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Principal component analysis is a long-standing go-to method for exploring multivariate data. The principal components are linear combinations of the original variables, ordered by descending variance. The first few components typically…
We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
Pattern extraction algorithms are enabling insights into the ever-growing amount of today's datasets by translating reoccurring data properties into compact representations. Yet, a practical problem arises: With increasing data volumes and…
Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…
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.…
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…
A classifier for two or more samples is proposed when the data are high-dimensional and the underlying distributions may be non-normal. The classifier is constructed as a linear combination of two easily computable and interpretable…
Matrix factor models have been growing popular dimension reduction tools for large-dimensional matrix time series. However, the heteroscedasticity of the idiosyncratic components has barely received any attention. Starting from the pseudo…
'Big' high-dimensional data are commonly analyzed in low-dimensions, after performing a dimensionality-reduction step that inherently distorts the data structure. For the same purpose, clustering methods are also often used. These methods…
Some recent results showed that renormalization group can be considered as a promising framework to address open issues in data analysis. In this work, we focus on one of these aspects, closely related to principal component analysis for…
We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented…
Dimensionality reduction (DR) is frequently used for analyzing and visualizing high-dimensional data as it provides a good first glance of the data. However, to interpret the DR result for gaining useful insights from the data, it would…
For high dimensional data, some of the standard statistical techniques do not work well. So modification or further development of statistical methods are necessary. In this paper, we explore these modifications. We start with the important…
We show that when a high-dimensional data matrix is the sum of a low-rank matrix and a random error matrix with independent entries, the low-rank component can be consistently estimated by solving a convex minimization problem. We develop a…
Unsupervised learning makes manifest the underlying structure of data without curated training and specific problem definitions. However, the inference of relationships between data points is frustrated by the `curse of dimensionality' in…
Simpson's paradox, a long-standing statistical phenomenon, describes the reversal of an observed association when data are disaggregated into sub-populations. It has critical implications across statistics, epidemiology, economics, and…
Principal Components Regression (PCR) is a traditional tool for dimension reduction in linear regression that has been both criticized and defended. One concern about PCR is that obtaining the leading principal components tends to be…
Principal component analysis is a statistical method, which lowers the number of important variables in a data set. The use of this method for the bursts' spectra and afterglows is discussed in this paper. The analysis indicates that three…
Parallel coordinate plots (PCPs) are among the most useful techniques for the visualization and exploration of high-dimensional data spaces. They are especially useful for the representation of correlations among the dimensions, which…