منابع مشابه
PCA-Kernel Estimation
Many statistical estimation techniques for high-dimensional or functional data are based on a preliminary dimension reduction step, which consists in projecting the sample X1, . . . ,Xn onto the first D eigenvectors of the Principal Component Analysis (PCA) associated with the empirical projector Π̂D. Classical nonparametric inference methods such as kernel density estimation or kernel regressio...
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We present three generalisations of Kernel Principal Components Analysis (KPCA) which incorporate knowledge of the class labels of a subset of the data points. The first, MV-KPCA, penalises within class variances similar to Fisher discriminant analysis. The second, LSKPCA is a hybrid of least squares regression and kernel PCA. The final LR-KPCA is an iteratively reweighted version of the previo...
متن کاملFast Iterative Kernel PCA
We introduce two methods to improve convergence of the Kernel Hebbian Algorithm (KHA) for iterative kernel PCA. KHA has a scalar gain parameter which is either held constant or decreased as 1/t, leading to slow convergence. Our KHA/et algorithm accelerates KHA by incorporating the reciprocal of the current estimated eigenvalues as a gain vector. We then derive and apply Stochastic MetaDescent (...
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We present the first model and algorithm for L1-norm kernel PCA. While L2-norm kernel PCA has been widely studied, there has been no work on L1-norm kernel PCA. For this non-convex and non-smooth problem, we offer geometric understandings through reformulations and present an efficient algorithm where the kernel trick is applicable. To attest the efficiency of the algorithm, we provide a conver...
متن کاملStochastic Optimization for Kernel PCA
Kernel Principal Component Analysis (PCA) is a popular extension of PCA which is able to find nonlinear patterns from data. However, the application of kernel PCA to largescale problems remains a big challenge, due to its quadratic space complexity and cubic time complexity in the number of examples. To address this limitation, we utilize techniques from stochastic optimization to solve kernel ...
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ژورنال
عنوان ژورنال: Statistics & Risk Modeling
سال: 2012
ISSN: 2193-1402
DOI: 10.1524/strm.2012.1084