Recently, kernel Principal Component Analysis is becoming a popular technique for feature extraction. It enables us to extract nonlinear features and therefore performs as a powerful preprocessing step for classification. There is one drawback, however, that extracted feature components are sensitive to outliers contained in data. This is a characteristic common to all PCA-based techniques. In ...

Kernel principal component analysis (kernel PCA) is a non-linear extension of PCA. This study introduces and investigates the use of kernel PCA for novelty detection. Training data are mapped into an infinite-dimensional feature space. In this space, kernel PCA extracts the principal components of the data distribution. The squared distance to the corresponding principal subspace is the measure...

Kernel principal component analysis (KPCA) extracts features of samples with an efficiency in inverse proportion to the size of the training sample set. In this paper, we develop a novel method to improve KPCA-based feature extraction. The developed method is the first one that is methodologically consistent with KPCA. Experiments on several benchmark datasets illustrate that the feature extrac...

Problem Statement Experimental data to be analyzed is often represented as a number of vectors of fixed dimensionality. A single vector could for example be a set of temperature measurements across Germany. Taking such a vector of measurements at different times results in a number of vectors that altogether constitute the data. Each vector can also be interpreted as a point in a high dimension...

Principal component analysis (PCA) is widely used in data processing and dimensionality reduction. However, PCA suffers from the fact that each principal component is a linear combination of all the original variables, thus it is often difficult to interpret the results. We introduce a new method called sparse principal component analysis (SPCA) using the lasso (elastic net) to produce modified...

Recently, many l1-norm based PCA methods have been developed for dimensionality reduction, but they do not explicitly consider the reconstruction error. Moreover, they do not take into account the relationship between reconstruction error and variance of projected data. This reduces the robustness of algorithms. To handle this problem, a novel formulation for PCA, namely angle PCA, is proposed....

When modeling multivariate data, one might have an extra parameter of contextual information that could be used to treat some observations as more similar to others. For example, images of faces can vary by age, and one would expect the face of a 40 year old to be more similar to the face of a 30 year old than to a baby face. We introduce a novel manifold approximation method, parameterized pri...

Principal components analysis (PCA) is a dimensionality reduction technique that can be used to give a compact representation of data while minimising information loss. Suppose we are given a set of data, represented as vectors in a high-dimensional space. It may be that many of the variables are correlated and that the data closely fits a lower dimensional linear manifold. In this case, PCA fi...

We propose two new principal component analysis methods in this paper utilizing a semiparametric model. The according methods are named Copula Component Analysis (COCA) and Copula PCA. The semiparametric model assumes that, after unspecified marginally monotone transformations, the distributions are multivariate Gaussian. The COCA and Copula PCA accordingly estimate the leading eigenvectors of ...

Principal Component Analysis (PCA) aims to learn compact and informative representations for data and has wide applications in machine learning, text mining and computer vision. Classical PCA based on a Gaussian noise model is fragile to noise of large magnitude. Laplace noise assumption based PCA methods cannot deal with dense noise effectively. In this paper, we propose Cauchy Principal Compo...