Multivariate Gaussianization for Data Processing

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Intro Iterative Gaussianization Experiments ConclusionsExperiment 1: Density estimation toy examplesDensity estimation with RBIG1: Input: Given data x (0) = [x 1, . . . , x d ] ⊤ ∈ R d2: Learn the sequence of Gaussianization transforms, G, such that y = G(x)3: Compute its Jacobian, J G4: The p y(y) is a multivariate Gaussian:(1p y(y) = p y(G(x)) =( √ 2π|Σ|) exp − 1 )d 2 (G(x) − µ y) ⊤ Σ −1 (G(x) − µ y )5: Compute the probability in the input space with:p x(x) = p y(y) · |∇ xG|AdvantagesRobustness to high dimensional problemsNo data distribution assumptions, no parametric model eitherLow computational cost
Intro Iterative Gaussianization Experiments ConclusionsExperiment 1: Density estimation toy examplesToy exampleTheoretical PDF Scatter plot Histogram G-PCA PDFe 3. Example of 10PDF 2 samples estimation. usedFrom left to right: theoretical PDF, scatter plot of the data used in the estimaram estimation Much usingsmoother a number of estimation bins to obtain the same resolution as in the G-PCA estimation.5. EXPERIMENTAL RESULTSroposed method is illustrated in two experiments and will be compared to standard SVDD because ofive similarity (cf. Section 3.1). The first 2D experiment on synthetic data illustrates the capabilities ood in non-linearly separable and badly sampled one-class problems. The second experiment deals withspectral and multisource data and illustrates the advantages of G-PCA in real and challenging scenarExperiment 1: 2D non-linearly separable problems.is 2D experiment the problem is detecting outliers from the target class represented by dots in Fig. 4.
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Multivariate Gaussianization for Data Processing

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