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In this paper, we propose a novel approach named by Discriminative Principal Component Analysis which is abbreviated as Discriminative PCA in order to enhance separability of PCA by Linear Discriminant Analysis (LDA). The proposed method…
Discovering dominant patterns and exploring dynamic behaviors especially critical state transitions and tipping points in high-dimensional time-series data are challenging tasks in study of real-world complex systems, which demand…
Dimensionality reduction is a critical step in scaling machine learning pipelines. Principal component analysis (PCA) is a standard tool for dimensionality reduction, but performing PCA over a full dataset can be prohibitively expensive. As…
The high-dimensional feature space of the hyperspectral imagery poses major challenges to the processing and analysis of the hyperspectral data sets. In such a case, dimensionality reduction is necessary to decrease the computational…
The topic of this tutorial is Least Squares Sparse Principal Components Analysis (LS SPCA) which is a simple method for computing approximated Principal Components which are combinations of only a few of the observed variables. Analogously…
In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…
A novel text data dimension reduction technique, called the tree-structured multi-linear principal component anal- ysis (TMPCA), is proposed in this work. Being different from traditional text dimension reduction methods that deal with the…
Probabilistic principal component analysis (PPCA) is a probabilistic reformulation of principal component analysis (PCA), under the framework of a Gaussian latent variable model. To improve the robustness of PPCA, it has been proposed to…
Dimensionality reduction is critical across various domains of science including neuroscience. Probabilistic Principal Component Analysis (PPCA) is a prominent dimensionality reduction method that provides a probabilistic approach unlike…
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…
In this paper, we consider the alignment between an upstream dimensionality reduction task of learning a low-dimensional representation of a set of high-dimensional data and a downstream optimization task of solving a stochastic program…
This article focuses on the robust principal component analysis (PCA) of high-dimensional data with elliptical distributions. We investigate the PCA of the sample spatial-sign covariance matrix in both nonsparse and sparse contexts,…
Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and thus, various robust PCA methods have been proposed.…
Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…
Principal component regression (PCR) is a widely used two-stage procedure: principal component analysis (PCA), followed by regression in which the selected principal components are regarded as new explanatory variables in the model. Note…
A PCA based sequence-to-vector (seq2vec) dimension reduction method for the text classification problem, called the tree-structured multi-stage principal component analysis (TMPCA) is presented in this paper. Theoretical analysis and…
We discuss the problem of estimating the number of principal components in Principal Com- ponents Analysis (PCA). Despite of the importance of the problem and the multitude of solutions proposed in the literature, it comes as a surprise…
Principal Component Analysis (PCA) is a powerful and popular dimensionality reduction technique. However, due to its linear nature, it often fails to capture the complex underlying structure of real-world data. While Kernel PCA (kPCA)…
Principal component regression (PCR) is a two-stage procedure: the first stage performs principal component analysis (PCA) and the second stage constructs a regression model whose explanatory variables are replaced by principal components…
Data reconciliation (DR) and Principal Component Analysis (PCA) are two popular data analysis techniques in process industries. Data reconciliation is used to obtain accurate and consistent estimates of variables and parameters from…