précipitations dans la région des Bois-francs et de l'Estrie par l'analyse en composantes principales

1998 ◽  
Vol 25 (6) ◽  
pp. 1050-1058 ◽  
Author(s):  
T O Siew-Yan-Yu ◽  
J Rousselle ◽  
G Jacques ◽  
V.-T.-V. Nguyen
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Precipitation Regime ◽  
Regional Patterns ◽  
Air Masses ◽  
Orographic Effect ◽  
High Precipitation ◽  
Definition Of ◽  
Homogeneous Regions

A definition of homogeneous regions in terms of precipitation regime is achieved by the use of principal component analysis (PCA). The method has been shown to be a reliable regionalization tool even though it was applied to a territory showing rather complex physiography and high precipitation variation. Results based on the application of the PCA to the interstation correlation matrix of precipitation have indicated four distinct homogeneous regions. These regional patterns can be explained by the orographic effect and by the circulation of air masses within the study region.Key words: homogeneous regions, rainfall, principal component analysis, orographic effect.

scholarly journals Microsaccade characterization using the continuous wavelet transform and principal component analysis

2010 ◽  
Vol 3 (5) ◽  
Author(s):  
Mario Bettenbühl ◽  
Claudia Paladini ◽  
Konstantin Mergenthaler ◽  
Reinhold Kliegl ◽  
Ralf Engbert ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Wavelet Transform ◽  
Eye Movements ◽  
Continuous Wavelet Transform ◽  
Principal Component ◽  
Real Data ◽  
Component Analysis ◽  
Continuous Wavelet ◽  
Fixational Eye Movements ◽  
Definition Of

During visual fixation on a target, humans perform miniature (or fixational) eye movements consisting of three components, i.e., tremor, drift, and microsaccades. Microsaccades are high velocity components with small amplitudes within fixational eye movements. However, microsaccade shapes and statistical properties vary between individual observers. Here we show that microsaccades can be formally represented with two significant shapes which we identfied using the mathematical definition of singularities for the detection of the former in real data with the continuous wavelet transform. For character-ization and model selection, we carried out a principal component analysis, which identified a step shape with an overshoot as first and a bump which regulates the overshoot as second component. We conclude that microsaccades are singular events with an overshoot component which can be detected by the continuous wavelet transform.

scholarly journals SLIC Superpixel-Based l2,1-Norm Robust Principal Component Analysis for Hyperspectral Image Classification

Sensors ◽  
2019 ◽  
Vol 19 (3) ◽  
pp. 479 ◽  
Author(s):  
Baokai Zu ◽  
Kewen Xia ◽  
Tiejun Li ◽  
Ziping He ◽  
Yafang Li ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Dimensionality Reduction ◽  
Hyperspectral Image ◽  
Principal Component ◽  
Component Analysis ◽  
Curse Of Dimensionality ◽  
Hyperspectral Images ◽  
Robust Principal Component Analysis ◽  
Superpixel Segmentation ◽  
Homogeneous Regions

Hyperspectral Images (HSIs) contain enriched information due to the presence of various bands, which have gained attention for the past few decades. However, explosive growth in HSIs’ scale and dimensions causes “Curse of dimensionality” and “Hughes phenomenon”. Dimensionality reduction has become an important means to overcome the “Curse of dimensionality”. In hyperspectral images, labeled samples are more difficult to collect because they require many labor and material resources. Semi-supervised dimensionality reduction is very important in mining high-dimensional data due to the lack of costly-labeled samples. The promotion of the supervised dimensionality reduction method to the semi-supervised method is mostly done by graph, which is a powerful tool for characterizing data relationships and manifold exploration. To take advantage of the spatial information of data, we put forward a novel graph construction method for semi-supervised learning, called SLIC Superpixel-based l 2 , 1 -norm Robust Principal Component Analysis (SURPCA2,1), which integrates superpixel segmentation method Simple Linear Iterative Clustering (SLIC) into Low-rank Decomposition. First, the SLIC algorithm is adopted to obtain the spatial homogeneous regions of HSI. Then, the l 2 , 1 -norm RPCA is exploited in each superpixel area, which captures the global information of homogeneous regions and preserves spectral subspace segmentation of HSIs very well. Therefore, we have explored the spatial and spectral information of hyperspectral image simultaneously by combining superpixel segmentation with RPCA. Finally, a semi-supervised dimensionality reduction framework based on SURPCA2,1 graph is used for feature extraction task. Extensive experiments on multiple HSIs showed that the proposed spectral-spatial SURPCA2,1 is always comparable to other compared graphs with few labeled samples.

