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Principal component regression (PCR) is a useful method for regularizing linear regression. Although conceptually simple, straightforward implementations of PCR have high computational costs and so are inappropriate when learning with large…
In the current context of data explosion, online techniques that do not require storing all data in memory are indispensable to routinely perform tasks like principal component analysis (PCA). Recursive algorithms that update the PCA with…
In this paper, we propose an acceleration scheme for online memory-limited PCA methods. Our scheme converges to the first $k>1$ eigenvectors in a single data pass. We provide empirical convergence results of our scheme based on the spiked…
Principal component analysis (PCA) is one of the most powerful tools in machine learning. The simplest method for PCA, the power iteration, requires $\mathcal O(1/\Delta)$ full-data passes to recover the principal component of a matrix with…
Recently years, the attempts on distilling mobile data into useful knowledge has been led to the deployment of machine learning algorithms at the network edge. Principal component analysis (PCA) is a classic technique for extracting the…
Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of $n$ observations (samples), each with $p$ variables. In this paper, using a matrix perturbation approach, we study the nonasymptotic relation…
We present a novel view on principal component analysis (PCA) as a competitive game in which each approximate eigenvector is controlled by a player whose goal is to maximize their own utility function. We analyze the properties of this PCA…
A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, in which a prominent eigenvector is planted into a random matrix. These distributions form natural statistical models for principal…
In this paper, we study the problem of sparse Principal Component Analysis (PCA) in the high-dimensional setting with missing observations. Our goal is to estimate the first principal component when we only have access to partial…
Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the…
We consider the problem of monotone, submodular maximization over a ground set of size $n$ subject to cardinality constraint $k$. For this problem, we introduce the first deterministic algorithms with linear time complexity; these…
We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the…
Principal component analysis (PCA) is an exploratory tool widely used in data analysis to uncover dominant patterns of variability within a population. Despite its ability to represent a data set in a low-dimensional space, the…
PCA is a classical statistical technique whose simplicity and maturity has seen it find widespread use as an anomaly detection technique. However, it is limited in this regard by being sensitive to gross perturbations of the input, and by…
Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…
Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional…
The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…
Network data are commonly collected in a variety of applications, representing either directly measured or statistically inferred connections between features of interest. In an increasing number of domains, these networks are collected…
Incremental versions of batch algorithms are often desired, for increased time efficiency in the streaming data setting, or increased memory efficiency in general. In this paper we present a novel algorithm for incremental kernel PCA, based…
Principal component analysis (PCA) is a widely used unsupervised dimensionality reduction technique in machine learning, applied across various fields such as bioinformatics, computer vision and finance. However, when the response variables…