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Principal component analysis (PCA) is widely used for dimension reduction and embedding of real data in social network analysis, information retrieval, and natural language processing, etc. In this work we propose a fast randomized PCA…
Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…
Many machine learning systems are vulnerable to small perturbations made to inputs either at test time or at training time. This has received much recent interest on the empirical front due to applications where reliability and security are…
Sparse Principal Component Analysis (sPCA) is a popular matrix factorization approach based on Principal Component Analysis (PCA) that combines variance maximization and sparsity with the ultimate goal of improving data interpretation. When…
Spectral methods have been the mainstay in several domains such as machine learning and scientific computing. They involve finding a certain kind of spectral decomposition to obtain basis functions that can capture important structures for…
In multiple-input multiple-output communications, channel estimation is paramount to keep base stations and users on track. This paper proposes a novel PCA-based-principal component analysis-channel estimation approach for MIMO orthogonal…
Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be…
Missing data is a commonly occurring problem in practice. Many imputation methods have been developed to fill in the missing entries. However, not all of them can scale to high-dimensional data, especially the multiple imputation…
We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…
Principal Component Analysis (PCA) 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…
In recent years, Artificial Intelligence techniques have proved to be very successful when applied to problems in physical sciences. Here we apply an unsupervised Machine Learning (ML) algorithm called Principal Component Analysis (PCA) as…
Many statistical estimation techniques for high-dimensional or functional data are based on a preliminary dimension reduction step, which consists in projecting the sample $\bX_1, \hdots, \bX_n$ onto the first $D$ eigenvectors of the…
In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant…
Principal component analysis (PCA) is a fundamental technique for dimensionality reduction and denoising; however, its application to three-dimensional data with arbitrary orientations -- common in structural biology -- presents significant…
Principal component analysis (PCA) can be significantly limited when there is too few examples of the target data of interest. We propose a transfer learning approach to PCA (TL-PCA) where knowledge from a related source task is used in…
Efficient representations of data are essential for processing, exploration, and human understanding, and Principal Component Analysis (PCA) is one of the most common dimensionality reduction techniques used for the analysis of large,…
Principal component analysis (PCA) is a fundamental tool in multivariate statistics, yet its sensitivity to outliers and limitations in distributed environments restrict its effectiveness in modern large-scale applications. To address these…
In sparse principal component analysis we are given noisy observations of a low-rank matrix of dimension $n\times p$ and seek to reconstruct it under additional sparsity assumptions. In particular, we assume here each of the principal…
Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…
Principal Component Analysis (PCA) is a workhorse of modern data science. While PCA assumes the data conforms to Euclidean geometry, for specific data types, such as hierarchical and cyclic data structures, other spaces are more…