Principal Component Analysis Using the Factor Procedure

2010 ◽  
pp. 171-193
Author(s):  
Sean Eom
Keyword(s):  
Principal Component Analysis ◽  
Factor Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Statistical Techniques ◽  
Data Input ◽  
Number Of Factors ◽  
Rotation Method ◽  
Definition Of

This chapter describes the factor procedure. The first section of the chapter begins with the definition of factor analysis. This is the statistical techniques whose common objective is to represent a set of variables in terms of a smaller number of hypothetical variables (factor). ACA uses principal component analysis to group authors into several catagories with similar lines of research. We also present many different approaches of preparing datasets including manual data inputs, in-file statement, and permanent datasets. We discuss each of the key SAS statements including DATA, INPUT, CARDS, PROC, and RUN. In addition, we examine several options statements to specify the followings: method for extracting factors; number of factors, rotation method, and displaying output options.

Regional Taiwan rainfall frequency analysis using principal component analysis, self-organizing maps and L-moments

2012 ◽  
Vol 43 (3) ◽  
pp. 275-285 ◽  
Author(s):  
Lu-Hsien Chen ◽  
Yu-Ting Hong
Keyword(s):  
Principal Component Analysis ◽  
Frequency Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Return Periods ◽  
Self Organizing Maps ◽  
Ungauged Sites ◽  
Rainfall Frequency ◽  
Rainfall Frequency Analysis ◽  
Homogeneous Regions

The objective of this paper is to propose an approach, which consists of principal component analysis (PCA), self-organizing maps (SOM) and the L-moment method, for improving estimation of desired rainfall quantiles of ungauged sites. Firstly, PCA is applied to obtain the principal components. Then SOM is applied to group the rain gauges into specific clusters and the number of clusters can be objectively decided by visual inspection. Moreover, the L-moment based discordancy and heterogeneity are used to test whether clusters may be acceptable as being homogeneous. After the gauges are grouped into specific clusters, the homogeneous regions are then delineated. Finally, goodness-of-fit measure is used to select the regional probability distributions and the design rainfall quantiles with various return periods for each region can be estimated. The proposed approach is applied to analyze and quantify regional rainfalls in Taiwan. The proposed approach is a robust and efficient way for regional rainfall frequency analysis. Moreover, one can easily assign an ungauged site to a previously defined cluster according to a map of homogeneous regions. Therefore, the proposed approach is expected to be useful for providing the design rainfall quantiles with various return periods at ungauged sites.

CONDITIONS FOR THE APPLICABILITY OF THE PRINCIPAL COMPONENT ANALYSIS TO THE CHARACTERIZATION OF THE 1/f-NOISE

2006 ◽  
Vol 06 (01) ◽  
pp. L17-L28 ◽  
Author(s):  
JOSÉ MANUEL LÓPEZ-ALONSO ◽  
JAVIER ALDA
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Random Variable ◽  
Component Analysis ◽  
Optical Systems ◽  
Data Sets ◽  
Regular Time ◽  
Pca Method ◽  
Definition Of

Principal Component Analysis (PCA) has been applied to the characterization of the 1/f-noise. The application of the PCA to the 1/f noise requires the definition of a stochastic multidimensional variable. The components of this variable describe the temporal evolution of the phenomena sampled at regular time intervals. In this paper we analyze the conditions about the number of observations and the dimension of the multidimensional random variable necessary to use the PCA method in a sound manner. We have tested the obtained conditions for simulated and experimental data sets obtained from imaging optical systems. The results can be extended to other fields where this kind of noise is relevant.

