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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…
In the past decade, sparse principal component analysis has emerged as an archetypal problem for illustrating statistical-computational tradeoffs. This trend has largely been driven by a line of research aiming to characterize the…
Optimization algorithms play a central role in chemistry since optimization is the computational keystone of most molecular and electronic structure calculations. Herein, we introduce the iterative power algorithm (IPA) for global…
Principal components analysis (PCA) is a fundamental algorithm in data analysis. Its memory-restricted online versions are useful in many modern applications, where the data are too large to fit in memory, or when data arrive as a stream of…
Principal Component analysis (PCA) is a useful statistical technique that is commonly used for multivariate analysis of correlated variables. It is usually applied as a dimension reduction method: the top principal components (PCs)…
We consider the problem of outlier robust PCA (OR-PCA) where the goal is to recover principal directions despite the presence of outlier data points. That is, given a data matrix $M^*$, where $(1-\alpha)$ fraction of the points are noisy…
Principal component analysis (PCA) is an unsupervised method for learning low-dimensional features with orthogonal projections. Multilinear PCA methods extend PCA to deal with multidimensional data (tensors) directly via tensor-to-tensor…
Principal component analysis (PCA) is a powerful tool for dimensionality reduction. Unfortunately, it is sensitive to outliers, so that various robust PCA variants were proposed in the literature. Among them the so-called rotational…
Data integration, or the strategic analysis of multiple sources of data simultaneously, can often lead to discoveries that may be hidden in individualistic analyses of a single data source. We develop a new unsupervised data integration…
Principal component analysis (PCA) is an indispensable tool in many learning tasks that finds the best linear representation for data. Classically, principal components of a dataset are interpreted as the directions that preserve most of…
Sparse Principal Component Analysis (SPCA) is an important technique for high-dimensional data analysis, improving interpretability by imposing sparsity on principal components. However, existing methods often fail to simultaneously…
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…
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…
Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The…
Fair Principal Component Analysis (PCA) is a problem setting where we aim to perform PCA while making the resulting representation fair in that the projected distributions, conditional on the sensitive attributes, match one another.…
Principal component analysis has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the…
We present quasicyclic principal component analysis (QPCA), a generalization of principal component analysis (PCA), that determines an optimized basis for a dataset in terms of families of shift-orthogonal principal vectors. This is of…
Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating…
Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are…
An iterative algorithm is presented for solving the RPA equations of linear response. The method optimally computes the energy-weighted moments of the strength function, allowing one to match the computational effort to the intrinsic…