Related papers: Principal Component Analysis for Experiments
Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…
The selection of best variables is a challenging problem in supervised and unsupervised learning, especially in high dimensional contexts where the number of variables is usually much larger than the number of observations. In this paper,…
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…
We propose a new method to impute missing values in mixed datasets. It is based on a principal components method, the factorial analysis for mixed data, which balances the influence of all the variables that are continuous and categorical…
Recurrence plots were introduced to help aid the detection of signals in complicated data series. This effort was furthered by the quantification of recurrence plot elements. We now demonstrate the utility of combining recurrence…
The network traffic matrix is widely used in network operation and management. It is therefore of crucial importance to analyze the components and the structure of the network traffic matrix, for which several mathematical approaches such…
In datasets where the number of parameters is fixed and the number of samples is large, principal component analysis (PCA) is a powerful dimension reduction tool. However, in many contemporary datasets, when the number of parameters is…
Methods for global measurement of transcript abundance such as microarrays and RNA-Seq generate datasets in which the number of measured features far exceeds the number of observations. Extracting biologically meaningful and experimentally…
The article discusses selected problems related to both principal component analysis (PCA) and factor analysis (FA). In particular, both types of analysis were compared. A vector interpretation for both PCA and FA has also been proposed.…
In this paper we analyze different ways of performing principal component analysis throughout three different approaches: robust covariance and correlation matrix estimation, projection pursuit approach and non-parametric maximum entropy…
Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…
The tensorial principal component analysis is a generalization of ordinary principal component analysis, focusing on data which are suitably described by tensors rather than matrices. This paper aims at giving the nonperturbative…
In this paper the exact linear relation between the leading eigenvectors of the modularity matrix and the singular vectors of an uncentered data matrix is developed. Based on this analysis the concept of a modularity component is defined,…
This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…
Principal component analysis and factor analysis are fundamental multivariate analysis methods. In this paper a unified framework to connect them is introduced. Under a general latent variable model, we present matrix optimization problems…
One develops a fast computational methodology for principal component analysis on manifolds. Instead of estimating intrinsic principal components on an object space with a Riemannian structure, one embeds the object space in a numerical…
Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…
A general asymptotic framework is developed for studying consis- tency properties of principal component analysis (PCA). Our frame- work includes several previously studied domains of asymptotics as special cases and allows one to…