scholarly journals Convex Formulations for Fair Principal Component Analysis

2019 ◽  
Vol 33 ◽  
pp. 663-670 ◽  
Author(s):  
Matt Olfat ◽  
Anil Aswani
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Health Data ◽  
Kernel Pca ◽  
Semidefinite Programs ◽  
Data Points ◽  
Insurance Rates ◽  
Definition Of ◽  
Reduced Data

Though there is a growing literature on fairness for supervised learning, incorporating fairness into unsupervised learning has been less well-studied. This paper studies fairness in the context of principal component analysis (PCA). We first define fairness for dimensionality reduction, and our definition can be interpreted as saying a reduction is fair if information about a protected class (e.g., race or gender) cannot be inferred from the dimensionality-reduced data points. Next, we develop convex optimization formulations that can improve the fairness (with respect to our definition) of PCA and kernel PCA. These formulations are semidefinite programs, and we demonstrate their effectiveness using several datasets. We conclude by showing how our approach can be used to perform a fair (with respect to age) clustering of health data that may be used to set health insurance rates.

scholarly journals Principal component analysis for Riemannian manifolds, with an application to triangular shape spaces

2006 ◽  
Vol 38 (2) ◽  
pp. 299-319 ◽  
Author(s):  
Stephan Huckemann ◽  
Herbert Ziezold
Keyword(s):  
Principal Component Analysis ◽  
Riemannian Manifolds ◽  
Principal Component ◽  
Component Analysis ◽  
Intrinsic Metric ◽  
Shape Spaces ◽  
Intrinsic Mean ◽  
Pass Through ◽  
Definition Of ◽  
Euclidean Mean

Classical principal component analysis on manifolds, for example on Kendall's shape spaces, is carried out in the tangent space of a Euclidean mean equipped with a Euclidean metric. We propose a method of principal component analysis for Riemannian manifolds based on geodesics of the intrinsic metric, and provide a numerical implementation in the case of spheres. This method allows us, for example, to compare principal component geodesics of different data samples. In order to determine principal component geodesics, we show that in general, owing to curvature, the principal component geodesics do not pass through the intrinsic mean. As a consequence, means other than the intrinsic mean are considered, allowing for several choices of definition of geodesic variance. In conclusion we apply our method to the space of planar triangular shapes and compare our findings with those of standard Euclidean principal component analysis.

scholarly journals Sensitivity of the CMIP5 models to precipitation in Tropical Brazil

2020 ◽  
Vol 12 (1) ◽  
pp. 180-191
Author(s):  
Naurinete De Jesus da Costa Barreto ◽  
David Mendes ◽  
Paulo Sérgio Lucio
Keyword(s):  
Principal Component Analysis ◽  
Coupled Model ◽  
Austral Summer ◽  
Principal Component ◽  
Component Analysis ◽  
Cmip5 Models ◽  
Precipitation Regime ◽  
Temporal Space ◽  
Dominant Pattern ◽  
Intercomparison Project

The main objective of this study is to evaluate the ability of the fifth phase of the Coupled Model Intercomparison Project (CMIP5) models to simulate weekly rainfall over Tropical Brazil. Twenty-four years of the historical experiment of sixteen models for the austral summer and fall seasons were evaluated. In the analyzes performed in this study, frequency distribution and correlation were used to evaluate temporal variability. Principal Component Analysis to ascertain the characteristics of the dominant pattern of each model. The results suggest that some models have difficulty in simulating the spatial pattern of regional precipitation, especially related to the frequency of events and temporal variation, however, the dominant pattern found by the Principal Component Analysis showed that at least six models (ACCESS1-0, CanESM2, EC-EARTH, GFDL-CM3, MIROC5 and MRI-CGCM3) reasonably represented the temporal-space precipitation regime over Tropical Brazil.

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