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Statements

Subject Item
dbr:Empirical_orthogonal_functions
rdfs:label
経験的直交関数 Empirical orthogonal functions Décomposition orthogonale aux valeurs propres
rdfs:comment
In statistics and signal processing, the method of empirical orthogonal function (EOF) analysis is a decomposition of a signal or data set in terms of orthogonal basis functions which are determined from the data. The term is also interchangeable with the geographically weighted Principal components analysis in geophysics. The i th basis function is chosen to be orthogonal to the basis functions from the first through i − 1, and to minimize the residual variance. That is, the basis functions are chosen to be different from each other, and to account for as much variance as possible. En statistique et traitement du signal, la méthode décomposition orthogonale aux valeurs propres consiste à décomposer des données avec des fonctions orthogonales déterminées à partir des données (en anglais : empirical orthogonal functions, abrégé en EOF). C'est la même chose que de faire une analyse en composante principale excepté que les EOF permettent d'obtenir à la fois des formes (patterns) temporelles et spatiales. Les EOF sont aussi appelés PCA en géophysique. Pour faire simple : les EOF permettent de synthétiser l'information pour faciliter l'analyse. 経験的直交関数（けいけんてきちょっこうかんすう、Empirical Orthogonal Function）とは多変量解析の手法の1つである主成分分析を用いて計算された主成分ベクトルのこと。複数の変数同士の共分散（または相関）を計算して共分散行列（または相関行列）を作成し、その最も大きな固有値に対応する固有ベクトルを第一主成分（EOF-1）とする。共分散行列の固有値は分散の大きさを表すので、EOF-1は最も分散を大きくするような成分となる。第二主成分（EOF-2）は、EOF-1に直交する成分のうち最も分散を大きくするような（EOF-1に対応する固有値を除けば最も固有値の大きな）固有ベクトルである。
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dbc:Statistical_signal_processing dbc:Spatial_analysis
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1087385357
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dbr:Kernel_(matrix) dbr:Covariance_matrix dbr:Kernel_trick dbr:Eigenvector dbr:Signal_processing dbr:Principal_components_analysis dbr:Transform_coding dbr:Varimax_rotation dbr:Mercer's_theorem dbr:Basis_function dbr:Signal_separation dbr:Variance dbr:Blind_signal_separation dbr:Statistics dbr:Orthogonal_matrix dbr:Geophysics dbc:Statistical_signal_processing dbr:Harmonic_analysis dbr:Orthogonal dbr:Singular_spectrum_analysis dbr:Kernel_(statistics) dbr:Frequency dbr:Multilinear_subspace_learning dbr:Biometrika dbr:Nonlinear_dimensionality_reduction dbr:Multilinear_PCA dbc:Spatial_analysis
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dbo:abstract
経験的直交関数（けいけんてきちょっこうかんすう、Empirical Orthogonal Function）とは多変量解析の手法の1つである主成分分析を用いて計算された主成分ベクトルのこと。複数の変数同士の共分散（または相関）を計算して共分散行列（または相関行列）を作成し、その最も大きな固有値に対応する固有ベクトルを第一主成分（EOF-1）とする。共分散行列の固有値は分散の大きさを表すので、EOF-1は最も分散を大きくするような成分となる。第二主成分（EOF-2）は、EOF-1に直交する成分のうち最も分散を大きくするような（EOF-1に対応する固有値を除けば最も固有値の大きな）固有ベクトルである。 In statistics and signal processing, the method of empirical orthogonal function (EOF) analysis is a decomposition of a signal or data set in terms of orthogonal basis functions which are determined from the data. The term is also interchangeable with the geographically weighted Principal components analysis in geophysics. The i th basis function is chosen to be orthogonal to the basis functions from the first through i − 1, and to minimize the residual variance. That is, the basis functions are chosen to be different from each other, and to account for as much variance as possible. The method of EOF analysis is similar in spirit to harmonic analysis, but harmonic analysis typically uses predetermined orthogonal functions, for example, sine and cosine functions at fixed frequencies. In some cases the two methods may yield essentially the same results. The basis functions are typically found by computing the eigenvectors of the covariance matrix of the data set. A more advanced technique is to form a kernel out of the data, using a fixed kernel. The basis functions from the eigenvectors of the kernel matrix are thus non-linear in the location of the data (see Mercer's theorem and the kernel trick for more information). En statistique et traitement du signal, la méthode décomposition orthogonale aux valeurs propres consiste à décomposer des données avec des fonctions orthogonales déterminées à partir des données (en anglais : empirical orthogonal functions, abrégé en EOF). C'est la même chose que de faire une analyse en composante principale excepté que les EOF permettent d'obtenir à la fois des formes (patterns) temporelles et spatiales. Les EOF sont aussi appelés PCA en géophysique. Pour faire simple : les EOF permettent de synthétiser l'information pour faciliter l'analyse.
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dbr:Decomposition
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